Ensemble Data Assimilation Without Ensembles: Methodology and Application to Ocean Data Assimilation

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele M.; Kovach, Robin M.; Vernieres, Guillaume

2013-01-01

Two methods to estimate background error covariances for data assimilation are introduced. While both share properties with the ensemble Kalman filter (EnKF), they differ from it in that they do not require the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The first method is referred-to as SAFE (Space Adaptive Forecast error Estimation) because it estimates error covariances from the spatial distribution of model variables within a single state vector. It can thus be thought of as sampling an ensemble in space. The second method, named FAST (Flow Adaptive error Statistics from a Time series), constructs an ensemble sampled from a moving window along a model trajectory. The underlying assumption in these methods is that forecast errors in data assimilation are primarily phase errors in space and/or time.

Use of an OSSE to Evaluate Background Error Covariances Estimated by the 'NMC Method'

NASA Technical Reports Server (NTRS)

Errico, Ronald M.; Prive, Nikki C.; Gu, Wei

2014-01-01

The NMC method has proven utility for prescribing approximate background-error covariances required by variational data assimilation systems. Here, untunedNMCmethod estimates are compared with explicitly determined error covariances produced within an OSSE context by exploiting availability of the true simulated states. Such a comparison provides insights into what kind of rescaling is required to render the NMC method estimates usable. It is shown that rescaling of variances and directional correlation lengths depends greatly on both pressure and latitude. In particular, some scaling coefficients appropriate in the Tropics are the reciprocal of those in the Extratropics. Also, the degree of dynamic balance is grossly overestimated by the NMC method. These results agree with previous examinations of the NMC method which used ensembles as an alternative for estimating background-error statistics.

Numerical Differentiation Methods for Computing Error Covariance Matrices in Item Response Theory Modeling: An Evaluation and a New Proposal

ERIC Educational Resources Information Center

Tian, Wei; Cai, Li; Thissen, David; Xin, Tao

2013-01-01

In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…

Comparison of bias-corrected covariance estimators for MMRM analysis in longitudinal data with dropouts.

PubMed

Gosho, Masahiko; Hirakawa, Akihiro; Noma, Hisashi; Maruo, Kazushi; Sato, Yasunori

2017-10-01

In longitudinal clinical trials, some subjects will drop out before completing the trial, so their measurements towards the end of the trial are not obtained. Mixed-effects models for repeated measures (MMRM) analysis with "unstructured" (UN) covariance structure are increasingly common as a primary analysis for group comparisons in these trials. Furthermore, model-based covariance estimators have been routinely used for testing the group difference and estimating confidence intervals of the difference in the MMRM analysis using the UN covariance. However, using the MMRM analysis with the UN covariance could lead to convergence problems for numerical optimization, especially in trials with a small-sample size. Although the so-called sandwich covariance estimator is robust to misspecification of the covariance structure, its performance deteriorates in settings with small-sample size. We investigated the performance of the sandwich covariance estimator and covariance estimators adjusted for small-sample bias proposed by Kauermann and Carroll ( J Am Stat Assoc 2001; 96: 1387-1396) and Mancl and DeRouen ( Biometrics 2001; 57: 126-134) fitting simpler covariance structures through a simulation study. In terms of the type 1 error rate and coverage probability of confidence intervals, Mancl and DeRouen's covariance estimator with compound symmetry, first-order autoregressive (AR(1)), heterogeneous AR(1), and antedependence structures performed better than the original sandwich estimator and Kauermann and Carroll's estimator with these structures in the scenarios where the variance increased across visits. The performance based on Mancl and DeRouen's estimator with these structures was nearly equivalent to that based on the Kenward-Roger method for adjusting the standard errors and degrees of freedom with the UN structure. The model-based covariance estimator with the UN structure under unadjustment of the degrees of freedom, which is frequently used in applications, resulted in substantial inflation of the type 1 error rate. We recommend the use of Mancl and DeRouen's estimator in MMRM analysis if the number of subjects completing is ( n + 5) or less, where n is the number of planned visits. Otherwise, the use of Kenward and Roger's method with UN structure should be the best way.

Directional variance adjustment: bias reduction in covariance matrices based on factor analysis with an application to portfolio optimization.

PubMed

Bartz, Daniel; Hatrick, Kerr; Hesse, Christian W; Müller, Klaus-Robert; Lemm, Steven

2013-01-01

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation.

Directional Variance Adjustment: Bias Reduction in Covariance Matrices Based on Factor Analysis with an Application to Portfolio Optimization

PubMed Central

Bartz, Daniel; Hatrick, Kerr; Hesse, Christian W.; Müller, Klaus-Robert; Lemm, Steven

2013-01-01

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation. PMID:23844016

Galaxy–galaxy lensing estimators and their covariance properties

DOE PAGES

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uros; ...

2017-07-21

Here, we study the covariance properties of real space correlation function estimators – primarily galaxy–shear correlations, or galaxy–galaxy lensing – using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens densitymore » field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.« less

Galaxy–galaxy lensing estimators and their covariance properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uros

Here, we study the covariance properties of real space correlation function estimators – primarily galaxy–shear correlations, or galaxy–galaxy lensing – using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens densitymore » field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.« less

Galaxy-galaxy lensing estimators and their covariance properties

NASA Astrophysics Data System (ADS)

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uroš; Slosar, Anže; Vazquez Gonzalez, Jose

2017-11-01

We study the covariance properties of real space correlation function estimators - primarily galaxy-shear correlations, or galaxy-galaxy lensing - using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens density field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.

Bounding filter - A simple solution to lack of exact a priori statistics.

NASA Technical Reports Server (NTRS)

Nahi, N. E.; Weiss, I. M.

1972-01-01

Wiener and Kalman-Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for Wiener filter and the signal and noise dynamic system and disturbing noise representations for Kalman-Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents its apparent divergence.

Precomputing Process Noise Covariance for Onboard Sequential Filters

NASA Technical Reports Server (NTRS)

Olson, Corwin G.; Russell, Ryan P.; Carpenter, J. Russell

2017-01-01

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis studies is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

Precomputing Process Noise Covariance for Onboard Sequential Filters

NASA Technical Reports Server (NTRS)

Olson, Corwin G.; Russell, Ryan P.; Carpenter, J. Russell

2017-01-01

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory, using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis publications is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

Error due to unresolved scales in estimation problems for atmospheric data assimilation

NASA Astrophysics Data System (ADS)

Janjic, Tijana

The error arising due to unresolved scales in data assimilation procedures is examined. The problem of estimating the projection of the state of a passive scalar undergoing advection at a sequence of times is considered. The projection belongs to a finite- dimensional function space and is defined on the continuum. Using the continuum projection of the state of a passive scalar, a mathematical definition is obtained for the error arising due to the presence, in the continuum system, of scales unresolved by the discrete dynamical model. This error affects the estimation procedure through point observations that include the unresolved scales. In this work, two approximate methods for taking into account the error due to unresolved scales and the resulting correlations are developed and employed in the estimation procedure. The resulting formulas resemble the Schmidt-Kalman filter and the usual discrete Kalman filter, respectively. For this reason, the newly developed filters are called the Schmidt-Kalman filter and the traditional filter. In order to test the assimilation methods, a two- dimensional advection model with nonstationary spectrum was developed for passive scalar transport in the atmosphere. An analytical solution on the sphere was found depicting the model dynamics evolution. Using this analytical solution the model error is avoided, and the error due to unresolved scales is the only error left in the estimation problem. It is demonstrated that the traditional and the Schmidt- Kalman filter work well provided the exact covariance function of the unresolved scales is known. However, this requirement is not satisfied in practice, and the covariance function must be modeled. The Schmidt-Kalman filter cannot be computed in practice without further approximations. Therefore, the traditional filter is better suited for practical use. Also, the traditional filter does not require modeling of the full covariance function of the unresolved scales, but only modeling of the covariance matrix obtained by evaluating the covariance function at the observation points. We first assumed that this covariance matrix is stationary and that the unresolved scales are not correlated between the observation points, i.e., the matrix is diagonal, and that the values along the diagonal are constant. Tests with these assumptions were unsuccessful, indicating that a more sophisticated model of the covariance is needed for assimilation of data with nonstationary spectrum. A new method for modeling the covariance matrix based on an extended set of modeling assumptions is proposed. First, it is assumed that the covariance matrix is diagonal, that is, that the unresolved scales are not correlated between the observation points. It is postulated that the values on the diagonal depend on a wavenumber that is characteristic for the unresolved part of the spectrum. It is further postulated that this characteristic wavenumber can be diagnosed from the observations and from the estimate of the projection of the state that is being estimated. It is demonstrated that the new method successfully overcomes previously encountered difficulties.

Correcting for Measurement Error in Time-Varying Covariates in Marginal Structural Models.

PubMed

Kyle, Ryan P; Moodie, Erica E M; Klein, Marina B; Abrahamowicz, Michał

2016-08-01

Unbiased estimation of causal parameters from marginal structural models (MSMs) requires a fundamental assumption of no unmeasured confounding. Unfortunately, the time-varying covariates used to obtain inverse probability weights are often error-prone. Although substantial measurement error in important confounders is known to undermine control of confounders in conventional unweighted regression models, this issue has received comparatively limited attention in the MSM literature. Here we propose a novel application of the simulation-extrapolation (SIMEX) procedure to address measurement error in time-varying covariates, and we compare 2 approaches. The direct approach to SIMEX-based correction targets outcome model parameters, while the indirect approach corrects the weights estimated using the exposure model. We assess the performance of the proposed methods in simulations under different clinically plausible assumptions. The simulations demonstrate that measurement errors in time-dependent covariates may induce substantial bias in MSM estimators of causal effects of time-varying exposures, and that both proposed SIMEX approaches yield practically unbiased estimates in scenarios featuring low-to-moderate degrees of error. We illustrate the proposed approach in a simple analysis of the relationship between sustained virological response and liver fibrosis progression among persons infected with hepatitis C virus, while accounting for measurement error in γ-glutamyltransferase, using data collected in the Canadian Co-infection Cohort Study from 2003 to 2014. © The Author 2016. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

A heteroskedastic error covariance matrix estimator using a first-order conditional autoregressive Markov simulation for deriving asympotical efficient estimates from ecological sampled Anopheles arabiensis aquatic habitat covariates

PubMed Central

Jacob, Benjamin G; Griffith, Daniel A; Muturi, Ephantus J; Caamano, Erick X; Githure, John I; Novak, Robert J

2009-01-01

Background Autoregressive regression coefficients for Anopheles arabiensis aquatic habitat models are usually assessed using global error techniques and are reported as error covariance matrices. A global statistic, however, will summarize error estimates from multiple habitat locations. This makes it difficult to identify where there are clusters of An. arabiensis aquatic habitats of acceptable prediction. It is therefore useful to conduct some form of spatial error analysis to detect clusters of An. arabiensis aquatic habitats based on uncertainty residuals from individual sampled habitats. In this research, a method of error estimation for spatial simulation models was demonstrated using autocorrelation indices and eigenfunction spatial filters to distinguish among the effects of parameter uncertainty on a stochastic simulation of ecological sampled Anopheles aquatic habitat covariates. A test for diagnostic checking error residuals in an An. arabiensis aquatic habitat model may enable intervention efforts targeting productive habitats clusters, based on larval/pupal productivity, by using the asymptotic distribution of parameter estimates from a residual autocovariance matrix. The models considered in this research extends a normal regression analysis previously considered in the literature. Methods Field and remote-sampled data were collected during July 2006 to December 2007 in Karima rice-village complex in Mwea, Kenya. SAS 9.1.4® was used to explore univariate statistics, correlations, distributions, and to generate global autocorrelation statistics from the ecological sampled datasets. A local autocorrelation index was also generated using spatial covariance parameters (i.e., Moran's Indices) in a SAS/GIS® database. The Moran's statistic was decomposed into orthogonal and uncorrelated synthetic map pattern components using a Poisson model with a gamma-distributed mean (i.e. negative binomial regression). The eigenfunction values from the spatial configuration matrices were then used to define expectations for prior distributions using a Markov chain Monte Carlo (MCMC) algorithm. A set of posterior means were defined in WinBUGS 1.4.3®. After the model had converged, samples from the conditional distributions were used to summarize the posterior distribution of the parameters. Thereafter, a spatial residual trend analyses was used to evaluate variance uncertainty propagation in the model using an autocovariance error matrix. Results By specifying coefficient estimates in a Bayesian framework, the covariate number of tillers was found to be a significant predictor, positively associated with An. arabiensis aquatic habitats. The spatial filter models accounted for approximately 19% redundant locational information in the ecological sampled An. arabiensis aquatic habitat data. In the residual error estimation model there was significant positive autocorrelation (i.e., clustering of habitats in geographic space) based on log-transformed larval/pupal data and the sampled covariate depth of habitat. Conclusion An autocorrelation error covariance matrix and a spatial filter analyses can prioritize mosquito control strategies by providing a computationally attractive and feasible description of variance uncertainty estimates for correctly identifying clusters of prolific An. arabiensis aquatic habitats based on larval/pupal productivity. PMID:19772590

Simultaneous Estimation of Model State Variables and Observation and Forecast Biases Using a Two-Stage Hybrid Kalman Filter

NASA Technical Reports Server (NTRS)

Pauwels, V. R. N.; DeLannoy, G. J. M.; Hendricks Franssen, H.-J.; Vereecken, H.

2013-01-01

In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.

A New Formulation of the Filter-Error Method for Aerodynamic Parameter Estimation in Turbulence

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2015-01-01

A new formulation of the filter-error method for estimating aerodynamic parameters in nonlinear aircraft dynamic models during turbulence was developed and demonstrated. The approach uses an estimate of the measurement noise covariance to identify the model parameters, their uncertainties, and the process noise covariance, in a relaxation method analogous to the output-error method. Prior information on the model parameters and uncertainties can be supplied, and a post-estimation correction to the uncertainty was included to account for colored residuals not considered in the theory. No tuning parameters, needing adjustment by the analyst, are used in the estimation. The method was demonstrated in simulation using the NASA Generic Transport Model, then applied to the subscale T-2 jet-engine transport aircraft flight. Modeling results in different levels of turbulence were compared with results from time-domain output error and frequency- domain equation error methods to demonstrate the effectiveness of the approach.

Trajectory prediction for ballistic missiles based on boost-phase LOS measurements

NASA Astrophysics Data System (ADS)

Yeddanapudi, Murali; Bar-Shalom, Yaakov

1997-10-01

This paper addresses the problem of the estimation of the trajectory of a tactical ballistic missile using line of sight (LOS) measurements from one or more passive sensors (typically satellites). The major difficulties of this problem include: the estimation of the unknown time of launch, incorporation of (inaccurate) target thrust profiles to model the target dynamics during the boost phase and an overall ill-conditioning of the estimation problem due to poor observability of the target motion via the LOS measurements. We present a robust estimation procedure based on the Levenberg-Marquardt algorithm that provides both the target state estimate and error covariance taking into consideration the complications mentioned above. An important consideration in the defense against tactical ballistic missiles is the determination of the target position and error covariance at the acquisition range of a surveillance radar in the vicinity of the impact point. We present a systematic procedure to propagate the target state and covariance to a nominal time, when it is within the detection range of a surveillance radar to obtain a cueing volume. Mont Carlo simulation studies on typical single and two sensor scenarios indicate that the proposed algorithms are accurate in terms of the estimates and the estimator calculated covariances are consistent with the errors.

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

NASA Technical Reports Server (NTRS)

Menga, G.

1975-01-01

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Covariance analysis for evaluating head trackers

NASA Astrophysics Data System (ADS)

Kang, Donghoon

2017-10-01

Existing methods for evaluating the performance of head trackers usually rely on publicly available face databases, which contain facial images and the ground truths of their corresponding head orientations. However, most of the existing publicly available face databases are constructed by assuming that a frontal head orientation can be determined by compelling the person under examination to look straight ahead at the camera on the first video frame. Since nobody can accurately direct one's head toward the camera, this assumption may be unrealistic. Rather than obtaining estimation errors, we present a method for computing the covariance of estimation error rotations to evaluate the reliability of head trackers. As an uncertainty measure of estimators, the Schatten 2-norm of a square root of error covariance (or the algebraic average of relative error angles) can be used. The merit of the proposed method is that it does not disturb the person under examination by asking him to direct his head toward certain directions. Experimental results using real data validate the usefulness of our method.

Estimating restricted mean treatment effects with stacked survival models

PubMed Central

Wey, Andrew; Vock, David M.; Connett, John; Rudser, Kyle

2016-01-01

The difference in restricted mean survival times between two groups is a clinically relevant summary measure. With observational data, there may be imbalances in confounding variables between the two groups. One approach to account for such imbalances is estimating a covariate-adjusted restricted mean difference by modeling the covariate-adjusted survival distribution, and then marginalizing over the covariate distribution. Since the estimator for the restricted mean difference is defined by the estimator for the covariate-adjusted survival distribution, it is natural to expect that a better estimator of the covariate-adjusted survival distribution is associated with a better estimator of the restricted mean difference. We therefore propose estimating restricted mean differences with stacked survival models. Stacked survival models estimate a weighted average of several survival models by minimizing predicted error. By including a range of parametric, semi-parametric, and non-parametric models, stacked survival models can robustly estimate a covariate-adjusted survival distribution and, therefore, the restricted mean treatment effect in a wide range of scenarios. We demonstrate through a simulation study that better performance of the covariate-adjusted survival distribution often leads to better mean-squared error of the restricted mean difference although there are notable exceptions. In addition, we demonstrate that the proposed estimator can perform nearly as well as Cox regression when the proportional hazards assumption is satisfied and significantly better when proportional hazards is violated. Finally, the proposed estimator is illustrated with data from the United Network for Organ Sharing to evaluate post-lung transplant survival between large and small-volume centers. PMID:26934835

SEPARABLE FACTOR ANALYSIS WITH APPLICATIONS TO MORTALITY DATA

PubMed Central

Fosdick, Bailey K.; Hoff, Peter D.

2014-01-01

Human mortality data sets can be expressed as multiway data arrays, the dimensions of which correspond to categories by which mortality rates are reported, such as age, sex, country and year. Regression models for such data typically assume an independent error distribution or an error model that allows for dependence along at most one or two dimensions of the data array. However, failing to account for other dependencies can lead to inefficient estimates of regression parameters, inaccurate standard errors and poor predictions. An alternative to assuming independent errors is to allow for dependence along each dimension of the array using a separable covariance model. However, the number of parameters in this model increases rapidly with the dimensions of the array and, for many arrays, maximum likelihood estimates of the covariance parameters do not exist. In this paper, we propose a submodel of the separable covariance model that estimates the covariance matrix for each dimension as having factor analytic structure. This model can be viewed as an extension of factor analysis to array-valued data, as it uses a factor model to estimate the covariance along each dimension of the array. We discuss properties of this model as they relate to ordinary factor analysis, describe maximum likelihood and Bayesian estimation methods, and provide a likelihood ratio testing procedure for selecting the factor model ranks. We apply this methodology to the analysis of data from the Human Mortality Database, and show in a cross-validation experiment how it outperforms simpler methods. Additionally, we use this model to impute mortality rates for countries that have no mortality data for several years. Unlike other approaches, our methodology is able to estimate similarities between the mortality rates of countries, time periods and sexes, and use this information to assist with the imputations. PMID:25489353

Bio-Optical Data Assimilation With Observational Error Covariance Derived From an Ensemble of Satellite Images

NASA Astrophysics Data System (ADS)

Shulman, Igor; Gould, Richard W.; Frolov, Sergey; McCarthy, Sean; Penta, Brad; Anderson, Stephanie; Sakalaukus, Peter

2018-03-01

An ensemble-based approach to specify observational error covariance in the data assimilation of satellite bio-optical properties is proposed. The observational error covariance is derived from statistical properties of the generated ensemble of satellite MODIS-Aqua chlorophyll (Chl) images. The proposed observational error covariance is used in the Optimal Interpolation scheme for the assimilation of MODIS-Aqua Chl observations. The forecast error covariance is specified in the subspace of the multivariate (bio-optical, physical) empirical orthogonal functions (EOFs) estimated from a month-long model run. The assimilation of surface MODIS-Aqua Chl improved surface and subsurface model Chl predictions. Comparisons with surface and subsurface water samples demonstrate that data assimilation run with the proposed observational error covariance has higher RMSE than the data assimilation run with "optimistic" assumption about observational errors (10% of the ensemble mean), but has smaller or comparable RMSE than data assimilation run with an assumption that observational errors equal to 35% of the ensemble mean (the target error for satellite data product for chlorophyll). Also, with the assimilation of the MODIS-Aqua Chl data, the RMSE between observed and model-predicted fractions of diatoms to the total phytoplankton is reduced by a factor of two in comparison to the nonassimilative run.

Covariate Imbalance and Precision in Measuring Treatment Effects

ERIC Educational Resources Information Center

Liu, Xiaofeng Steven

2011-01-01

Covariate adjustment can increase the precision of estimates by removing unexplained variance from the error in randomized experiments, although chance covariate imbalance tends to counteract the improvement in precision. The author develops an easy measure to examine chance covariate imbalance in randomization by standardizing the average…

A Study on Mutil-Scale Background Error Covariances in 3D-Var Data Assimilation

NASA Astrophysics Data System (ADS)

Zhang, Xubin; Tan, Zhe-Min

2017-04-01

The construction of background error covariances is a key component of three-dimensional variational data assimilation. There are different scale background errors and interactions among them in the numerical weather Prediction. However, the influence of these errors and their interactions cannot be represented in the background error covariances statistics when estimated by the leading methods. So, it is necessary to construct background error covariances influenced by multi-scale interactions among errors. With the NMC method, this article firstly estimates the background error covariances at given model-resolution scales. And then the information of errors whose scales are larger and smaller than the given ones is introduced respectively, using different nesting techniques, to estimate the corresponding covariances. The comparisons of three background error covariances statistics influenced by information of errors at different scales reveal that, the background error variances enhance particularly at large scales and higher levels when introducing the information of larger-scale errors by the lateral boundary condition provided by a lower-resolution model. On the other hand, the variances reduce at medium scales at the higher levels, while those show slight improvement at lower levels in the nested domain, especially at medium and small scales, when introducing the information of smaller-scale errors by nesting a higher-resolution model. In addition, the introduction of information of larger- (smaller-) scale errors leads to larger (smaller) horizontal and vertical correlation scales of background errors. Considering the multivariate correlations, the Ekman coupling increases (decreases) with the information of larger- (smaller-) scale errors included, whereas the geostrophic coupling in free atmosphere weakens in both situations. The three covariances obtained in above work are used in a data assimilation and model forecast system respectively, and then the analysis-forecast cycles for a period of 1 month are conducted. Through the comparison of both analyses and forecasts from this system, it is found that the trends for variation in analysis increments with information of different scale errors introduced are consistent with those for variation in variances and correlations of background errors. In particular, introduction of smaller-scale errors leads to larger amplitude of analysis increments for winds at medium scales at the height of both high- and low- level jet. And analysis increments for both temperature and humidity are greater at the corresponding scales at middle and upper levels under this circumstance. These analysis increments improve the intensity of jet-convection system which includes jets at different levels and coupling between them associated with latent heat release, and these changes in analyses contribute to the better forecasts for winds and temperature in the corresponding areas. When smaller-scale errors are included, analysis increments for humidity enhance significantly at large scales at lower levels to moisten southern analyses. This humidification devotes to correcting dry bias there and eventually improves forecast skill of humidity. Moreover, inclusion of larger- (smaller-) scale errors is beneficial for forecast quality of heavy (light) precipitation at large (small) scales due to the amplification (diminution) of intensity and area in precipitation forecasts but tends to overestimate (underestimate) light (heavy) precipitation .

Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models.

PubMed

Haem, Elham; Harling, Kajsa; Ayatollahi, Seyyed Mohammad Taghi; Zare, Najaf; Karlsson, Mats O

2017-02-01

One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

NASA Technical Reports Server (NTRS)

Tsaoussi, Lucia S.; Koblinsky, Chester J.

1994-01-01

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Analyzing average and conditional effects with multigroup multilevel structural equation models

PubMed Central

Mayer, Axel; Nagengast, Benjamin; Fletcher, John; Steyer, Rolf

2014-01-01

Conventionally, multilevel analysis of covariance (ML-ANCOVA) has been the recommended approach for analyzing treatment effects in quasi-experimental multilevel designs with treatment application at the cluster-level. In this paper, we introduce the generalized ML-ANCOVA with linear effect functions that identifies average and conditional treatment effects in the presence of treatment-covariate interactions. We show how the generalized ML-ANCOVA model can be estimated with multigroup multilevel structural equation models that offer considerable advantages compared to traditional ML-ANCOVA. The proposed model takes into account measurement error in the covariates, sampling error in contextual covariates, treatment-covariate interactions, and stochastic predictors. We illustrate the implementation of ML-ANCOVA with an example from educational effectiveness research where we estimate average and conditional effects of early transition to secondary schooling on reading comprehension. PMID:24795668

True covariance simulation of the EUVE update filter

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Harman, R. R.

1989-01-01

A covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft is presented. The linearized dynamics and measurement equations of the error states are derived which constitute the truth model describing the real behavior of the systems involved. The design model used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A true covariance analysis has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

The Infinitesimal Jackknife with Exploratory Factor Analysis

ERIC Educational Resources Information Center

Zhang, Guangjian; Preacher, Kristopher J.; Jennrich, Robert I.

2012-01-01

The infinitesimal jackknife, a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices. Both…

Fast and accurate estimation of the covariance between pairwise maximum likelihood distances.

PubMed

Gil, Manuel

2014-01-01

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account to increase precision in any process that compares or combines distances. This paper introduces a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei & Jin, 1989) which links the covariance to path lengths. It is proven here under a simple symmetric substitution model. A simulation shows that the estimator outperforms previously published ones in terms of the mean squared error.

Fast and accurate estimation of the covariance between pairwise maximum likelihood distances

PubMed Central

2014-01-01

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account to increase precision in any process that compares or combines distances. This paper introduces a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei & Jin, 1989) which links the covariance to path lengths. It is proven here under a simple symmetric substitution model. A simulation shows that the estimator outperforms previously published ones in terms of the mean squared error. PMID:25279263

Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.

PubMed

Sztepanacz, Jacqueline L; Blows, Mark W

2017-07-01

The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix. Copyright © 2017 by the Genetics Society of America.

A note on variance estimation in random effects meta-regression.

PubMed

Sidik, Kurex; Jonkman, Jeffrey N

2005-01-01

For random effects meta-regression inference, variance estimation for the parameter estimates is discussed. Because estimated weights are used for meta-regression analysis in practice, the assumed or estimated covariance matrix used in meta-regression is not strictly correct, due to possible errors in estimating the weights. Therefore, this note investigates the use of a robust variance estimation approach for obtaining variances of the parameter estimates in random effects meta-regression inference. This method treats the assumed covariance matrix of the effect measure variables as a working covariance matrix. Using an example of meta-analysis data from clinical trials of a vaccine, the robust variance estimation approach is illustrated in comparison with two other methods of variance estimation. A simulation study is presented, comparing the three methods of variance estimation in terms of bias and coverage probability. We find that, despite the seeming suitability of the robust estimator for random effects meta-regression, the improved variance estimator of Knapp and Hartung (2003) yields the best performance among the three estimators, and thus may provide the best protection against errors in the estimated weights.

Model selection for marginal regression analysis of longitudinal data with missing observations and covariate measurement error.

PubMed

Shen, Chung-Wei; Chen, Yi-Hau

2015-10-01

Missing observations and covariate measurement error commonly arise in longitudinal data. However, existing methods for model selection in marginal regression analysis of longitudinal data fail to address the potential bias resulting from these issues. To tackle this problem, we propose a new model selection criterion, the Generalized Longitudinal Information Criterion, which is based on an approximately unbiased estimator for the expected quadratic error of a considered marginal model accounting for both data missingness and covariate measurement error. The simulation results reveal that the proposed method performs quite well in the presence of missing data and covariate measurement error. On the contrary, the naive procedures without taking care of such complexity in data may perform quite poorly. The proposed method is applied to data from the Taiwan Longitudinal Study on Aging to assess the relationship of depression with health and social status in the elderly, accommodating measurement error in the covariate as well as missing observations. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Robust Adaptive Beamforming with Sensor Position Errors Using Weighted Subspace Fitting-Based Covariance Matrix Reconstruction.

PubMed

Chen, Peng; Yang, Yixin; Wang, Yong; Ma, Yuanliang

2018-05-08

When sensor position errors exist, the performance of recently proposed interference-plus-noise covariance matrix (INCM)-based adaptive beamformers may be severely degraded. In this paper, we propose a weighted subspace fitting-based INCM reconstruction algorithm to overcome sensor displacement for linear arrays. By estimating the rough signal directions, we construct a novel possible mismatched steering vector (SV) set. We analyze the proximity of the signal subspace from the sample covariance matrix (SCM) and the space spanned by the possible mismatched SV set. After solving an iterative optimization problem, we reconstruct the INCM using the estimated sensor position errors. Then we estimate the SV of the desired signal by solving an optimization problem with the reconstructed INCM. The main advantage of the proposed algorithm is its robustness against SV mismatches dominated by unknown sensor position errors. Numerical examples show that even if the position errors are up to half of the assumed sensor spacing, the output signal-to-interference-plus-noise ratio is only reduced by 4 dB. Beam patterns plotted using experiment data show that the interference suppression capability of the proposed beamformer outperforms other tested beamformers.

Multivariate Error Covariance Estimates by Monte-Carlo Simulation for Assimilation Studies in the Pacific Ocean

NASA Technical Reports Server (NTRS)

Borovikov, Anna; Rienecker, Michele M.; Keppenne, Christian; Johnson, Gregory C.

2004-01-01

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Here a comparison is made between a univariate Optimal Interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature. In the UOI case only temperature is updated using a Gaussian covariance function and in the MvOI salinity, zonal and meridional velocities as well as temperature, are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimation of the model error statistics is made by Monte-Carlo techniques from an ensemble of model integrations. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere-Ocean array have been assimilated in this study. In order to investigate the efficacy of the multivariate scheme two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity and temperature. For reference, a third control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when multivariate correction is used, as evident from the analyses of the rms differences of these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating the water masses with properties close to the observed, while the UOI failed to maintain the temperature and salinity structure.

Comparison of Kalman filter and optimal smoother estimates of spacecraft attitude

NASA Technical Reports Server (NTRS)

Sedlak, J.

1994-01-01

Given a valid system model and adequate observability, a Kalman filter will converge toward the true system state with error statistics given by the estimated error covariance matrix. The errors generally do not continue to decrease. Rather, a balance is reached between the gain of information from new measurements and the loss of information during propagation. The errors can be further reduced, however, by a second pass through the data with an optimal smoother. This algorithm obtains the optimally weighted average of forward and backward propagating Kalman filters. It roughly halves the error covariance by including future as well as past measurements in each estimate. This paper investigates whether such benefits actually accrue in the application of an optimal smoother to spacecraft attitude determination. Tests are performed both with actual spacecraft data from the Extreme Ultraviolet Explorer (EUVE) and with simulated data for which the true state vector and noise statistics are exactly known.

Predicting the geographic distribution of a species from presence-only data subject to detection errors

USGS Publications Warehouse

Dorazio, Robert M.

2012-01-01

Several models have been developed to predict the geographic distribution of a species by combining measurements of covariates of occurrence at locations where the species is known to be present with measurements of the same covariates at other locations where species occurrence status (presence or absence) is unknown. In the absence of species detection errors, spatial point-process models and binary-regression models for case-augmented surveys provide consistent estimators of a species’ geographic distribution without prior knowledge of species prevalence. In addition, these regression models can be modified to produce estimators of species abundance that are asymptotically equivalent to those of the spatial point-process models. However, if species presence locations are subject to detection errors, neither class of models provides a consistent estimator of covariate effects unless the covariates of species abundance are distinct and independently distributed from the covariates of species detection probability. These analytical results are illustrated using simulation studies of data sets that contain a wide range of presence-only sample sizes. Analyses of presence-only data of three avian species observed in a survey of landbirds in western Montana and northern Idaho are compared with site-occupancy analyses of detections and nondetections of these species.

Covariate Measurement Error Correction for Student Growth Percentiles Using the SIMEX Method

ERIC Educational Resources Information Center

Shang, Yi; VanIwaarden, Adam; Betebenner, Damian W.

2015-01-01

In this study, we examined the impact of covariate measurement error (ME) on the estimation of quantile regression and student growth percentiles (SGPs), and find that SGPs tend to be overestimated among students with higher prior achievement and underestimated among those with lower prior achievement, a problem we describe as ME endogeneity in…

Tests for detecting overdispersion in models with measurement error in covariates.

PubMed

Yang, Yingsi; Wong, Man Yu

2015-11-30

Measurement error in covariates can affect the accuracy in count data modeling and analysis. In overdispersion identification, the true mean-variance relationship can be obscured under the influence of measurement error in covariates. In this paper, we propose three tests for detecting overdispersion when covariates are measured with error: a modified score test and two score tests based on the proposed approximate likelihood and quasi-likelihood, respectively. The proposed approximate likelihood is derived under the classical measurement error model, and the resulting approximate maximum likelihood estimator is shown to have superior efficiency. Simulation results also show that the score test based on approximate likelihood outperforms the test based on quasi-likelihood and other alternatives in terms of empirical power. By analyzing a real dataset containing the health-related quality-of-life measurements of a particular group of patients, we demonstrate the importance of the proposed methods by showing that the analyses with and without measurement error correction yield significantly different results. Copyright © 2015 John Wiley & Sons, Ltd.

Adaptive Error Estimation in Linearized Ocean General Circulation Models

NASA Technical Reports Server (NTRS)

Chechelnitsky, Michael Y.

1999-01-01

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large representation error, i.e. the dominance of the mesoscale eddies in the T/P signal, which are not part of the 21 by 1" GCM. Therefore, the impact of the observations on the assimilation is very small even after the adjustment of the error statistics. This work demonstrates that simult&neous estimation of the model and measurement error statistics for data assimilation with global ocean data sets and linearized GCMs is possible. However, the error covariance estimation problem is in general highly underdetermined, much more so than the state estimation problem. In other words there exist a very large number of statistical models that can be made consistent with the available data. Therefore, methods for obtaining quantitative error estimates, powerful though they may be, cannot replace physical insight. Used in the right context, as a tool for guiding the choice of a small number of model error parameters, covariance matching can be a useful addition to the repertory of tools available to oceanographers.

Are Low-order Covariance Estimates Useful in Error Analyses?

NASA Astrophysics Data System (ADS)

Baker, D. F.; Schimel, D.

2005-12-01

Atmospheric trace gas inversions, using modeled atmospheric transport to infer surface sources and sinks from measured concentrations, are most commonly done using least-squares techniques that return not only an estimate of the state (the surface fluxes) but also the covariance matrix describing the uncertainty in that estimate. Besides allowing one to place error bars around the estimate, the covariance matrix may be used in simulation studies to learn what uncertainties would be expected from various hypothetical observing strategies. This error analysis capability is routinely used in designing instrumentation, measurement campaigns, and satellite observing strategies. For example, Rayner, et al (2002) examined the ability of satellite-based column-integrated CO2 measurements to constrain monthly-average CO2 fluxes for about 100 emission regions using this approach. Exact solutions for both state vector and covariance matrix become computationally infeasible, however, when the surface fluxes are solved at finer resolution (e.g., daily in time, under 500 km in space). It is precisely at these finer scales, however, that one would hope to be able to estimate fluxes using high-density satellite measurements. Non-exact estimation methods such as variational data assimilation or the ensemble Kalman filter could be used, but they achieve their computational savings by obtaining an only approximate state estimate and a low-order approximation of the true covariance. One would like to be able to use this covariance matrix to do the same sort of error analyses as are done with the full-rank covariance, but is it correct to do so? Here we compare uncertainties and `information content' derived from full-rank covariance matrices obtained from a direct, batch least squares inversion to those from the incomplete-rank covariance matrices given by a variational data assimilation approach solved with a variable metric minimization technique (the Broyden-Fletcher- Goldfarb-Shanno algorithm). Two cases are examined: a toy problem in which CO2 fluxes for 3 latitude bands are estimated for only 2 time steps per year, and for the monthly fluxes for 22 regions across 1988-2003 solved for in the TransCom3 interannual flux inversion of Baker, et al (2005). The usefulness of the uncertainty estimates will be assessed as a function of the number of minimization steps used in the variational approach; this will help determine whether they will also be useful in the high-resolution cases that we would most like to apply the non-exact methods to. Baker, D.F., et al., TransCom3 inversion intercomparison: Impact of transport model errors on the interannual variability of regional CO2 fluxes, 1988-2003, Glob. Biogeochem. Cycles, doi:10.1029/2004GB002439, 2005, in press. Rayner, P.J., R.M. Law, D.M. O'Brien, T.M. Butler, and A.C. Dilley, Global observations of the carbon budget, 3, Initial assessment of the impact of satellite orbit, scan geometry, and cloud on measuring CO2 from space, J. Geophys. Res., 107(D21), 4557, doi:10.1029/2001JD000618, 2002.

Generalized Linear Covariance Analysis

NASA Technical Reports Server (NTRS)

Carpenter, James R.; Markley, F. Landis

2014-01-01

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2011-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Precision matrix expansion - efficient use of numerical simulations in estimating errors on cosmological parameters

NASA Astrophysics Data System (ADS)

Friedrich, Oliver; Eifler, Tim

2018-01-01

Computing the inverse covariance matrix (or precision matrix) of large data vectors is crucial in weak lensing (and multiprobe) analyses of the large-scale structure of the Universe. Analytically computed covariances are noise-free and hence straightforward to invert; however, the model approximations might be insufficient for the statistical precision of future cosmological data. Estimating covariances from numerical simulations improves on these approximations, but the sample covariance estimator is inherently noisy, which introduces uncertainties in the error bars on cosmological parameters and also additional scatter in their best-fitting values. For future surveys, reducing both effects to an acceptable level requires an unfeasibly large number of simulations. In this paper we describe a way to expand the precision matrix around a covariance model and show how to estimate the leading order terms of this expansion from simulations. This is especially powerful if the covariance matrix is the sum of two contributions, C = A+B, where A is well understood analytically and can be turned off in simulations (e.g. shape noise for cosmic shear) to yield a direct estimate of B. We test our method in mock experiments resembling tomographic weak lensing data vectors from the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope (LSST). For DES we find that 400 N-body simulations are sufficient to achieve negligible statistical uncertainties on parameter constraints. For LSST this is achieved with 2400 simulations. The standard covariance estimator would require >105 simulations to reach a similar precision. We extend our analysis to a DES multiprobe case finding a similar performance.

A bias correction for covariance estimators to improve inference with generalized estimating equations that use an unstructured correlation matrix.

PubMed

Westgate, Philip M

2013-07-20

Generalized estimating equations (GEEs) are routinely used for the marginal analysis of correlated data. The efficiency of GEE depends on how closely the working covariance structure resembles the true structure, and therefore accurate modeling of the working correlation of the data is important. A popular approach is the use of an unstructured working correlation matrix, as it is not as restrictive as simpler structures such as exchangeable and AR-1 and thus can theoretically improve efficiency. However, because of the potential for having to estimate a large number of correlation parameters, variances of regression parameter estimates can be larger than theoretically expected when utilizing the unstructured working correlation matrix. Therefore, standard error estimates can be negatively biased. To account for this additional finite-sample variability, we derive a bias correction that can be applied to typical estimators of the covariance matrix of parameter estimates. Via simulation and in application to a longitudinal study, we show that our proposed correction improves standard error estimation and statistical inference. Copyright © 2012 John Wiley & Sons, Ltd.

Covariance Matrix Estimation for Massive MIMO

NASA Astrophysics Data System (ADS)

Upadhya, Karthik; Vorobyov, Sergiy A.

2018-04-01

We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase-shift. The covariance matrix of a particular user is obtained by computing the sample cross-correlation of the channel estimates obtained from the two pilot sequences. This approach relaxes the requirement that all the users transmit their uplink pilots over the same set of symbols. We derive expressions for the achievable rate and the mean-squared error of the covariance matrix estimate when the proposed method is used with staggered pilots. The performance of the proposed method is compared with existing methods through simulations.

A Comparison of Pseudo-Maximum Likelihood and Asymptotically Distribution-Free Dynamic Factor Analysis Parameter Estimation in Fitting Covariance Structure Models to Block-Toeplitz Matrices Representing Single-Subject Multivariate Time-Series.

ERIC Educational Resources Information Center

Molenaar, Peter C. M.; Nesselroade, John R.

1998-01-01

Pseudo-Maximum Likelihood (p-ML) and Asymptotically Distribution Free (ADF) estimation methods for estimating dynamic factor model parameters within a covariance structure framework were compared through a Monte Carlo simulation. Both methods appear to give consistent model parameter estimates, but only ADF gives standard errors and chi-square…

Triple collocation-based estimation of spatially correlated observation error covariance in remote sensing soil moisture data assimilation

NASA Astrophysics Data System (ADS)

Wu, Kai; Shu, Hong; Nie, Lei; Jiao, Zhenhang

2018-01-01

Spatially correlated errors are typically ignored in data assimilation, thus degenerating the observation error covariance R to a diagonal matrix. We argue that a nondiagonal R carries more observation information making assimilation results more accurate. A method, denoted TC_Cov, was proposed for soil moisture data assimilation to estimate spatially correlated observation error covariance based on triple collocation (TC). Assimilation experiments were carried out to test the performance of TC_Cov. AMSR-E soil moisture was assimilated with a diagonal R matrix computed using the TC and assimilated using a nondiagonal R matrix, as estimated by proposed TC_Cov. The ensemble Kalman filter was considered as the assimilation method. Our assimilation results were validated against climate change initiative data and ground-based soil moisture measurements using the Pearson correlation coefficient and unbiased root mean square difference metrics. These experiments confirmed that deterioration of diagonal R assimilation results occurred when model simulation is more accurate than observation data. Furthermore, nondiagonal R achieved higher correlation coefficient and lower ubRMSD values over diagonal R in experiments and demonstrated the effectiveness of TC_Cov to estimate richly structuralized R in data assimilation. In sum, compared with diagonal R, nondiagonal R may relieve the detrimental effects of assimilation when simulated model results outperform observation data.

Examination of various roles for covariance matrices in the development, evaluation, and application of nuclear data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, D.L.

The last decade has been a period of rapid development in the implementation of covariance-matrix methodology in nuclear data research. This paper offers some perspective on the progress which has been made, on some of the unresolved problems, and on the potential yet to be realized. These discussions address a variety of issues related to the development of nuclear data. Topics examined are: the importance of designing and conducting experiments so that error information is conveniently generated; the procedures for identifying error sources and quantifying their magnitudes and correlations; the combination of errors; the importance of consistent and well-characterized measurementmore » standards; the role of covariances in data parameterization (fitting); the estimation of covariances for values calculated from mathematical models; the identification of abnormalities in covariance matrices and the analysis of their consequences; the problems encountered in representing covariance information in evaluated files; the role of covariances in the weighting of diverse data sets; the comparison of various evaluations; the influence of primary-data covariance in the analysis of covariances for derived quantities (sensitivity); and the role of covariances in the merging of the diverse nuclear data information. 226 refs., 2 tabs.« less

Quantifying Adventitious Error in a Covariance Structure as a Random Effect

PubMed Central

Wu, Hao; Browne, Michael W.

2017-01-01

We present an approach to quantifying errors in covariance structures in which adventitious error, identified as the process underlying the discrepancy between the population and the structured model, is explicitly modeled as a random effect with a distribution, and the dispersion parameter of this distribution to be estimated gives a measure of misspecification. Analytical properties of the resultant procedure are investigated and the measure of misspecification is found to be related to the RMSEA. An algorithm is developed for numerical implementation of the procedure. The consistency and asymptotic sampling distributions of the estimators are established under a new asymptotic paradigm and an assumption weaker than the standard Pitman drift assumption. Simulations validate the asymptotic sampling distributions and demonstrate the importance of accounting for the variations in the parameter estimates due to adventitious error. Two examples are also given as illustrations. PMID:25813463

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

NASA Astrophysics Data System (ADS)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Information matrix estimation procedures for cognitive diagnostic models.

PubMed

Liu, Yanlou; Xin, Tao; Andersson, Björn; Tian, Wei

2018-03-06

Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models (CDMs), the inverse of the observed information matrix and the sandwich-type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross-product information matrix, the sandwich-type covariance matrix and the two approaches proposed by de la Torre (2009, J. Educ. Behav. Stat., 34, 115) are discussed. Simulation results show that, for a correctly specified CDM and Q-matrix or with a slightly misspecified probability model, the observed information matrix and the sandwich-type covariance matrix exhibit good performance with respect to providing consistent standard errors of item parameter estimates. However, with substantial model misspecification only the sandwich-type covariance matrix exhibits robust performance. © 2018 The British Psychological Society.

Radial orbit error reduction and sea surface topography determination using satellite altimetry

NASA Technical Reports Server (NTRS)

Engelis, Theodossios

1987-01-01

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

High dimensional linear regression models under long memory dependence and measurement error

NASA Astrophysics Data System (ADS)

Kaul, Abhishek

This dissertation consists of three chapters. The first chapter introduces the models under consideration and motivates problems of interest. A brief literature review is also provided in this chapter. The second chapter investigates the properties of Lasso under long range dependent model errors. Lasso is a computationally efficient approach to model selection and estimation, and its properties are well studied when the regression errors are independent and identically distributed. We study the case, where the regression errors form a long memory moving average process. We establish a finite sample oracle inequality for the Lasso solution. We then show the asymptotic sign consistency in this setup. These results are established in the high dimensional setup (p> n) where p can be increasing exponentially with n. Finally, we show the consistency, n½ --d-consistency of Lasso, along with the oracle property of adaptive Lasso, in the case where p is fixed. Here d is the memory parameter of the stationary error sequence. The performance of Lasso is also analysed in the present setup with a simulation study. The third chapter proposes and investigates the properties of a penalized quantile based estimator for measurement error models. Standard formulations of prediction problems in high dimension regression models assume the availability of fully observed covariates and sub-Gaussian and homogeneous model errors. This makes these methods inapplicable to measurement errors models where covariates are unobservable and observations are possibly non sub-Gaussian and heterogeneous. We propose weighted penalized corrected quantile estimators for the regression parameter vector in linear regression models with additive measurement errors, where unobservable covariates are nonrandom. The proposed estimators forgo the need for the above mentioned model assumptions. We study these estimators in both the fixed dimension and high dimensional sparse setups, in the latter setup, the dimensionality can grow exponentially with the sample size. In the fixed dimensional setting we provide the oracle properties associated with the proposed estimators. In the high dimensional setting, we provide bounds for the statistical error associated with the estimation, that hold with asymptotic probability 1, thereby providing the ℓ1-consistency of the proposed estimator. We also establish the model selection consistency in terms of the correctly estimated zero components of the parameter vector. A simulation study that investigates the finite sample accuracy of the proposed estimator is also included in this chapter.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied. PMID:22661790

On the use of the covariance matrix to fit correlated data

NASA Astrophysics Data System (ADS)

D'Agostini, G.

1994-07-01

Best fits to data which are affected by systematic uncertainties on the normalization factor have the tendency to produce curves lower than expected if the covariance matrix of the data points is used in the definition of the χ2. This paper shows that the effect is a direct consequence of the hypothesis used to estimate the empirical covariance matrix, namely the linearization on which the usual error propagation relies. The bias can become unacceptable if the normalization error is large, or a large number of data points are fitted.

Bootstrap-based methods for estimating standard errors in Cox's regression analyses of clustered event times.

PubMed

Xiao, Yongling; Abrahamowicz, Michal

2010-03-30

We propose two bootstrap-based methods to correct the standard errors (SEs) from Cox's model for within-cluster correlation of right-censored event times. The cluster-bootstrap method resamples, with replacement, only the clusters, whereas the two-step bootstrap method resamples (i) the clusters, and (ii) individuals within each selected cluster, with replacement. In simulations, we evaluate both methods and compare them with the existing robust variance estimator and the shared gamma frailty model, which are available in statistical software packages. We simulate clustered event time data, with latent cluster-level random effects, which are ignored in the conventional Cox's model. For cluster-level covariates, both proposed bootstrap methods yield accurate SEs, and type I error rates, and acceptable coverage rates, regardless of the true random effects distribution, and avoid serious variance under-estimation by conventional Cox-based standard errors. However, the two-step bootstrap method over-estimates the variance for individual-level covariates. We also apply the proposed bootstrap methods to obtain confidence bands around flexible estimates of time-dependent effects in a real-life analysis of cluster event times.

Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Miller, Brad A.; Howard, Samuel A.

2008-01-01

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Regression dilution in the proportional hazards model.

PubMed

Hughes, M D

1993-12-01

The problem of regression dilution arising from covariate measurement error is investigated for survival data using the proportional hazards model. The naive approach to parameter estimation is considered whereby observed covariate values are used, inappropriately, in the usual analysis instead of the underlying covariate values. A relationship between the estimated parameter in large samples and the true parameter is obtained showing that the bias does not depend on the form of the baseline hazard function when the errors are normally distributed. With high censorship, adjustment of the naive estimate by the factor 1 + lambda, where lambda is the ratio of within-person variability about an underlying mean level to the variability of these levels in the population sampled, removes the bias. As censorship increases, the adjustment required increases and when there is no censorship is markedly higher than 1 + lambda and depends also on the true risk relationship.

Non-linear matter power spectrum covariance matrix errors and cosmological parameter uncertainties

NASA Astrophysics Data System (ADS)

Blot, L.; Corasaniti, P. S.; Amendola, L.; Kitching, T. D.

2016-06-01

The covariance of the matter power spectrum is a key element of the analysis of galaxy clustering data. Independent realizations of observational measurements can be used to sample the covariance, nevertheless statistical sampling errors will propagate into the cosmological parameter inference potentially limiting the capabilities of the upcoming generation of galaxy surveys. The impact of these errors as function of the number of realizations has been previously evaluated for Gaussian distributed data. However, non-linearities in the late-time clustering of matter cause departures from Gaussian statistics. Here, we address the impact of non-Gaussian errors on the sample covariance and precision matrix errors using a large ensemble of N-body simulations. In the range of modes where finite volume effects are negligible (0.1 ≲ k [h Mpc-1] ≲ 1.2), we find deviations of the variance of the sample covariance with respect to Gaussian predictions above ˜10 per cent at k > 0.3 h Mpc-1. Over the entire range these reduce to about ˜5 per cent for the precision matrix. Finally, we perform a Fisher analysis to estimate the effect of covariance errors on the cosmological parameter constraints. In particular, assuming Euclid-like survey characteristics we find that a number of independent realizations larger than 5000 is necessary to reduce the contribution of sampling errors to the cosmological parameter uncertainties at subpercent level. We also show that restricting the analysis to large scales k ≲ 0.2 h Mpc-1 results in a considerable loss in constraining power, while using the linear covariance to include smaller scales leads to an underestimation of the errors on the cosmological parameters.

Spatio-Temporal EEG Models for Brain Interfaces

PubMed Central

Gonzalez-Navarro, P.; Moghadamfalahi, M.; Akcakaya, M.; Erdogmus, D.

2016-01-01

Multichannel electroencephalography (EEG) is widely used in non-invasive brain computer interfaces (BCIs) for user intent inference. EEG can be assumed to be a Gaussian process with unknown mean and autocovariance, and the estimation of parameters is required for BCI inference. However, the relatively high dimensionality of the EEG feature vectors with respect to the number of labeled observations lead to rank deficient covariance matrix estimates. In this manuscript, to overcome ill-conditioned covariance estimation, we propose a structure for the covariance matrices of the multichannel EEG signals. Specifically, we assume that these covariances can be modeled as a Kronecker product of temporal and spatial covariances. Our results over the experimental data collected from the users of a letter-by-letter typing BCI show that with less number of parameter estimations, the system can achieve higher classification accuracies compared to a method that uses full unstructured covariance estimation. Moreover, in order to illustrate that the proposed Kronecker product structure could enable shortening the BCI calibration data collection sessions, using Cramer-Rao bound analysis on simulated data, we demonstrate that a model with structured covariance matrices will achieve the same estimation error as a model with no covariance structure using fewer labeled EEG observations. PMID:27713590

Development of a multi-data assimilation scheme to integrate Bio-Argo floats data with ocean colour satellite data into the CMEMS MFC-Biogeochemistry

NASA Astrophysics Data System (ADS)

Cossarini, Gianpiero; D'Ortenzio, Fabrizio; Mariotti, Laura; Mignot, Alexandre; Salon, Stefano

2017-04-01

The Mediterranean Sea is a very promising site to develop and test the assimilation of Bio-Argo data since 1) the Bio-Argo network is one of the densest of the global ocean, and 2) a consolidate data assimilation framework of biogeochemical variables (3DVAR-BIO, presently based on assimilation of satellite-estimated surface chlorophyll data) already exists within the CMEMS biogeochemical model system for Mediterranean Sea. The MASSIMILI project, granted by the CMEMS Service Evolution initiative, is aimed to develop the assimilation of Bio-Argo Floats data into the CMEMS biogeochemical model system of the Mediterranean Sea, by means of an upgrade of the 3DVAR-BIO scheme. Specific developments of the 3DVAR-BIO scheme focus on the estimate of new operators of the variational decomposition of the background error covariance matrix and on the implementation of the new observation operator specifically for the Bio-Argo float vertical profile data. In particular, a new horizontal covariance operator for chlorophyll, nitrate and oxygen is based on 3D fields of horizontal correlation radius calculated from a long-term reanalysis simulation. A new vertical covariance operator is built on monthly and spatial varying EOF decomposition to account for the spatiotemporal variability of vertical structure of the three variables error covariance. Further, the observation error covariance is a key factor for an effective assimilation of the Bio-Argo data into the model dynamics. The sensitivities of assimilation to the different factors are estimated. First results of the implementation of the new 3DVAR-BIO scheme show the impact of Bio-Argo data on the 3D fields of chlorophyll, nitrate and oxygen. Tuning the length scale factors of horizontal covariance, analysing the sensitivity of the observation error covariance, introducing non-diagonal biogeochemical covariance operator and non-diagonal multi-platform operator (i.e. Bio-Argo and satellite) are crucial future steps for the success of the MASSIMILI project. In our contribute, we will discuss the recent and promising advancements this strategic project has been having in the past year and its potential for the whole operational biogeochemical modelling community.

Orbit/attitude estimation with LANDSAT Landmark data

NASA Technical Reports Server (NTRS)

Hall, D. L.; Waligora, S.

1979-01-01

The use of LANDSAT landmark data for orbit/attitude and camera bias estimation was studied. The preliminary results of these investigations are presented. The Goddard Trajectory Determination System (GTDS) error analysis capability was used to perform error analysis studies. A number of questions were addressed including parameter observability and sensitivity, effects on the solve-for parameter errors of data span, density, and distribution an a priori covariance weighting. The use of the GTDS differential correction capability with acutal landmark data was examined. The rms line and element observation residuals were studied as a function of the solve-for parameter set, a priori covariance weighting, force model, attitude model and data characteristics. Sample results are presented. Finally, verfication and preliminary system evaluation of the LANDSAT NAVPAK system for sequential (extended Kalman Filter) estimation of orbit, and camera bias parameters is given.

Using aggregate data to estimate the standard error of a treatment-covariate interaction in an individual patient data meta-analysis.

PubMed

Kovalchik, Stephanie A; Cumberland, William G

2012-05-01

Subgroup analyses are important to medical research because they shed light on the heterogeneity of treatment effectts. A treatment-covariate interaction in an individual patient data (IPD) meta-analysis is the most reliable means to estimate how a subgroup factor modifies a treatment's effectiveness. However, owing to the challenges in collecting participant data, an approach based on aggregate data might be the only option. In these circumstances, it would be useful to assess the relative efficiency and power loss of a subgroup analysis without patient-level data. We present methods that use aggregate data to estimate the standard error of an IPD meta-analysis' treatment-covariate interaction for regression models of a continuous or dichotomous patient outcome. Numerical studies indicate that the estimators have good accuracy. An application to a previously published meta-regression illustrates the practical utility of the methodology. © 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Comparing Parameter Estimation Techniques for an Electrical Power Transformer Oil Temperature Prediction Model

NASA Technical Reports Server (NTRS)

Morris, A. Terry

1999-01-01

This paper examines various sources of error in MIT's improved top oil temperature rise over ambient temperature model and estimation process. The sources of error are the current parameter estimation technique, quantization noise, and post-processing of the transformer data. Results from this paper will show that an output error parameter estimation technique should be selected to replace the current least squares estimation technique. The output error technique obtained accurate predictions of transformer behavior, revealed the best error covariance, obtained consistent parameter estimates, and provided for valid and sensible parameters. This paper will also show that the output error technique should be used to minimize errors attributed to post-processing (decimation) of the transformer data. Models used in this paper are validated using data from a large transformer in service.

Analysis of filter tuning techniques for sequential orbit determination

NASA Technical Reports Server (NTRS)

Lee, T.; Yee, C.; Oza, D.

1995-01-01

This paper examines filter tuning techniques for a sequential orbit determination (OD) covariance analysis. Recently, there has been a renewed interest in sequential OD, primarily due to the successful flight qualification of the Tracking and Data Relay Satellite System (TDRSS) Onboard Navigation System (TONS) using Doppler data extracted onboard the Extreme Ultraviolet Explorer (EUVE) spacecraft. TONS computes highly accurate orbit solutions onboard the spacecraft in realtime using a sequential filter. As the result of the successful TONS-EUVE flight qualification experiment, the Earth Observing System (EOS) AM-1 Project has selected TONS as the prime navigation system. In addition, sequential OD methods can be used successfully for ground OD. Whether data are processed onboard or on the ground, a sequential OD procedure is generally favored over a batch technique when a realtime automated OD system is desired. Recently, OD covariance analyses were performed for the TONS-EUVE and TONS-EOS missions using the sequential processing options of the Orbit Determination Error Analysis System (ODEAS). ODEAS is the primary covariance analysis system used by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). The results of these analyses revealed a high sensitivity of the OD solutions to the state process noise filter tuning parameters. The covariance analysis results show that the state estimate error contributions from measurement-related error sources, especially those due to the random noise and satellite-to-satellite ionospheric refraction correction errors, increase rapidly as the state process noise increases. These results prompted an in-depth investigation of the role of the filter tuning parameters in sequential OD covariance analysis. This paper analyzes how the spacecraft state estimate errors due to dynamic and measurement-related error sources are affected by the process noise level used. This information is then used to establish guidelines for determining optimal filter tuning parameters in a given sequential OD scenario for both covariance analysis and actual OD. Comparisons are also made with corresponding definitive OD results available from the TONS-EUVE analysis.

Conflict Probability Estimation for Free Flight

NASA Technical Reports Server (NTRS)

Paielli, Russell A.; Erzberger, Heinz

1996-01-01

The safety and efficiency of free flight will benefit from automated conflict prediction and resolution advisories. Conflict prediction is based on trajectory prediction and is less certain the farther in advance the prediction, however. An estimate is therefore needed of the probability that a conflict will occur, given a pair of predicted trajectories and their levels of uncertainty. A method is developed in this paper to estimate that conflict probability. The trajectory prediction errors are modeled as normally distributed, and the two error covariances for an aircraft pair are combined into a single equivalent covariance of the relative position. A coordinate transformation is then used to derive an analytical solution. Numerical examples and Monte Carlo validation are presented.

An algorithm for propagating the square-root covariance matrix in triangular form

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Choe, C. Y.

1976-01-01

A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the conventional sequential estimation algorithm with regard to computation time.

Triangular covariance factorizations for. Ph.D. Thesis. - Calif. Univ.

NASA Technical Reports Server (NTRS)

Thornton, C. L.

1976-01-01

An improved computational form of the discrete Kalman filter is derived using an upper triangular factorization of the error covariance matrix. The covariance P is factored such that P = UDUT where U is unit upper triangular and D is diagonal. Recursions are developed for propagating the U-D covariance factors together with the corresponding state estimate. The resulting algorithm, referred to as the U-D filter, combines the superior numerical precision of square root filtering techniques with an efficiency comparable to that of Kalman's original formula. Moreover, this method is easily implemented and involves no more computer storage than the Kalman algorithm. These characteristics make the U-D method an attractive realtime filtering technique. A new covariance error analysis technique is obtained from an extension of the U-D filter equations. This evaluation method is flexible and efficient and may provide significantly improved numerical results. Cost comparisons show that for a large class of problems the U-D evaluation algorithm is noticeably less expensive than conventional error analysis methods.

Large Covariance Estimation by Thresholding Principal Orthogonal Complements

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented. PMID:24348088

Large Covariance Estimation by Thresholding Principal Orthogonal Complements.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2013-09-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.

The search for causal inferences: using propensity scores post hoc to reduce estimation error with nonexperimental research.

PubMed

Tumlinson, Samuel E; Sass, Daniel A; Cano, Stephanie M

2014-03-01

While experimental designs are regarded as the gold standard for establishing causal relationships, such designs are usually impractical owing to common methodological limitations. The objective of this article is to illustrate how propensity score matching (PSM) and using propensity scores (PS) as a covariate are viable alternatives to reduce estimation error when experimental designs cannot be implemented. To mimic common pediatric research practices, data from 140 simulated participants were used to resemble an experimental and nonexperimental design that assessed the effect of treatment status on participant weight loss for diabetes. Pretreatment participant characteristics (age, gender, physical activity, etc.) were then used to generate PS for use in the various statistical approaches. Results demonstrate how PSM and using the PS as a covariate can be used to reduce estimation error and improve statistical inferences. References for issues related to the implementation of these procedures are provided to assist researchers.

A fully redundant double difference algorithm for obtaining minimum variance estimates from GPS observations

NASA Technical Reports Server (NTRS)

Melbourne, William G.

1986-01-01

In double differencing a regression system obtained from concurrent Global Positioning System (GPS) observation sequences, one either undersamples the system to avoid introducing colored measurement statistics, or one fully samples the system incurring the resulting non-diagonal covariance matrix for the differenced measurement errors. A suboptimal estimation result will be obtained in the undersampling case and will also be obtained in the fully sampled case unless the color noise statistics are taken into account. The latter approach requires a least squares weighting matrix derived from inversion of a non-diagonal covariance matrix for the differenced measurement errors instead of inversion of the customary diagonal one associated with white noise processes. Presented is the so-called fully redundant double differencing algorithm for generating a weighted double differenced regression system that yields equivalent estimation results, but features for certain cases a diagonal weighting matrix even though the differenced measurement error statistics are highly colored.

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

A Reduced Dimension Static, Linearized Kalman Filter and Smoother

NASA Technical Reports Server (NTRS)

Fukumori, I.

1995-01-01

An approximate Kalman filter and smoother, based on approximations of the state estimation error covariance matrix, is described. Approximations include a reduction of the effective state dimension, use of a static asymptotic error limit, and a time-invariant linearization of the dynamic model for error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. Examples of use come from TOPEX/POSEIDON.

Simplified Estimation and Testing in Unbalanced Repeated Measures Designs.

PubMed

Spiess, Martin; Jordan, Pascal; Wendt, Mike

2018-05-07

In this paper we propose a simple estimator for unbalanced repeated measures design models where each unit is observed at least once in each cell of the experimental design. The estimator does not require a model of the error covariance structure. Thus, circularity of the error covariance matrix and estimation of correlation parameters and variances are not necessary. Together with a weak assumption about the reason for the varying number of observations, the proposed estimator and its variance estimator are unbiased. As an alternative to confidence intervals based on the normality assumption, a bias-corrected and accelerated bootstrap technique is considered. We also propose the naive percentile bootstrap for Wald-type tests where the standard Wald test may break down when the number of observations is small relative to the number of parameters to be estimated. In a simulation study we illustrate the properties of the estimator and the bootstrap techniques to calculate confidence intervals and conduct hypothesis tests in small and large samples under normality and non-normality of the errors. The results imply that the simple estimator is only slightly less efficient than an estimator that correctly assumes a block structure of the error correlation matrix, a special case of which is an equi-correlation matrix. Application of the estimator and the bootstrap technique is illustrated using data from a task switch experiment based on an experimental within design with 32 cells and 33 participants.

Kalman Filter for Spinning Spacecraft Attitude Estimation

NASA Technical Reports Server (NTRS)

Markley, F. Landis; Sedlak, Joseph E.

2008-01-01

This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Miller, Brad A.; Howard, Samuel A.

2008-01-01

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

On using summary statistics from an external calibration sample to correct for covariate measurement error.

PubMed

Guo, Ying; Little, Roderick J; McConnell, Daniel S

2012-01-01

Covariate measurement error is common in epidemiologic studies. Current methods for correcting measurement error with information from external calibration samples are insufficient to provide valid adjusted inferences. We consider the problem of estimating the regression of an outcome Y on covariates X and Z, where Y and Z are observed, X is unobserved, but a variable W that measures X with error is observed. Information about measurement error is provided in an external calibration sample where data on X and W (but not Y and Z) are recorded. We describe a method that uses summary statistics from the calibration sample to create multiple imputations of the missing values of X in the regression sample, so that the regression coefficients of Y on X and Z and associated standard errors can be estimated using simple multiple imputation combining rules, yielding valid statistical inferences under the assumption of a multivariate normal distribution. The proposed method is shown by simulation to provide better inferences than existing methods, namely the naive method, classical calibration, and regression calibration, particularly for correction for bias and achieving nominal confidence levels. We also illustrate our method with an example using linear regression to examine the relation between serum reproductive hormone concentrations and bone mineral density loss in midlife women in the Michigan Bone Health and Metabolism Study. Existing methods fail to adjust appropriately for bias due to measurement error in the regression setting, particularly when measurement error is substantial. The proposed method corrects this deficiency.

Progress in navigation filter estimate fusion and its application to spacecraft rendezvous

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

1994-01-01

A new derivation of an algorithm which fuses the outputs of two Kalman filters is presented within the context of previous research in this field. Unlike other works, this derivation clearly shows the combination of estimates to be optimal, minimizing the trace of the fused covariance matrix. The algorithm assumes that the filters use identical models, and are stable and operating optimally with respect to their own local measurements. Evidence is presented which indicates that the error ellipsoid derived from the covariance of the optimally fused estimate is contained within the intersections of the error ellipsoids of the two filters being fused. Modifications which reduce the algorithm's data transmission requirements are also presented, including a scalar gain approximation, a cross-covariance update formula which employs only the two contributing filters' autocovariances, and a form of the algorithm which can be used to reinitialize the two Kalman filters. A sufficient condition for using the optimally fused estimates to periodically reinitialize the Kalman filters in this fashion is presented and proved as a theorem. When these results are applied to an optimal spacecraft rendezvous problem, simulated performance results indicate that the use of optimally fused data leads to significantly improved robustness to initial target vehicle state errors. The following applications of estimate fusion methods to spacecraft rendezvous are also described: state vector differencing, and redundancy management.

Estimating the Uncertainty In Diameter Growth Model Predictions and Its Effects On The Uncertainty of Annual Inventory Estimates

Treesearch

Ronald E. McRoberts; Veronica C. Lessard

2001-01-01

Uncertainty in diameter growth predictions is attributed to three general sources: measurement error or sampling variability in predictor variables, parameter covariances, and residual or unexplained variation around model expectations. Using measurement error and sampling variability distributions obtained from the literature and Monte Carlo simulation methods, the...

Robust Mean and Covariance Structure Analysis through Iteratively Reweighted Least Squares.

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Bentler, Peter M.

2000-01-01

Adapts robust schemes to mean and covariance structures, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is weighted according to its distance, based on first and second order moments. Test statistics and standard error estimators are given. (SLD)

Rigorous covariance propagation of geoid errors to geodetic MDT estimates

NASA Astrophysics Data System (ADS)

Pail, R.; Albertella, A.; Fecher, T.; Savcenko, R.

2012-04-01

The mean dynamic topography (MDT) is defined as the difference between the mean sea surface (MSS) derived from satellite altimetry, averaged over several years, and the static geoid. Assuming geostrophic conditions, from the MDT the ocean surface velocities as important component of global ocean circulation can be derived from it. Due to the availability of GOCE gravity field models, for the very first time MDT can now be derived solely from satellite observations (altimetry and gravity) down to spatial length-scales of 100 km and even below. Global gravity field models, parameterized in terms of spherical harmonic coefficients, are complemented by the full variance-covariance matrix (VCM). Therefore, for the geoid component a realistic statistical error estimate is available, while the error description of the altimetric component is still an open issue and is, if at all, attacked empirically. In this study we make the attempt to perform, based on the full gravity VCM, rigorous error propagation to derived geostrophic surface velocities, thus also considering all correlations. For the definition of the static geoid we use the third release of the time-wise GOCE model, as well as the satellite-only combination model GOCO03S. In detail, we will investigate the velocity errors resulting from the geoid component in dependence of the harmonic degree, and the impact of using/no using covariances on the MDT errors and its correlations. When deriving an MDT, it is spectrally filtered to a certain maximum degree, which is usually driven by the signal content of the geoid model, by applying isotropic or non-isotropic filters. Since this filtering is acting also on the geoid component, the consistent integration of this filter process into the covariance propagation shall be performed, and its impact shall be quantified. The study will be performed for MDT estimates in specific test areas of particular oceanographic interest.

The Importance of Semi-Major Axis Knowledge in the Determination of Near-Circular Orbits

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Schiesser, Emil R.

1998-01-01

Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.

Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables

NASA Technical Reports Server (NTRS)

Sedlak, Joseph E.; Harman, Richard

2004-01-01

There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.

Regression-assisted deconvolution.

PubMed

McIntyre, Julie; Stefanski, Leonard A

2011-06-30

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean-variance function regression model, where regression errors are normally distributed and independent of the measurement errors. Simulations suggest that the estimator achieves a much lower integrated squared error than the observed-data kernel density estimator when models are correctly specified and the assumption of normal regression errors is met. We illustrate the method using anthropometric measurements of newborns to estimate the density function of newborn length. Copyright © 2011 John Wiley & Sons, Ltd.

An adaptive filter method for spacecraft using gravity assist

NASA Astrophysics Data System (ADS)

Ning, Xiaolin; Huang, Panpan; Fang, Jiancheng; Liu, Gang; Ge, Shuzhi Sam

2015-04-01

Celestial navigation (CeleNav) has been successfully used during gravity assist (GA) flyby for orbit determination in many deep space missions. Due to spacecraft attitude errors, ephemeris errors, the camera center-finding bias, and the frequency of the images before and after the GA flyby, the statistics of measurement noise cannot be accurately determined, and yet have time-varying characteristics, which may introduce large estimation error and even cause filter divergence. In this paper, an unscented Kalman filter (UKF) with adaptive measurement noise covariance, called ARUKF, is proposed to deal with this problem. ARUKF scales the measurement noise covariance according to the changes in innovation and residual sequences. Simulations demonstrate that ARUKF is robust to the inaccurate initial measurement noise covariance matrix and time-varying measurement noise. The impact factors in the ARUKF are also investigated.

Investigating the Impact of Uncertainty about Item Parameters on Ability Estimation

ERIC Educational Resources Information Center

Zhang, Jinming; Xie, Minge; Song, Xiaolan; Lu, Ting

2011-01-01

Asymptotic expansions of the maximum likelihood estimator (MLE) and weighted likelihood estimator (WLE) of an examinee's ability are derived while item parameter estimators are treated as covariates measured with error. The asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators.…

A fast Monte Carlo EM algorithm for estimation in latent class model analysis with an application to assess diagnostic accuracy for cervical neoplasia in women with AGC

PubMed Central

Kang, Le; Carter, Randy; Darcy, Kathleen; Kauderer, James; Liao, Shu-Yuan

2013-01-01

In this article we use a latent class model (LCM) with prevalence modeled as a function of covariates to assess diagnostic test accuracy in situations where the true disease status is not observed, but observations on three or more conditionally independent diagnostic tests are available. A fast Monte Carlo EM (MCEM) algorithm with binary (disease) diagnostic data is implemented to estimate parameters of interest; namely, sensitivity, specificity, and prevalence of the disease as a function of covariates. To obtain standard errors for confidence interval construction of estimated parameters, the missing information principle is applied to adjust information matrix estimates. We compare the adjusted information matrix based standard error estimates with the bootstrap standard error estimates both obtained using the fast MCEM algorithm through an extensive Monte Carlo study. Simulation demonstrates that the adjusted information matrix approach estimates the standard error similarly with the bootstrap methods under certain scenarios. The bootstrap percentile intervals have satisfactory coverage probabilities. We then apply the LCM analysis to a real data set of 122 subjects from a Gynecologic Oncology Group (GOG) study of significant cervical lesion (S-CL) diagnosis in women with atypical glandular cells of undetermined significance (AGC) to compare the diagnostic accuracy of a histology-based evaluation, a CA-IX biomarker-based test and a human papillomavirus (HPV) DNA test. PMID:24163493

Robust covariance estimation of galaxy-galaxy weak lensing: validation and limitation of jackknife covariance

NASA Astrophysics Data System (ADS)

Shirasaki, Masato; Takada, Masahiro; Miyatake, Hironao; Takahashi, Ryuichi; Hamana, Takashi; Nishimichi, Takahiro; Murata, Ryoma

2017-09-01

We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations and their inherent halo catalogues. Using the mock catalogue to study the error covariance matrix of galaxy-galaxy weak lensing, we compare the full covariance with the 'jackknife' (JK) covariance, the method often used in the literature that estimates the covariance from the resamples of the data itself. We show that there exists the variation of JK covariance over realizations of mock lensing measurements, while the average JK covariance over mocks can give a reasonably accurate estimation of the true covariance up to separations comparable with the size of JK subregion. The scatter in JK covariances is found to be ∼10 per cent after we subtract the lensing measurement around random points. However, the JK method tends to underestimate the covariance at the larger separations, more increasingly for a survey with a higher number density of source galaxies. We apply our method to the Sloan Digital Sky Survey (SDSS) data, and show that the 48 mock SDSS catalogues nicely reproduce the signals and the JK covariance measured from the real data. We then argue that the use of the accurate covariance, compared to the JK covariance, allows us to use the lensing signals at large scales beyond a size of the JK subregion, which contains cleaner cosmological information in the linear regime.

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

USGS Publications Warehouse

Langbein, John O.

2017-01-01

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/fα">1/fα1/fα with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi:10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

NASA Astrophysics Data System (ADS)

Langbein, John

2017-08-01

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/f^{α } with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi: 10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

A new method for determining the optimal lagged ensemble

PubMed Central

DelSole, T.; Tippett, M. K.; Pegion, K.

2017-01-01

Abstract We propose a general methodology for determining the lagged ensemble that minimizes the mean square forecast error. The MSE of a lagged ensemble is shown to depend only on a quantity called the cross‐lead error covariance matrix, which can be estimated from a short hindcast data set and parameterized in terms of analytic functions of time. The resulting parameterization allows the skill of forecasts to be evaluated for an arbitrary ensemble size and initialization frequency. Remarkably, the parameterization also can estimate the MSE of a burst ensemble simply by taking the limit of an infinitely small interval between initialization times. This methodology is applied to forecasts of the Madden Julian Oscillation (MJO) from version 2 of the Climate Forecast System version 2 (CFSv2). For leads greater than a week, little improvement is found in the MJO forecast skill when ensembles larger than 5 days are used or initializations greater than 4 times per day. We find that if the initialization frequency is too infrequent, important structures of the lagged error covariance matrix are lost. Lastly, we demonstrate that the forecast error at leads ≥10 days can be reduced by optimally weighting the lagged ensemble members. The weights are shown to depend only on the cross‐lead error covariance matrix. While the methodology developed here is applied to CFSv2, the technique can be easily adapted to other forecast systems. PMID:28580050

Using Least Squares for Error Propagation

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2015-01-01

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

Accounting for response misclassification and covariate measurement error improves power and reduces bias in epidemiologic studies.

PubMed

Cheng, Dunlei; Branscum, Adam J; Stamey, James D

2010-07-01

To quantify the impact of ignoring misclassification of a response variable and measurement error in a covariate on statistical power, and to develop software for sample size and power analysis that accounts for these flaws in epidemiologic data. A Monte Carlo simulation-based procedure is developed to illustrate the differences in design requirements and inferences between analytic methods that properly account for misclassification and measurement error to those that do not in regression models for cross-sectional and cohort data. We found that failure to account for these flaws in epidemiologic data can lead to a substantial reduction in statistical power, over 25% in some cases. The proposed method substantially reduced bias by up to a ten-fold margin compared to naive estimates obtained by ignoring misclassification and mismeasurement. We recommend as routine practice that researchers account for errors in measurement of both response and covariate data when determining sample size, performing power calculations, or analyzing data from epidemiological studies. 2010 Elsevier Inc. All rights reserved.

ILIAD Testing; and a Kalman Filter for 3-D Pose Estimation

NASA Technical Reports Server (NTRS)

Richardson, A. O.

1996-01-01

This report presents the results of a two-part project. The first part presents results of performance assessment tests on an Internet Library Information Assembly Data Base (ILIAD). It was found that ILLAD performed best when queries were short (one-to-three keywords), and were made up of rare, unambiguous words. In such cases as many as 64% of the typically 25 returned documents were found to be relevant. It was also found that a query format that was not so rigid with respect to spelling errors and punctuation marks would be more user-friendly. The second part of the report shows the design of a Kalman Filter for estimating motion parameters of a three dimensional object from sequences of noisy data derived from two-dimensional pictures. Given six measured deviation values represendng X, Y, Z, pitch, yaw, and roll, twelve parameters were estimated comprising the six deviations and their time rate of change. Values for the state transiton matrix, the observation matrix, the system noise covariance matrix, and the observation noise covariance matrix were determined. A simple way of initilizing the error covariance matrix was pointed out.

Filter Tuning Using the Chi-Squared Statistic

NASA Technical Reports Server (NTRS)

Lilly-Salkowski, Tyler

2017-01-01

The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) performs orbit determination (OD) for the Aqua and Aura satellites. Both satellites are located in low Earth orbit (LEO), and are part of what is considered the A-Train satellite constellation. Both spacecraft are currently in the science phase of their respective missions. The FDF has recently been tasked with delivering definitive covariance for each satellite.The main source of orbit determination used for these missions is the Orbit Determination Toolkit developed by Analytical Graphics Inc. (AGI). This software uses an Extended Kalman Filter (EKF) to estimate the states of both spacecraft. The filter incorporates force modelling, ground station and space network measurements to determine spacecraft states. It also generates a covariance at each measurement. This covariance can be useful for evaluating the overall performance of the tracking data measurements and the filter itself. An accurate covariance is also useful for covariance propagation which is utilized in collision avoidance operations. It is also valuable when attempting to determine if the current orbital solution will meet mission requirements in the future.This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The Chi-square statistic is calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance.For the EKF to correctly calculate the covariance, error models associated with tracking data measurements must be accurately tuned. Over estimating or under estimating these error values can have detrimental effects on the overall filter performance. The filter incorporates ground station measurements, which can be tuned based on the accuracy of the individual ground stations. It also includes measurements from the NASA space network (SN), which can be affected by the assumed accuracy of the TDRS satellite state at the time of the measurement.The force modelling in the EKF is also an important factor that affects the propagation accuracy and covariance sizing. The dominant force in the LEO orbit regime is the drag force caused by atmospheric drag. Accurate accounting of the drag force is especially important for the accuracy of the propagated state. The implementation of a box and wing model to improve drag estimation accuracy, and its overall effect on the covariance state is explored.The process of tuning the EKF for Aqua and Aura support is described, including examination of the measurement errors of available observation types (Doppler and range), and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-square statistic, calculated based of the ODTK EKF solutions, are assessed versus accepted norms for the orbit regime.

Replica approach to mean-variance portfolio optimization

NASA Astrophysics Data System (ADS)

Varga-Haszonits, Istvan; Caccioli, Fabio; Kondor, Imre

2016-12-01

We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the solution does not need to be assumed, but emerges as the unique solution of the optimization problem. We also check the stability of this solution and find that the eigenvalues of the Hessian are positive for r  =  N/T  <  1, where N is the dimension of the portfolio and T the length of the time series used to estimate the covariance matrix. At the critical point r  =  1 a phase transition is taking place. The out of sample estimation error blows up at this point as 1/(1  -  r), independently of the covariance matrix or the expected return, displaying the universality not only of the critical exponent, but also the critical point. As a conspicuous illustration of the dangers of in-sample estimates, the optimal in-sample variance is found to vanish at the critical point inversely proportional to the divergent estimation error.

Stochastic modeling for time series InSAR: with emphasis on atmospheric effects

NASA Astrophysics Data System (ADS)

Cao, Yunmeng; Li, Zhiwei; Wei, Jianchao; Hu, Jun; Duan, Meng; Feng, Guangcai

2018-02-01

Despite the many applications of time series interferometric synthetic aperture radar (TS-InSAR) techniques in geophysical problems, error analysis and assessment have been largely overlooked. Tropospheric propagation error is still the dominant error source of InSAR observations. However, the spatiotemporal variation of atmospheric effects is seldom considered in the present standard TS-InSAR techniques, such as persistent scatterer interferometry and small baseline subset interferometry. The failure to consider the stochastic properties of atmospheric effects not only affects the accuracy of the estimators, but also makes it difficult to assess the uncertainty of the final geophysical results. To address this issue, this paper proposes a network-based variance-covariance estimation method to model the spatiotemporal variation of tropospheric signals, and to estimate the temporal variance-covariance matrix of TS-InSAR observations. The constructed stochastic model is then incorporated into the TS-InSAR estimators both for parameters (e.g., deformation velocity, topography residual) estimation and uncertainty assessment. It is an incremental and positive improvement to the traditional weighted least squares methods to solve the multitemporal InSAR time series. The performance of the proposed method is validated by using both simulated and real datasets.

Multilevel Multidimensional Item Response Model with a Multilevel Latent Covariate

ERIC Educational Resources Information Center

Cho, Sun-Joo; Bottge, Brian A.

2015-01-01

In a pretest-posttest cluster-randomized trial, one of the methods commonly used to detect an intervention effect involves controlling pre-test scores and other related covariates while estimating an intervention effect at post-test. In many applications in education, the total post-test and pre-test scores that ignores measurement error in the…

Two-step estimation in ratio-of-mediator-probability weighted causal mediation analysis.

PubMed

Bein, Edward; Deutsch, Jonah; Hong, Guanglei; Porter, Kristin E; Qin, Xu; Yang, Cheng

2018-04-15

This study investigates appropriate estimation of estimator variability in the context of causal mediation analysis that employs propensity score-based weighting. Such an analysis decomposes the total effect of a treatment on the outcome into an indirect effect transmitted through a focal mediator and a direct effect bypassing the mediator. Ratio-of-mediator-probability weighting estimates these causal effects by adjusting for the confounding impact of a large number of pretreatment covariates through propensity score-based weighting. In step 1, a propensity score model is estimated. In step 2, the causal effects of interest are estimated using weights derived from the prior step's regression coefficient estimates. Statistical inferences obtained from this 2-step estimation procedure are potentially problematic if the estimated standard errors of the causal effect estimates do not reflect the sampling uncertainty in the estimation of the weights. This study extends to ratio-of-mediator-probability weighting analysis a solution to the 2-step estimation problem by stacking the score functions from both steps. We derive the asymptotic variance-covariance matrix for the indirect effect and direct effect 2-step estimators, provide simulation results, and illustrate with an application study. Our simulation results indicate that the sampling uncertainty in the estimated weights should not be ignored. The standard error estimation using the stacking procedure offers a viable alternative to bootstrap standard error estimation. We discuss broad implications of this approach for causal analysis involving propensity score-based weighting. Copyright © 2018 John Wiley & Sons, Ltd.

Analysis and application of minimum variance discrete time system identification

NASA Technical Reports Server (NTRS)

Kaufman, H.; Kotob, S.

1975-01-01

An on-line minimum variance parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise. The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean square convergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Multilevel Models for Intensive Longitudinal Data with Heterogeneous Autoregressive Errors: The Effect of Misspecification and Correction with Cholesky Transformation

PubMed Central

Jahng, Seungmin; Wood, Phillip K.

2017-01-01

Intensive longitudinal studies, such as ecological momentary assessment studies using electronic diaries, are gaining popularity across many areas of psychology. Multilevel models (MLMs) are most widely used analytical tools for intensive longitudinal data (ILD). Although ILD often have individually distinct patterns of serial correlation of measures over time, inferences of the fixed effects, and random components in MLMs are made under the assumption that all variance and autocovariance components are homogenous across individuals. In the present study, we introduced a multilevel model with Cholesky transformation to model ILD with individually heterogeneous covariance structure. In addition, the performance of the transformation method and the effects of misspecification of heterogeneous covariance structure were investigated through a Monte Carlo simulation. We found that, if individually heterogeneous covariances are incorrectly assumed as homogenous independent or homogenous autoregressive, MLMs produce highly biased estimates of the variance of random intercepts and the standard errors of the fixed intercept and the fixed effect of a level 2 covariate when the average autocorrelation is high. For intensive longitudinal data with individual specific residual covariance, the suggested transformation method showed lower bias in those estimates than the misspecified models when the number of repeated observations within individuals is 50 or more. PMID:28286490

Semiparametric Bayesian analysis of gene-environment interactions with error in measurement of environmental covariates and missing genetic data.

PubMed

Lobach, Iryna; Mallick, Bani; Carroll, Raymond J

2011-01-01

Case-control studies are widely used to detect gene-environment interactions in the etiology of complex diseases. Many variables that are of interest to biomedical researchers are difficult to measure on an individual level, e.g. nutrient intake, cigarette smoking exposure, long-term toxic exposure. Measurement error causes bias in parameter estimates, thus masking key features of data and leading to loss of power and spurious/masked associations. We develop a Bayesian methodology for analysis of case-control studies for the case when measurement error is present in an environmental covariate and the genetic variable has missing data. This approach offers several advantages. It allows prior information to enter the model to make estimation and inference more precise. The environmental covariates measured exactly are modeled completely nonparametrically. Further, information about the probability of disease can be incorporated in the estimation procedure to improve quality of parameter estimates, what cannot be done in conventional case-control studies. A unique feature of the procedure under investigation is that the analysis is based on a pseudo-likelihood function therefore conventional Bayesian techniques may not be technically correct. We propose an approach using Markov Chain Monte Carlo sampling as well as a computationally simple method based on an asymptotic posterior distribution. Simulation experiments demonstrated that our method produced parameter estimates that are nearly unbiased even for small sample sizes. An application of our method is illustrated using a population-based case-control study of the association between calcium intake with the risk of colorectal adenoma development.

Processing arctic eddy-flux data using a simple carbon-exchange model embedded in the ensemble Kalman filter.

PubMed

Rastetter, Edward B; Williams, Mathew; Griffin, Kevin L; Kwiatkowski, Bonnie L; Tomasky, Gabrielle; Potosnak, Mark J; Stoy, Paul C; Shaver, Gaius R; Stieglitz, Marc; Hobbie, John E; Kling, George W

2010-07-01

Continuous time-series estimates of net ecosystem carbon exchange (NEE) are routinely made using eddy covariance techniques. Identifying and compensating for errors in the NEE time series can be automated using a signal processing filter like the ensemble Kalman filter (EnKF). The EnKF compares each measurement in the time series to a model prediction and updates the NEE estimate by weighting the measurement and model prediction relative to a specified measurement error estimate and an estimate of the model-prediction error that is continuously updated based on model predictions of earlier measurements in the time series. Because of the covariance among model variables, the EnKF can also update estimates of variables for which there is no direct measurement. The resulting estimates evolve through time, enabling the EnKF to be used to estimate dynamic variables like changes in leaf phenology. The evolving estimates can also serve as a means to test the embedded model and reconcile persistent deviations between observations and model predictions. We embedded a simple arctic NEE model into the EnKF and filtered data from an eddy covariance tower located in tussock tundra on the northern foothills of the Brooks Range in northern Alaska, USA. The model predicts NEE based only on leaf area, irradiance, and temperature and has been well corroborated for all the major vegetation types in the Low Arctic using chamber-based data. This is the first application of the model to eddy covariance data. We modified the EnKF by adding an adaptive noise estimator that provides a feedback between persistent model data deviations and the noise added to the ensemble of Monte Carlo simulations in the EnKF. We also ran the EnKF with both a specified leaf-area trajectory and with the EnKF sequentially recalibrating leaf-area estimates to compensate for persistent model-data deviations. When used together, adaptive noise estimation and sequential recalibration substantially improved filter performance, but it did not improve performance when used individually. The EnKF estimates of leaf area followed the expected springtime canopy phenology. However, there were also diel fluctuations in the leaf-area estimates; these are a clear indication of a model deficiency possibly related to vapor pressure effects on canopy conductance.

Using Fisher Information Criteria for Chemical Sensor Selection via Convex Optimization Methods

DTIC Science & Technology

2016-11-16

determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a suitable...pro- ceeds from the determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a...design of statistical estimators (i.e. sensors) as their respective inverses act as lower bounds to the (co)variances of the subject estimator, a property

Improved characterisation of measurement errors in electrical resistivity tomography (ERT) surveys

NASA Astrophysics Data System (ADS)

Tso, C. H. M.; Binley, A. M.; Kuras, O.; Graham, J.

2016-12-01

Measurement errors can play a pivotal role in geophysical inversion. Most inverse models require users to prescribe a statistical model of data errors before inversion. Wrongly prescribed error levels can lead to over- or under-fitting of data, yet commonly used models of measurement error are relatively simplistic. With the heightening interests in uncertainty estimation across hydrogeophysics, better characterisation and treatment of measurement errors is needed to provide more reliable estimates of uncertainty. We have analysed two time-lapse electrical resistivity tomography (ERT) datasets; one contains 96 sets of direct and reciprocal data collected from a surface ERT line within a 24h timeframe, while the other is a year-long cross-borehole survey at a UK nuclear site with over 50,000 daily measurements. Our study included the characterisation of the spatial and temporal behaviour of measurement errors using autocorrelation and covariance analysis. We find that, in addition to well-known proportionality effects, ERT measurements can also be sensitive to the combination of electrodes used. This agrees with reported speculation in previous literature that ERT errors could be somewhat correlated. Based on these findings, we develop a new error model that allows grouping based on electrode number in additional to fitting a linear model to transfer resistance. The new model fits the observed measurement errors better and shows superior inversion and uncertainty estimates in synthetic examples. It is robust, because it groups errors together based on the number of the four electrodes used to make each measurement. The new model can be readily applied to the diagonal data weighting matrix commonly used in classical inversion methods, as well as to the data covariance matrix in the Bayesian inversion framework. We demonstrate its application using extensive ERT monitoring datasets from the two aforementioned sites.

A Complementary Note to 'A Lag-1 Smoother Approach to System-Error Estimation': The Intrinsic Limitations of Residual Diagnostics

NASA Technical Reports Server (NTRS)

Todling, Ricardo

2015-01-01

Recently, this author studied an approach to the estimation of system error based on combining observation residuals derived from a sequential filter and fixed lag-1 smoother. While extending the methodology to a variational formulation, experimenting with simple models and making sure consistency was found between the sequential and variational formulations, the limitations of the residual-based approach came clearly to the surface. This note uses the sequential assimilation application to simple nonlinear dynamics to highlight the issue. Only when some of the underlying error statistics are assumed known is it possible to estimate the unknown component. In general, when considerable uncertainties exist in the underlying statistics as a whole, attempts to obtain separate estimates of the various error covariances are bound to lead to misrepresentation of errors. The conclusions are particularly relevant to present-day attempts to estimate observation-error correlations from observation residual statistics. A brief illustration of the issue is also provided by comparing estimates of error correlations derived from a quasi-operational assimilation system and a corresponding Observing System Simulation Experiments framework.

Gossip and Distributed Kalman Filtering: Weak Consensus Under Weak Detectability

NASA Astrophysics Data System (ADS)

Kar, Soummya; Moura, José M. F.

2011-04-01

The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1. the GIKF error process remains stochastically bounded, irrespective of the instability properties of the random process dynamics; and 2. the network achieves \\emph{weak consensus}, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semi-definite matrices (independent of the initial state.) To prove these results, we interpret the filtered states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a non-stationary Markov chain on the network graph.

GRAVSAT/GEOPAUSE covariance analysis including geopotential aliasing

NASA Technical Reports Server (NTRS)

Koch, D. W.

1975-01-01

A conventional covariance analysis for the GRAVSAT/GEOPAUSE mission is described in which the uncertainties of approximately 200 parameters, including the geopotential coefficients to degree and order 12, are estimated over three different tracking intervals. The estimated orbital uncertainties for both GRAVSAT and GEOPAUSE reach levels more accurate than presently available. The adjusted measurement bias errors approach the mission goal. Survey errors in the low centimeter range are achieved after ten days of tracking. The ability of the mission to obtain accuracies of geopotential terms to (12, 12) one to two orders of magnitude superior to present accuracy levels is clearly shown. A unique feature of this report is that the aliasing structure of this (12, 12) field is examined. It is shown that uncertainties for unadjusted terms to (12, 12) still exert a degrading effect upon the adjusted error of an arbitrarily selected term of lower degree and order. Finally, the distribution of the aliasing from the unestimated uncertainty of a particular high degree and order geopotential term upon the errors of all remaining adjusted terms is listed in detail.

A study on characteristics of retrospective optimal interpolation with WRF testbed

NASA Astrophysics Data System (ADS)

Kim, S.; Noh, N.; Lim, G.

2012-12-01

This study presents the application of retrospective optimal interpolation (ROI) with Weather Research and Forecasting model (WRF). Song et al. (2009) suggest ROI method which is an optimal interpolation (OI) that gradually assimilates observations over the analysis window for variance-minimum estimate of an atmospheric state at the initial time of the analysis window. Song and Lim (2011) improve the method by incorporating eigen-decomposition and covariance inflation. ROI method assimilates the data at post analysis time using perturbation method (Errico and Raeder, 1999) without adjoint model. In this study, ROI method is applied to WRF model to validate the algorithm and to investigate the capability. The computational costs for ROI can be reduced due to the eigen-decomposition of background error covariance. Using the background error covariance in eigen-space, 1-profile assimilation experiment is performed. The difference between forecast errors with assimilation and without assimilation is obviously increased as time passed, which means the improvement of forecast error by assimilation. The characteristics and strength/weakness of ROI method are investigated by conducting the experiments with other data assimilation method.

A regularization corrected score method for nonlinear regression models with covariate error.

PubMed

Zucker, David M; Gorfine, Malka; Li, Yi; Tadesse, Mahlet G; Spiegelman, Donna

2013-03-01

Many regression analyses involve explanatory variables that are measured with error, and failing to account for this error is well known to lead to biased point and interval estimates of the regression coefficients. We present here a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation. We develop the theory in the setting of classical likelihood models; this setting covers, for example, linear regression, nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not involving assumptions on the distribution of the true covariate. We discuss the theoretical properties of the method and present simulation results in the logistic regression setting (univariate and multivariate). For illustration, we apply the method to data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer. Copyright © 2013, The International Biometric Society.

Adaptive error covariances estimation methods for ensemble Kalman filters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhen, Yicun, E-mail: zhen@math.psu.edu; Harlim, John, E-mail: jharlim@psu.edu

2015-08-01

This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of Belanger's recursive method, to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large. When we use only product of innovation processes up to one-lag, the computational cost is indeed comparable to a recently proposed method by Berry–Sauer's. However, our method is more flexible since it allows for usingmore » information from product of innovation processes of more than one-lag. Extensive numerical comparisons between the proposed method and both the original Belanger's and Berry–Sauer's schemes are shown in various examples, ranging from low-dimensional linear and nonlinear systems of SDEs and 40-dimensional stochastically forced Lorenz-96 model. Our numerical results suggest that the proposed scheme is as accurate as the original Belanger's scheme on low-dimensional problems and has a wider range of more accurate estimates compared to Berry–Sauer's method on L-96 example.« less

On-Board Event-Based State Estimation for Trajectory Approaching and Tracking of a Vehicle

PubMed Central

Martínez-Rey, Miguel; Espinosa, Felipe; Gardel, Alfredo; Santos, Carlos

2015-01-01

For the problem of pose estimation of an autonomous vehicle using networked external sensors, the processing capacity and battery consumption of these sensors, as well as the communication channel load should be optimized. Here, we report an event-based state estimator (EBSE) consisting of an unscented Kalman filter that uses a triggering mechanism based on the estimation error covariance matrix to request measurements from the external sensors. This EBSE generates the events of the estimator module on-board the vehicle and, thus, allows the sensors to remain in stand-by mode until an event is generated. The proposed algorithm requests a measurement every time the estimation distance root mean squared error (DRMS) value, obtained from the estimator's covariance matrix, exceeds a threshold value. This triggering threshold can be adapted to the vehicle's working conditions rendering the estimator even more efficient. An example of the use of the proposed EBSE is given, where the autonomous vehicle must approach and follow a reference trajectory. By making the threshold a function of the distance to the reference location, the estimator can halve the use of the sensors with a negligible deterioration in the performance of the approaching maneuver. PMID:26102489

Inference of reactive transport model parameters using a Bayesian multivariate approach

NASA Astrophysics Data System (ADS)

Carniato, Luca; Schoups, Gerrit; van de Giesen, Nick

2014-08-01

Parameter estimation of subsurface transport models from multispecies data requires the definition of an objective function that includes different types of measurements. Common approaches are weighted least squares (WLS), where weights are specified a priori for each measurement, and weighted least squares with weight estimation (WLS(we)) where weights are estimated from the data together with the parameters. In this study, we formulate the parameter estimation task as a multivariate Bayesian inference problem. The WLS and WLS(we) methods are special cases in this framework, corresponding to specific prior assumptions about the residual covariance matrix. The Bayesian perspective allows for generalizations to cases where residual correlation is important and for efficient inference by analytically integrating out the variances (weights) and selected covariances from the joint posterior. Specifically, the WLS and WLS(we) methods are compared to a multivariate (MV) approach that accounts for specific residual correlations without the need for explicit estimation of the error parameters. When applied to inference of reactive transport model parameters from column-scale data on dissolved species concentrations, the following results were obtained: (1) accounting for residual correlation between species provides more accurate parameter estimation for high residual correlation levels whereas its influence for predictive uncertainty is negligible, (2) integrating out the (co)variances leads to an efficient estimation of the full joint posterior with a reduced computational effort compared to the WLS(we) method, and (3) in the presence of model structural errors, none of the methods is able to identify the correct parameter values.

Multiple Imputation of a Randomly Censored Covariate Improves Logistic Regression Analysis.

PubMed

Atem, Folefac D; Qian, Jing; Maye, Jacqueline E; Johnson, Keith A; Betensky, Rebecca A

2016-01-01

Randomly censored covariates arise frequently in epidemiologic studies. The most commonly used methods, including complete case and single imputation or substitution, suffer from inefficiency and bias. They make strong parametric assumptions or they consider limit of detection censoring only. We employ multiple imputation, in conjunction with semi-parametric modeling of the censored covariate, to overcome these shortcomings and to facilitate robust estimation. We develop a multiple imputation approach for randomly censored covariates within the framework of a logistic regression model. We use the non-parametric estimate of the covariate distribution or the semiparametric Cox model estimate in the presence of additional covariates in the model. We evaluate this procedure in simulations, and compare its operating characteristics to those from the complete case analysis and a survival regression approach. We apply the procedures to an Alzheimer's study of the association between amyloid positivity and maternal age of onset of dementia. Multiple imputation achieves lower standard errors and higher power than the complete case approach under heavy and moderate censoring and is comparable under light censoring. The survival regression approach achieves the highest power among all procedures, but does not produce interpretable estimates of association. Multiple imputation offers a favorable alternative to complete case analysis and ad hoc substitution methods in the presence of randomly censored covariates within the framework of logistic regression.

Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: a Monte Carlo study.

PubMed

Chou, C P; Bentler, P M; Satorra, A

1991-11-01

Research studying robustness of maximum likelihood (ML) statistics in covariance structure analysis has concluded that test statistics and standard errors are biased under severe non-normality. An estimation procedure known as asymptotic distribution free (ADF), making no distributional assumption, has been suggested to avoid these biases. Corrections to the normal theory statistics to yield more adequate performance have also been proposed. This study compares the performance of a scaled test statistic and robust standard errors for two models under several non-normal conditions and also compares these with the results from ML and ADF methods. Both ML and ADF test statistics performed rather well in one model and considerably worse in the other. In general, the scaled test statistic seemed to behave better than the ML test statistic and the ADF statistic performed the worst. The robust and ADF standard errors yielded more appropriate estimates of sampling variability than the ML standard errors, which were usually downward biased, in both models under most of the non-normal conditions. ML test statistics and standard errors were found to be quite robust to the violation of the normality assumption when data had either symmetric and platykurtic distributions, or non-symmetric and zero kurtotic distributions.

Skylab water balance error analysis

NASA Technical Reports Server (NTRS)

Leonard, J. I.

1977-01-01

Estimates of the precision of the net water balance were obtained for the entire Skylab preflight and inflight phases as well as for the first two weeks of flight. Quantitative estimates of both total sampling errors and instrumentation errors were obtained. It was shown that measurement error is minimal in comparison to biological variability and little can be gained from improvement in analytical accuracy. In addition, a propagation of error analysis demonstrated that total water balance error could be accounted for almost entirely by the errors associated with body mass changes. Errors due to interaction between terms in the water balance equation (covariances) represented less than 10% of the total error. Overall, the analysis provides evidence that daily measurements of body water changes obtained from the indirect balance technique are reasonable, precise, and relaible. The method is not biased toward net retention or loss.

Missing continuous outcomes under covariate dependent missingness in cluster randomised trials

PubMed Central

Diaz-Ordaz, Karla; Bartlett, Jonathan W

2016-01-01

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group. PMID:27177885

Missing continuous outcomes under covariate dependent missingness in cluster randomised trials.

PubMed

Hossain, Anower; Diaz-Ordaz, Karla; Bartlett, Jonathan W

2017-06-01

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group.

Asteroid orbital error analysis: Theory and application

NASA Technical Reports Server (NTRS)

Muinonen, K.; Bowell, Edward

1992-01-01

We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).

Propensity Score Weighting with Error-Prone Covariates

ERIC Educational Resources Information Center

McCaffrey, Daniel F.; Lockwood, J. R.; Setodji, Claude M.

2011-01-01

Inverse probability weighting (IPW) estimates are widely used in applications where data are missing due to nonresponse or censoring or in observational studies of causal effects where the counterfactuals cannot be observed. This extensive literature has shown the estimators to be consistent and asymptotically normal under very general conditions,…

Effects of Employing Ridge Regression in Structural Equation Models.

ERIC Educational Resources Information Center

McQuitty, Shaun

1997-01-01

LISREL 8 invokes a ridge option when maximum likelihood or generalized least squares are used to estimate a structural equation model with a nonpositive definite covariance or correlation matrix. Implications of the ridge option for model fit, parameter estimates, and standard errors are explored through two examples. (SLD)

Fitting dynamic models to the Geosat sea level observations in the tropical Pacific Ocean. I - A free wave model

NASA Technical Reports Server (NTRS)

Fu, Lee-Lueng; Vazquez, Jorge; Perigaud, Claire

1991-01-01

Free, equatorially trapped sinusoidal wave solutions to a linear model on an equatorial beta plane are used to fit the Geosat altimetric sea level observations in the tropical Pacific Ocean. The Kalman filter technique is used to estimate the wave amplitude and phase from the data. The estimation is performed at each time step by combining the model forecast with the observation in an optimal fashion utilizing the respective error covariances. The model error covariance is determined such that the performance of the model forecast is optimized. It is found that the dominant observed features can be described qualitatively by basin-scale Kelvin waves and the first meridional-mode Rossby waves. Quantitatively, however, only 23 percent of the signal variance can be accounted for by this simple model.

Fitting direct covariance structures by the MSTRUCT modeling language of the CALIS procedure.

PubMed

Yung, Yiu-Fai; Browne, Michael W; Zhang, Wei

2015-02-01

This paper demonstrates the usefulness and flexibility of the general structural equation modelling (SEM) approach to fitting direct covariance patterns or structures (as opposed to fitting implied covariance structures from functional relationships among variables). In particular, the MSTRUCT modelling language (or syntax) of the CALIS procedure (SAS/STAT version 9.22 or later: SAS Institute, 2010) is used to illustrate the SEM approach. The MSTRUCT modelling language supports a direct covariance pattern specification of each covariance element. It also supports the input of additional independent and dependent parameters. Model tests, fit statistics, estimates, and their standard errors are then produced under the general SEM framework. By using numerical and computational examples, the following tests of basic covariance patterns are illustrated: sphericity, compound symmetry, and multiple-group covariance patterns. Specification and testing of two complex correlation structures, the circumplex pattern and the composite direct product models with or without composite errors and scales, are also illustrated by the MSTRUCT syntax. It is concluded that the SEM approach offers a general and flexible modelling of direct covariance and correlation patterns. In conjunction with the use of SAS macros, the MSTRUCT syntax provides an easy-to-use interface for specifying and fitting complex covariance and correlation structures, even when the number of variables or parameters becomes large. © 2014 The British Psychological Society.

The impact of covariance misspecification in multivariate Gaussian mixtures on estimation and inference: an application to longitudinal modeling.

PubMed

Heggeseth, Brianna C; Jewell, Nicholas P

2013-07-20

Multivariate Gaussian mixtures are a class of models that provide a flexible parametric approach for the representation of heterogeneous multivariate outcomes. When the outcome is a vector of repeated measurements taken on the same subject, there is often inherent dependence between observations. However, a common covariance assumption is conditional independence-that is, given the mixture component label, the outcomes for subjects are independent. In this paper, we study, through asymptotic bias calculations and simulation, the impact of covariance misspecification in multivariate Gaussian mixtures. Although maximum likelihood estimators of regression and mixing probability parameters are not consistent under misspecification, they have little asymptotic bias when mixture components are well separated or if the assumed correlation is close to the truth even when the covariance is misspecified. We also present a robust standard error estimator and show that it outperforms conventional estimators in simulations and can indicate that the model is misspecified. Body mass index data from a national longitudinal study are used to demonstrate the effects of misspecification on potential inferences made in practice. Copyright © 2013 John Wiley & Sons, Ltd.

New method for propagating the square root covariance matrix in triangular form. [using Kalman-Bucy filter

NASA Technical Reports Server (NTRS)

Choe, C. Y.; Tapley, B. D.

1975-01-01

A method proposed by Potter of applying the Kalman-Bucy filter to the problem of estimating the state of a dynamic system is described, in which the square root of the state error covariance matrix is used to process the observations. A new technique which propagates the covariance square root matrix in lower triangular form is given for the discrete observation case. The technique is faster than previously proposed algorithms and is well-adapted for use with the Carlson square root measurement algorithm.

Assessing the performance of the generalized propensity score for estimating the effect of quantitative or continuous exposures on binary outcomes

PubMed Central

2018-01-01

Propensity score methods are increasingly being used to estimate the effects of treatments and exposures when using observational data. The propensity score was initially developed for use with binary exposures. The generalized propensity score (GPS) is an extension of the propensity score for use with quantitative or continuous exposures (eg, dose or quantity of medication, income, or years of education). We used Monte Carlo simulations to examine the performance of different methods of using the GPS to estimate the effect of continuous exposures on binary outcomes. We examined covariate adjustment using the GPS and weighting using weights based on the inverse of the GPS. We examined both the use of ordinary least squares to estimate the propensity function and the use of the covariate balancing propensity score algorithm. The use of methods based on the GPS was compared with the use of G‐computation. All methods resulted in essentially unbiased estimation of the population dose‐response function. However, GPS‐based weighting tended to result in estimates that displayed greater variability and had higher mean squared error when the magnitude of confounding was strong. Of the methods based on the GPS, covariate adjustment using the GPS tended to result in estimates with lower variability and mean squared error when the magnitude of confounding was strong. We illustrate the application of these methods by estimating the effect of average neighborhood income on the probability of death within 1 year of hospitalization for an acute myocardial infarction. PMID:29508424

Assessing the performance of the generalized propensity score for estimating the effect of quantitative or continuous exposures on binary outcomes.

PubMed

Austin, Peter C

2018-05-20

Propensity score methods are increasingly being used to estimate the effects of treatments and exposures when using observational data. The propensity score was initially developed for use with binary exposures. The generalized propensity score (GPS) is an extension of the propensity score for use with quantitative or continuous exposures (eg, dose or quantity of medication, income, or years of education). We used Monte Carlo simulations to examine the performance of different methods of using the GPS to estimate the effect of continuous exposures on binary outcomes. We examined covariate adjustment using the GPS and weighting using weights based on the inverse of the GPS. We examined both the use of ordinary least squares to estimate the propensity function and the use of the covariate balancing propensity score algorithm. The use of methods based on the GPS was compared with the use of G-computation. All methods resulted in essentially unbiased estimation of the population dose-response function. However, GPS-based weighting tended to result in estimates that displayed greater variability and had higher mean squared error when the magnitude of confounding was strong. Of the methods based on the GPS, covariate adjustment using the GPS tended to result in estimates with lower variability and mean squared error when the magnitude of confounding was strong. We illustrate the application of these methods by estimating the effect of average neighborhood income on the probability of death within 1 year of hospitalization for an acute myocardial infarction. © 2018 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Accounting for spatial correlation errors in the assimilation of GRACE into hydrological models through localization

NASA Astrophysics Data System (ADS)

Khaki, M.; Schumacher, M.; Forootan, E.; Kuhn, M.; Awange, J. L.; van Dijk, A. I. J. M.

2017-10-01

Assimilation of terrestrial water storage (TWS) information from the Gravity Recovery And Climate Experiment (GRACE) satellite mission can provide significant improvements in hydrological modelling. However, the rather coarse spatial resolution of GRACE TWS and its spatially correlated errors pose considerable challenges for achieving realistic assimilation results. Consequently, successful data assimilation depends on rigorous modelling of the full error covariance matrix of the GRACE TWS estimates, as well as realistic error behavior for hydrological model simulations. In this study, we assess the application of local analysis (LA) to maximize the contribution of GRACE TWS in hydrological data assimilation. For this, we assimilate GRACE TWS into the World-Wide Water Resources Assessment system (W3RA) over the Australian continent while applying LA and accounting for existing spatial correlations using the full error covariance matrix. GRACE TWS data is applied with different spatial resolutions including 1° to 5° grids, as well as basin averages. The ensemble-based sequential filtering technique of the Square Root Analysis (SQRA) is applied to assimilate TWS data into W3RA. For each spatial scale, the performance of the data assimilation is assessed through comparison with independent in-situ ground water and soil moisture observations. Overall, the results demonstrate that LA is able to stabilize the inversion process (within the implementation of the SQRA filter) leading to less errors for all spatial scales considered with an average RMSE improvement of 54% (e.g., 52.23 mm down to 26.80 mm) for all the cases with respect to groundwater in-situ measurements. Validating the assimilated results with groundwater observations indicates that LA leads to 13% better (in terms of RMSE) assimilation results compared to the cases with Gaussian errors assumptions. This highlights the great potential of LA and the use of the full error covariance matrix of GRACE TWS estimates for improved data assimilation results.

Effects of error covariance structure on estimation of model averaging weights and predictive performance

USGS Publications Warehouse

Lu, Dan; Ye, Ming; Meyer, Philip D.; Curtis, Gary P.; Shi, Xiaoqing; Niu, Xu-Feng; Yabusaki, Steve B.

2013-01-01

When conducting model averaging for assessing groundwater conceptual model uncertainty, the averaging weights are often evaluated using model selection criteria such as AIC, AICc, BIC, and KIC (Akaike Information Criterion, Corrected Akaike Information Criterion, Bayesian Information Criterion, and Kashyap Information Criterion, respectively). However, this method often leads to an unrealistic situation in which the best model receives overwhelmingly large averaging weight (close to 100%), which cannot be justified by available data and knowledge. It was found in this study that this problem was caused by using the covariance matrix, CE, of measurement errors for estimating the negative log likelihood function common to all the model selection criteria. This problem can be resolved by using the covariance matrix, Cek, of total errors (including model errors and measurement errors) to account for the correlation between the total errors. An iterative two-stage method was developed in the context of maximum likelihood inverse modeling to iteratively infer the unknown Cek from the residuals during model calibration. The inferred Cek was then used in the evaluation of model selection criteria and model averaging weights. While this method was limited to serial data using time series techniques in this study, it can be extended to spatial data using geostatistical techniques. The method was first evaluated in a synthetic study and then applied to an experimental study, in which alternative surface complexation models were developed to simulate column experiments of uranium reactive transport. It was found that the total errors of the alternative models were temporally correlated due to the model errors. The iterative two-stage method using Cekresolved the problem that the best model receives 100% model averaging weight, and the resulting model averaging weights were supported by the calibration results and physical understanding of the alternative models. Using Cek obtained from the iterative two-stage method also improved predictive performance of the individual models and model averaging in both synthetic and experimental studies.

Random Weighting, Strong Tracking, and Unscented Kalman Filter for Soft Tissue Characterization.

PubMed

Shin, Jaehyun; Zhong, Yongmin; Oetomo, Denny; Gu, Chengfan

2018-05-21

This paper presents a new nonlinear filtering method based on the Hunt-Crossley model for online nonlinear soft tissue characterization. This method overcomes the problem of performance degradation in the unscented Kalman filter due to contact model error. It adopts the concept of Mahalanobis distance to identify contact model error, and further incorporates a scaling factor in predicted state covariance to compensate identified model error. This scaling factor is determined according to the principle of innovation orthogonality to avoid the cumbersome computation of Jacobian matrix, where the random weighting concept is adopted to improve the estimation accuracy of innovation covariance. A master-slave robotic indentation system is developed to validate the performance of the proposed method. Simulation and experimental results as well as comparison analyses demonstrate that the efficacy of the proposed method for online characterization of soft tissue parameters in the presence of contact model error.

UDU/T/ covariance factorization for Kalman filtering

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1980-01-01

There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

Application Of Multi-grid Method On China Seas' Temperature Forecast

NASA Astrophysics Data System (ADS)

Li, W.; Xie, Y.; He, Z.; Liu, K.; Han, G.; Ma, J.; Li, D.

2006-12-01

Correlation scales have been used in traditional scheme of 3-dimensional variational (3D-Var) data assimilation to estimate the background error covariance for the numerical forecast and reanalysis of atmosphere and ocean for decades. However there are still some drawbacks of this scheme. First, the correlation scales are difficult to be determined accurately. Second, the positive definition of the first-guess error covariance matrix cannot be guaranteed unless the correlation scales are sufficiently small. Xie et al. (2005) indicated that a traditional 3D-Var only corrects some certain wavelength errors and its accuracy depends on the accuracy of the first-guess covariance. And in general, short wavelength error can not be well corrected until long one is corrected and then inaccurate first-guess covariance may mistakenly take long wave error as short wave ones and result in erroneous analysis. For the purpose of quickly minimizing the errors of long and short waves successively, a new 3D-Var data assimilation scheme, called multi-grid data assimilation scheme, is proposed in this paper. By assimilating the shipboard SST and temperature profiles data into a numerical model of China Seas, we applied this scheme in two-month data assimilation and forecast experiment which ended in a favorable result. Comparing with the traditional scheme of 3D-Var, the new scheme has higher forecast accuracy and a lower forecast Root-Mean-Square (RMS) error. Furthermore, this scheme was applied to assimilate the SST of shipboard, AVHRR Pathfinder Version 5.0 SST and temperature profiles at the same time, and a ten-month forecast experiment on sea temperature of China Seas was carried out, in which a successful forecast result was obtained. Particularly, the new scheme is demonstrated a great numerical efficiency in these analyses.

Meta-STEPP: subpopulation treatment effect pattern plot for individual patient data meta-analysis.

PubMed

Wang, Xin Victoria; Cole, Bernard; Bonetti, Marco; Gelber, Richard D

2016-09-20

We have developed a method, called Meta-STEPP (subpopulation treatment effect pattern plot for meta-analysis), to explore treatment effect heterogeneity across covariate values in the meta-analysis setting for time-to-event data when the covariate of interest is continuous. Meta-STEPP forms overlapping subpopulations from individual patient data containing similar numbers of events with increasing covariate values, estimates subpopulation treatment effects using standard fixed-effects meta-analysis methodology, displays the estimated subpopulation treatment effect as a function of the covariate values, and provides a statistical test to detect possibly complex treatment-covariate interactions. Simulation studies show that this test has adequate type-I error rate recovery as well as power when reasonable window sizes are chosen. When applied to eight breast cancer trials, Meta-STEPP suggests that chemotherapy is less effective for tumors with high estrogen receptor expression compared with those with low expression. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Quantifying Carbon Flux Estimation Errors

NASA Astrophysics Data System (ADS)

Wesloh, D.

2017-12-01

Atmospheric Bayesian inversions have been used to estimate surface carbon dioxide (CO2) fluxes from global to sub-continental scales using atmospheric mixing ratio measurements. These inversions use an atmospheric transport model, coupled to a set of fluxes, in order to simulate mixing ratios that can then be compared to the observations. The comparison is then used to update the fluxes to better match the observations in a manner consistent with the uncertainties prescribed for each. However, inversion studies disagree with each other at continental scales, prompting further investigations to examine the causes of these differences. Inter-comparison studies have shown that the errors resulting from atmospheric transport inaccuracies are comparable to those from the errors in the prior fluxes. However, not as much effort has gone into studying the origins of the errors induced by errors in the transport as by errors in the prior distribution. This study uses a mesoscale transport model to evaluate the effects of representation errors in the observations and of incorrect descriptions of the transport. To obtain realizations of these errors, we performed an Observing System Simulation Experiments (OSSEs), with the transport model used for the inversion operating at two resolutions, one typical of a global inversion and the other of a mesoscale, and with various prior flux distributions to. Transport error covariances are inferred from an ensemble of perturbed mesoscale simulations while flux error covariances are computed using prescribed distributions and magnitudes. We examine how these errors can be diagnosed in the inversion process using aircraft, ground-based, and satellite observations of meteorological variables and CO2.

Modeling, simulation, and estimation of optical turbulence

NASA Astrophysics Data System (ADS)

Formwalt, Byron Paul

This dissertation documents three new contributions to simulation and modeling of optical turbulence. The first contribution is the formalization, optimization, and validation of a modeling technique called successively conditioned rendering (SCR). The SCR technique is empirically validated by comparing the statistical error of random phase screens generated with the technique. The second contribution is the derivation of the covariance delineation theorem, which provides theoretical bounds on the error associated with SCR. It is shown empirically that the theoretical bound may be used to predict relative algorithm performance. Therefore, the covariance delineation theorem is a powerful tool for optimizing SCR algorithms. For the third contribution, we introduce a new method for passively estimating optical turbulence parameters, and demonstrate the method using experimental data. The technique was demonstrated experimentally, using a 100 m horizontal path at 1.25 m above sun-heated tarmac on a clear afternoon. For this experiment, we estimated C2n ≈ 6.01 · 10-9 m-23 , l0 ≈ 17.9 mm, and L0 ≈ 15.5 m.

Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter. Pt. 2; Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics

NASA Technical Reports Server (NTRS)

Menard, Richard; Chang, Lang-Ping

1998-01-01

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

A model-data comparison of gross primary productivity: Results from the North American Carbon Program site synthesis

Treesearch

Kevin Schaefer; Christopher R. Schwalm; Chris Williams; M. Altaf Arain; Alan Barr; Jing M. Chen; Kenneth J. Davis; Dimitre Dimitrov; Timothy W. Hilton; David Y. Hollinger; Elyn Humphreys; Benjamin Poulter; Brett M. Raczka; Andrew D. Richardson; Alok Sahoo; Peter Thornton; Rodrigo Vargas; Hans Verbeeck; Ryan Anderson; Ian Baker; T. Andrew Black; Paul Bolstad; Jiquan Chen; Peter S. Curtis; Ankur R. Desai; Michael Dietze; Danilo Dragoni; Christopher Gough; Robert F. Grant; Lianhong Gu; Atul Jain; Chris Kucharik; Beverly Law; Shuguang Liu; Erandathie Lokipitiya; Hank A. Margolis; Roser Matamala; J. Harry McCaughey; Russ Monson; J. William Munger; Walter Oechel; Changhui Peng; David T. Price; Dan Ricciuto; William J. Riley; Nigel Roulet; Hanqin Tian; Christina Tonitto; Margaret Torn; Ensheng Weng; Xiaolu Zhou

2012-01-01

Accurately simulating gross primary productivity (GPP) in terrestrial ecosystem models is critical because errors in simulated GPP propagate through the model to introduce additional errors in simulated biomass and other fluxes. We evaluated simulated, daily average GPP from 26 models against estimated GPP at 39 eddy covariance flux tower sites across the United States...

Momentum Flux Determination Using the Multi-beam Poker Flat Incoherent Scatter Radar

NASA Technical Reports Server (NTRS)

Nicolls, M. J.; Fritts, D. C.; Janches, Diego; Heinselman, C. J.

2012-01-01

In this paper, we develop an estimator for the vertical flux of horizontal momentum with arbitrary beam pointing, applicable to the case of arbitrary but fixed beam pointing with systems such as the Poker Flat Incoherent Scatter Radar (PFISR). This method uses information from all available beams to resolve the variances of the wind field in addition to the vertical flux of both meridional and zonal momentum, targeted for high-frequency wave motions. The estimator utilises the full covariance of the distributed measurements, which provides a significant reduction in errors over the direct extension of previously developed techniques and allows for the calculation of an error covariance matrix of the estimated quantities. We find that for the PFISR experiment, we can construct an unbiased and robust estimator of the momentum flux if sufficient and proper beam orientations are chosen, which can in the future be optimized for the expected frequency distribution of momentum-containing scales. However, there is a potential trade-off between biases and standard errors introduced with the new approach, which must be taken into account when assessing the momentum fluxes. We apply the estimator to PFISR measurements on 23 April 2008 and 21 December 2007, from 60-85 km altitude, and show expected results as compared to mean winds and in relation to the measured vertical velocity variances.

Correcting Measurement Error in Latent Regression Covariates via the MC-SIMEX Method

ERIC Educational Resources Information Center

Rutkowski, Leslie; Zhou, Yan

2015-01-01

Given the importance of large-scale assessments to educational policy conversations, it is critical that subpopulation achievement is estimated reliably and with sufficient precision. Despite this importance, biased subpopulation estimates have been found to occur when variables in the conditioning model side of a latent regression model contain…

On the representation and estimation of spatial uncertainty. [for mobile robot

NASA Technical Reports Server (NTRS)

Smith, Randall C.; Cheeseman, Peter

1987-01-01

This paper describes a general method for estimating the nominal relationship and expected error (covariance) between coordinate frames representing the relative locations of objects. The frames may be known only indirectly through a series of spatial relationships, each with its associated error, arising from diverse causes, including positioning errors, measurement errors, or tolerances in part dimensions. This estimation method can be used to answer such questions as whether a camera attached to a robot is likely to have a particular reference object in its field of view. The calculated estimates agree well with those from an independent Monte Carlo simulation. The method makes it possible to decide in advance whether an uncertain relationship is known accurately enough for some task and, if not, how much of an improvement in locational knowledge a proposed sensor will provide. The method presented can be generalized to six degrees of freedom and provides a practical means of estimating the relationships (position and orientation) among objects, as well as estimating the uncertainty associated with the relationships.

Flexible Modeling of Survival Data with Covariates Subject to Detection Limits via Multiple Imputation.

PubMed

Bernhardt, Paul W; Wang, Huixia Judy; Zhang, Daowen

2014-01-01

Models for survival data generally assume that covariates are fully observed. However, in medical studies it is not uncommon for biomarkers to be censored at known detection limits. A computationally-efficient multiple imputation procedure for modeling survival data with covariates subject to detection limits is proposed. This procedure is developed in the context of an accelerated failure time model with a flexible seminonparametric error distribution. The consistency and asymptotic normality of the multiple imputation estimator are established and a consistent variance estimator is provided. An iterative version of the proposed multiple imputation algorithm that approximates the EM algorithm for maximum likelihood is also suggested. Simulation studies demonstrate that the proposed multiple imputation methods work well while alternative methods lead to estimates that are either biased or more variable. The proposed methods are applied to analyze the dataset from a recently-conducted GenIMS study.

The GEOS Ozone Data Assimilation System: Specification of Error Statistics

NASA Technical Reports Server (NTRS)

Stajner, Ivanka; Riishojgaard, Lars Peter; Rood, Richard B.

2000-01-01

A global three-dimensional ozone data assimilation system has been developed at the Data Assimilation Office of the NASA/Goddard Space Flight Center. The Total Ozone Mapping Spectrometer (TOMS) total ozone and the Solar Backscatter Ultraviolet (SBUV) or (SBUV/2) partial ozone profile observations are assimilated. The assimilation, into an off-line ozone transport model, is done using the global Physical-space Statistical Analysis Scheme (PSAS). This system became operational in December 1999. A detailed description of the statistical analysis scheme, and in particular, the forecast and observation error covariance models is given. A new global anisotropic horizontal forecast error correlation model accounts for a varying distribution of observations with latitude. Correlations are largest in the zonal direction in the tropics where data is sparse. Forecast error variance model is proportional to the ozone field. The forecast error covariance parameters were determined by maximum likelihood estimation. The error covariance models are validated using x squared statistics. The analyzed ozone fields in the winter 1992 are validated against independent observations from ozone sondes and HALOE. There is better than 10% agreement between mean Halogen Occultation Experiment (HALOE) and analysis fields between 70 and 0.2 hPa. The global root-mean-square (RMS) difference between TOMS observed and forecast values is less than 4%. The global RMS difference between SBUV observed and analyzed ozone between 50 and 3 hPa is less than 15%.

Adjustment of Measurements with Multiplicative Errors: Error Analysis, Estimates of the Variance of Unit Weight, and Effect on Volume Estimation from LiDAR-Type Digital Elevation Models

PubMed Central

Shi, Yun; Xu, Peiliang; Peng, Junhuan; Shi, Chuang; Liu, Jingnan

2014-01-01

Modern observation technology has verified that measurement errors can be proportional to the true values of measurements such as GPS, VLBI baselines and LiDAR. Observational models of this type are called multiplicative error models. This paper is to extend the work of Xu and Shimada published in 2000 on multiplicative error models to analytical error analysis of quantities of practical interest and estimates of the variance of unit weight. We analytically derive the variance-covariance matrices of the three least squares (LS) adjustments, the adjusted measurements and the corrections of measurements in multiplicative error models. For quality evaluation, we construct five estimators for the variance of unit weight in association of the three LS adjustment methods. Although LiDAR measurements are contaminated with multiplicative random errors, LiDAR-based digital elevation models (DEM) have been constructed as if they were of additive random errors. We will simulate a model landslide, which is assumed to be surveyed with LiDAR, and investigate the effect of LiDAR-type multiplicative error measurements on DEM construction and its effect on the estimate of landslide mass volume from the constructed DEM. PMID:24434880

The effect of covariate mean differences on the standard error and confidence interval for the comparison of treatment means.

PubMed

Liu, Xiaofeng Steven

2011-05-01

The use of covariates is commonly believed to reduce the unexplained error variance and the standard error for the comparison of treatment means, but the reduction in the standard error is neither guaranteed nor uniform over different sample sizes. The covariate mean differences between the treatment conditions can inflate the standard error of the covariate-adjusted mean difference and can actually produce a larger standard error for the adjusted mean difference than that for the unadjusted mean difference. When the covariate observations are conceived of as randomly varying from one study to another, the covariate mean differences can be related to a Hotelling's T(2) . Using this Hotelling's T(2) statistic, one can always find a minimum sample size to achieve a high probability of reducing the standard error and confidence interval width for the adjusted mean difference. ©2010 The British Psychological Society.

Statistical Analysis of Big Data on Pharmacogenomics

PubMed Central

Fan, Jianqing; Liu, Han

2013-01-01

This paper discusses statistical methods for estimating complex correlation structure from large pharmacogenomic datasets. We selectively review several prominent statistical methods for estimating large covariance matrix for understanding correlation structure, inverse covariance matrix for network modeling, large-scale simultaneous tests for selecting significantly differently expressed genes and proteins and genetic markers for complex diseases, and high dimensional variable selection for identifying important molecules for understanding molecule mechanisms in pharmacogenomics. Their applications to gene network estimation and biomarker selection are used to illustrate the methodological power. Several new challenges of Big data analysis, including complex data distribution, missing data, measurement error, spurious correlation, endogeneity, and the need for robust statistical methods, are also discussed. PMID:23602905

Complementary nonparametric analysis of covariance for logistic regression in a randomized clinical trial setting.

PubMed

Tangen, C M; Koch, G G

1999-03-01

In the randomized clinical trial setting, controlling for covariates is expected to produce variance reduction for the treatment parameter estimate and to adjust for random imbalances of covariates between the treatment groups. However, for the logistic regression model, variance reduction is not obviously obtained. This can lead to concerns about the assumptions of the logistic model. We introduce a complementary nonparametric method for covariate adjustment. It provides results that are usually compatible with expectations for analysis of covariance. The only assumptions required are based on randomization and sampling arguments. The resulting treatment parameter is a (unconditional) population average log-odds ratio that has been adjusted for random imbalance of covariates. Data from a randomized clinical trial are used to compare results from the traditional maximum likelihood logistic method with those from the nonparametric logistic method. We examine treatment parameter estimates, corresponding standard errors, and significance levels in models with and without covariate adjustment. In addition, we discuss differences between unconditional population average treatment parameters and conditional subpopulation average treatment parameters. Additional features of the nonparametric method, including stratified (multicenter) and multivariate (multivisit) analyses, are illustrated. Extensions of this methodology to the proportional odds model are also made.

Analysis of modified SMI method for adaptive array weight control

NASA Technical Reports Server (NTRS)

Dilsavor, R. L.; Moses, R. L.

1989-01-01

An adaptive array is applied to the problem of receiving a desired signal in the presence of weak interference signals which need to be suppressed. A modification, suggested by Gupta, of the sample matrix inversion (SMI) algorithm controls the array weights. In the modified SMI algorithm, interference suppression is increased by subtracting a fraction F of the noise power from the diagonal elements of the estimated covariance matrix. Given the true covariance matrix and the desired signal direction, the modified algorithm is shown to maximize a well-defined, intuitive output power ratio criterion. Expressions are derived for the expected value and variance of the array weights and output powers as a function of the fraction F and the number of snapshots used in the covariance matrix estimate. These expressions are compared with computer simulation and good agreement is found. A trade-off is found to exist between the desired level of interference suppression and the number of snapshots required in order to achieve that level with some certainty. The removal of noise eigenvectors from the covariance matrix inverse is also discussed with respect to this application. Finally, the type and severity of errors which occur in the covariance matrix estimate are characterized through simulation.

Systems Engineering Programmatic Estimation Using Technology Variance

NASA Technical Reports Server (NTRS)

Mog, Robert A.

2000-01-01

Unique and innovative system programmatic estimation is conducted using the variance of the packaged technologies. Covariance analysis is performed on the subsystems and components comprising the system of interest. Technological "return" and "variation" parameters are estimated. These parameters are combined with the model error to arrive at a measure of system development stability. The resulting estimates provide valuable information concerning the potential cost growth of the system under development.

Stochastic stability of sigma-point Unscented Predictive Filter.

PubMed

Cao, Lu; Tang, Yu; Chen, Xiaoqian; Zhao, Yong

2015-07-01

In this paper, the Unscented Predictive Filter (UPF) is derived based on unscented transformation for nonlinear estimation, which breaks the confine of conventional sigma-point filters by employing Kalman filter as subject investigated merely. In order to facilitate the new method, the algorithm flow of UPF is given firstly. Then, the theoretical analyses demonstrate that the estimate accuracy of the model error and system for the UPF is higher than that of the conventional PF. Moreover, the authors analyze the stochastic boundedness and the error behavior of Unscented Predictive Filter (UPF) for general nonlinear systems in a stochastic framework. In particular, the theoretical results present that the estimation error remains bounded and the covariance keeps stable if the system׳s initial estimation error, disturbing noise terms as well as the model error are small enough, which is the core part of the UPF theory. All of the results have been demonstrated by numerical simulations for a nonlinear example system. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Joint nonparametric correction estimator for excess relative risk regression in survival analysis with exposure measurement error

PubMed Central

Wang, Ching-Yun; Cullings, Harry; Song, Xiao; Kopecky, Kenneth J.

2017-01-01

SUMMARY Observational epidemiological studies often confront the problem of estimating exposure-disease relationships when the exposure is not measured exactly. In the paper, we investigate exposure measurement error in excess relative risk regression, which is a widely used model in radiation exposure effect research. In the study cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies a generalized version of the classical additive measurement error model, but it may or may not have repeated measurements. In addition, an instrumental variable is available for individuals in a subset of the whole cohort. We develop a nonparametric correction (NPC) estimator using data from the subcohort, and further propose a joint nonparametric correction (JNPC) estimator using all observed data to adjust for exposure measurement error. An optimal linear combination estimator of JNPC and NPC is further developed. The proposed estimators are nonparametric, which are consistent without imposing a covariate or error distribution, and are robust to heteroscedastic errors. Finite sample performance is examined via a simulation study. We apply the developed methods to data from the Radiation Effects Research Foundation, in which chromosome aberration is used to adjust for the effects of radiation dose measurement error on the estimation of radiation dose responses. PMID:29354018

Calibration of Ocean Forcing with satellite Flux Estimates (COFFEE)

NASA Astrophysics Data System (ADS)

Barron, Charlie; Jan, Dastugue; Jackie, May; Rowley, Clark; Smith, Scott; Spence, Peter; Gremes-Cordero, Silvia

2016-04-01

Predicting the evolution of ocean temperature in regional ocean models depends on estimates of surface heat fluxes and upper-ocean processes over the forecast period. Within the COFFEE project (Calibration of Ocean Forcing with satellite Flux Estimates, real-time satellite observations are used to estimate shortwave, longwave, sensible, and latent air-sea heat flux corrections to a background estimate from the prior day's regional or global model forecast. These satellite-corrected fluxes are used to prepare a corrected ocean hindcast and to estimate flux error covariances to project the heat flux corrections for a 3-5 day forecast. In this way, satellite remote sensing is applied to not only inform the initial ocean state but also to mitigate errors in surface heat flux and model representations affecting the distribution of heat in the upper ocean. While traditional assimilation of sea surface temperature (SST) observations re-centers ocean models at the start of each forecast cycle, COFFEE endeavors to appropriately partition and reduce among various surface heat flux and ocean dynamics sources. A suite of experiments in the southern California Current demonstrates a range of COFFEE capabilities, showing the impact on forecast error relative to a baseline three-dimensional variational (3DVAR) assimilation using operational global or regional atmospheric forcing. Experiment cases combine different levels of flux calibration with assimilation alternatives. The cases use the original fluxes, apply full satellite corrections during the forecast period, or extend hindcast corrections into the forecast period. Assimilation is either baseline 3DVAR or standard strong-constraint 4DVAR, with work proceeding to add a 4DVAR expanded to include a weak constraint treatment of the surface flux errors. Covariance of flux errors is estimated from the recent time series of forecast and calibrated flux terms. While the California Current examples are shown, the approach is equally applicable to other regions. These approaches within a 3DVAR application are anticipated to be useful for global and larger regional domains where a full 4DVAR methodology may be cost-prohibitive.

Developing a generalized allometric equation for aboveground biomass estimation

NASA Astrophysics Data System (ADS)

Xu, Q.; Balamuta, J. J.; Greenberg, J. A.; Li, B.; Man, A.; Xu, Z.

2015-12-01

A key potential uncertainty in estimating carbon stocks across multiple scales stems from the use of empirically calibrated allometric equations, which estimate aboveground biomass (AGB) from plant characteristics such as diameter at breast height (DBH) and/or height (H). The equations themselves contain significant and, at times, poorly characterized errors. Species-specific equations may be missing. Plant responses to their local biophysical environment may lead to spatially varying allometric relationships. The structural predictor may be difficult or impossible to measure accurately, particularly when derived from remote sensing data. All of these issues may lead to significant and spatially varying uncertainties in the estimation of AGB that are unexplored in the literature. We sought to quantify the errors in predicting AGB at the tree and plot level for vegetation plots in California. To accomplish this, we derived a generalized allometric equation (GAE) which we used to model the AGB on a full set of tree information such as DBH, H, taxonomy, and biophysical environment. The GAE was derived using published allometric equations in the GlobAllomeTree database. The equations were sparse in details about the error since authors provide the coefficient of determination (R2) and the sample size. A more realistic simulation of tree AGB should also contain the noise that was not captured by the allometric equation. We derived an empirically corrected variance estimate for the amount of noise to represent the errors in the real biomass. Also, we accounted for the hierarchical relationship between different species by treating each taxonomic level as a covariate nested within a higher taxonomic level (e.g. species < genus). This approach provides estimation under incomplete tree information (e.g. missing species) or blurred information (e.g. conjecture of species), plus the biophysical environment. The GAE allowed us to quantify contribution of each different covariate in estimating the AGB of trees. Lastly, we applied the GAE to an existing vegetation plot database - Forest Inventory and Analysis database - to derive per-tree and per-plot AGB estimations, their errors, and how much the error could be contributed to the original equations, the plant's taxonomy, and their biophysical environment.

Satellite-based Calibration of Heat Flux at the Ocean Surface

NASA Astrophysics Data System (ADS)

Barron, C. N.; Dastugue, J. M.; May, J. C.; Rowley, C. D.; Smith, S. R.; Spence, P. L.; Gremes-Cordero, S.

2016-02-01

Model forecasts of upper ocean heat content and variability on diurnal to daily scales are highly dependent on estimates of heat flux through the air-sea interface. Satellite remote sensing is applied to not only inform the initial ocean state but also to mitigate errors in surface heat flux and model representations affecting the distribution of heat in the upper ocean. Traditional assimilation of sea surface temperature (SST) observations re-centers ocean models at the start of each forecast cycle. Subsequent evolution depends on estimates of surface heat fluxes and upper-ocean processes over the forecast period. The COFFEE project (Calibration of Ocean Forcing with satellite Flux Estimates) endeavors to correct ocean forecast bias through a responsive error partition among surface heat flux and ocean dynamics sources. A suite of experiments in the southern California Current demonstrates a range of COFFEE capabilities, showing the impact on forecast error relative to a baseline three-dimensional variational (3DVAR) assimilation using Navy operational global or regional atmospheric forcing. COFFEE addresses satellite-calibration of surface fluxes to estimate surface error covariances and links these to the ocean interior. Experiment cases combine different levels of flux calibration with different assimilation alternatives. The cases may use the original fluxes, apply full satellite corrections during the forecast period, or extend hindcast corrections into the forecast period. Assimilation is either baseline 3DVAR or standard strong-constraint 4DVAR, with work proceeding to add a 4DVAR expanded to include a weak constraint treatment of the surface flux errors. Covariance of flux errors is estimated from the recent time series of forecast and calibrated flux terms. While the California Current examples are shown, the approach is equally applicable to other regions. These approaches within a 3DVAR application are anticipated to be useful for global and larger regional domains where a full 4DVAR methodology may be cost-prohibitive.

Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Markley, F. Landis; Gold, Dara

2013-01-01

We propose a Wald Sequential Probability Ratio Test for analysis of commonly available predictions associated with spacecraft conjunctions. Such predictions generally consist of a relative state and relative state error covariance at the time of closest approach, under the assumption that prediction errors are Gaussian. We show that under these circumstances, the likelihood ratio of the Wald test reduces to an especially simple form, involving the current best estimate of collision probability, and a similar estimate of collision probability that is based on prior assumptions about the likelihood of collision.

Application of Consider Covariance to the Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Lundberg, John B.

1996-01-01

The extended Kalman filter (EKF) is the basis for many applications of filtering theory to real-time problems where estimates of the state of a dynamical system are to be computed based upon some set of observations. The form of the EKF may vary somewhat from one application to another, but the fundamental principles are typically unchanged among these various applications. As is the case in many filtering applications, models of the dynamical system (differential equations describing the state variables) and models of the relationship between the observations and the state variables are created. These models typically employ a set of constants whose values are established my means of theory or experimental procedure. Since the estimates of the state are formed assuming that the models are perfect, any modeling errors will affect the accuracy of the computed estimates. Note that the modeling errors may be errors of commission (errors in terms included in the model) or omission (errors in terms excluded from the model). Consequently, it becomes imperative when evaluating the performance of real-time filters to evaluate the effect of modeling errors on the estimates of the state.

Variations of cosmic large-scale structure covariance matrices across parameter space

NASA Astrophysics Data System (ADS)

Reischke, Robert; Kiessling, Alina; Schäfer, Björn Malte

2017-03-01

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the non-linear evolution of the cosmic web. As highly non-linear clustering to date has only been described by numerical N-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work, we describe the change of the matter covariance and the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from non-linear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations, we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to ℓ ≤ 1300. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimizing interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

Quantifying the uncertainty of regional and national estimates of soil carbon stocks

NASA Astrophysics Data System (ADS)

Papritz, Andreas

2013-04-01

At regional and national scales, carbon (C) stocks are frequently estimated by means of regression models. Such statistical models link measurements of carbons stocks, recorded for a set of soil profiles or soil cores, to covariates that characterize soil formation conditions and land management. A prerequisite is that these covariates are available for any location within a region of interest G because they are used along with the fitted regression coefficients to predict the carbon stocks at the nodes of a fine-meshed grid that is laid over G. The mean C stock in G is then estimated by the arithmetic mean of the stock predictions for the grid nodes. Apart from the mean stock, the precision of the estimate is often also of interest, for example to judge whether the mean C stock has changed significantly between two inventories. The standard error of the estimated mean stock in G can be computed from the regression results as well. Two issues are thereby important: (i) How large is the area of G relative to the support of the measurements? (ii) Are the residuals of the regression model spatially auto-correlated or is the assumption of statistical independence tenable? Both issues are correctly handled if one adopts a geostatistical block kriging approach for estimating the mean C stock within a region and its standard error. In the presentation I shall summarize the main ideas of external drift block kriging. To compute the standard error of the mean stock, one has in principle to sum the elements a potentially very large covariance matrix of point prediction errors, but I shall show that the required term can be approximated very well by Monte Carlo techniques. I shall further illustrated with a few examples how the standard error of the mean stock estimate changes with the size of G and with the strenght of the auto-correlation of the regression residuals. As an application a robust variant of block kriging is used to quantify the mean carbon stock stored in the soils of Swiss forests (Nussbaum et al., 2012). Nussbaum, M., Papritz, A., Baltensweiler, A., and Walthert, L. (2012). Organic carbon stocks of swiss forest soils. Final report, Institute of Terrestrial Ecosystems, ETH Zürich and Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), pp. 51, http://e-collection.library.ethz.ch/eserv/eth:6027/eth-6027-01.pdf

BAO from Angular Clustering: Optimization and Mitigation of Theoretical Systematics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crocce, M.; et al.

We study the theoretical systematics and optimize the methodology in Baryon Acoustic Oscillations (BAO) detections using the angular correlation function with tomographic bins. We calibrate and optimize the pipeline for the Dark Energy Survey Year 1 dataset using 1800 mocks. We compare the BAO fitting results obtained with three estimators: the Maximum Likelihood Estimator (MLE), Profile Likelihood, and Markov Chain Monte Carlo. The MLE method yields the least bias in the fit results (bias/spreadmore » $$\\sim 0.02$$) and the error bar derived is the closest to the Gaussian results (1% from 68% Gaussian expectation). When there is mismatch between the template and the data either due to incorrect fiducial cosmology or photo-$z$ error, the MLE again gives the least-biased results. The BAO angular shift that is estimated based on the sound horizon and the angular diameter distance agree with the numerical fit. Various analysis choices are further tested: the number of redshift bins, cross-correlations, and angular binning. We propose two methods to correct the mock covariance when the final sample properties are slightly different from those used to create the mock. We show that the sample changes can be accommodated with the help of the Gaussian covariance matrix or more effectively using the eigenmode expansion of the mock covariance. The eigenmode expansion is significantly less susceptible to statistical fluctuations relative to the direct measurements of the covariance matrix because the number of free parameters is substantially reduced [$p$ parameters versus $p(p+1)/2$ from direct measurement].« less

Structural nested mean models for assessing time-varying effect moderation.

PubMed

Almirall, Daniel; Ten Have, Thomas; Murphy, Susan A

2010-03-01

This article considers the problem of assessing causal effect moderation in longitudinal settings in which treatment (or exposure) is time varying and so are the covariates said to moderate its effect. Intermediate causal effects that describe time-varying causal effects of treatment conditional on past covariate history are introduced and considered as part of Robins' structural nested mean model. Two estimators of the intermediate causal effects, and their standard errors, are presented and discussed: The first is a proposed two-stage regression estimator. The second is Robins' G-estimator. The results of a small simulation study that begins to shed light on the small versus large sample performance of the estimators, and on the bias-variance trade-off between the two estimators are presented. The methodology is illustrated using longitudinal data from a depression study.

An Upper Bound on High Speed Satellite Collision Probability When Only One Object has Position Uncertainty Information

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but potentially useful Pc upper bound.

Cluster mislocation in kinematic Sunyaev-Zel'dovich (kSZ) effect extraction

NASA Astrophysics Data System (ADS)

Calafut, Victoria Rose; Bean, Rachel; Yu, Byeonghee

2018-01-01

We investigate the impact of a variety of analysis assumptions that influence cluster identification and location on the kSZ pairwise momentum signal and covariance estimation. Photometric and spectroscopic galaxy tracers from SDSS, WISE, and DECaLs, spanning redshifts 0.05

A cautionary note on the use of the Analysis of Covariance (ANCOVA) in classification designs with and without within-subject factors

PubMed Central

Schneider, Bruce A.; Avivi-Reich, Meital; Mozuraitis, Mindaugas

2015-01-01

A number of statistical textbooks recommend using an analysis of covariance (ANCOVA) to control for the effects of extraneous factors that might influence the dependent measure of interest. However, it is not generally recognized that serious problems of interpretation can arise when the design contains comparisons of participants sampled from different populations (classification designs). Designs that include a comparison of younger and older adults, or a comparison of musicians and non-musicians are examples of classification designs. In such cases, estimates of differences among groups can be contaminated by differences in the covariate population means across groups. A second problem of interpretation will arise if the experimenter fails to center the covariate measures (subtracting the mean covariate score from each covariate score) whenever the design contains within-subject factors. Unless the covariate measures on the participants are centered, estimates of within-subject factors are distorted, and significant increases in Type I error rates, and/or losses in power can occur when evaluating the effects of within-subject factors. This paper: (1) alerts potential users of ANCOVA of the need to center the covariate measures when the design contains within-subject factors, and (2) indicates how they can avoid biases when one cannot assume that the expected value of the covariate measure is the same for all of the groups in a classification design. PMID:25954230

Improved Analysis of Time Series with Temporally Correlated Errors: An Algorithm that Reduces the Computation Time.

NASA Astrophysics Data System (ADS)

Langbein, J. O.

2016-12-01

Most time series of geophysical phenomena are contaminated with temporally correlated errors that limit the precision of any derived parameters. Ignoring temporal correlations will result in biased and unrealistic estimates of velocity and its error estimated from geodetic position measurements. Obtaining better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model when there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1/fn , with frequency, f. Time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. [2012] demonstrate one technique that substantially increases the efficiency of the MLE methods, but it provides only an approximate solution for power-law indices greater than 1.0. That restriction can be removed by simply forming a data-filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified and it provides robust results for a wide range of power-law indices. With the new formulation, the efficiency is typically improved by about a factor of 8 over previous MLE algorithms [Langbein, 2004]. The new algorithm can be downloaded at http://earthquake.usgs.gov/research/software/#est_noise. The main program provides a number of basic functions that can be used to model the time-dependent part of time series and a variety of models that describe the temporal covariance of the data. In addition, the program is packaged with a few companion programs and scripts that can help with data analysis and with interpretation of the noise modeling.

Testing a single regression coefficient in high dimensional linear models

PubMed Central

Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2017-01-01

In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z-test to assess the significance of each covariate. Based on the p-value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively. PMID:28663668

Testing a single regression coefficient in high dimensional linear models.

PubMed

Lan, Wei; Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2016-11-01

In linear regression models with high dimensional data, the classical z -test (or t -test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z -test to assess the significance of each covariate. Based on the p -value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively.

An improved error assessment for the GEM-T1 gravitational model

NASA Technical Reports Server (NTRS)

Lerch, F. J.; Marsh, J. G.; Klosko, S. M.; Pavlis, E. C.; Patel, G. B.; Chinn, D. S.; Wagner, C. A.

1988-01-01

Several tests were designed to determine the correct error variances for the Goddard Earth Model (GEM)-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment. These calibrations (utilizing each of the major data subsets within the solution) yield very stable calibration factors which vary by approximately 10 percent over the range of tests employed. Measurements of gravity anomalies obtained from altimetry were also used directly as observations to show that GEM-T1 is calibrated. The mathematical representation of the covariance error in the presence of unmodeled systematic error effects in the data is analyzed and an optimum weighting technique is developed for these conditions. This technique yields an internal self-calibration of the error model, a process which GEM-T1 is shown to approximate.

Inverse modeling for seawater intrusion in coastal aquifers: Insights about parameter sensitivities, variances, correlations and estimation procedures derived from the Henry problem

USGS Publications Warehouse

Sanz, E.; Voss, C.I.

2006-01-01

Inverse modeling studies employing data collected from the classic Henry seawater intrusion problem give insight into several important aspects of inverse modeling of seawater intrusion problems and effective measurement strategies for estimation of parameters for seawater intrusion. Despite the simplicity of the Henry problem, it embodies the behavior of a typical seawater intrusion situation in a single aquifer. Data collected from the numerical problem solution are employed without added noise in order to focus on the aspects of inverse modeling strategies dictated by the physics of variable-density flow and solute transport during seawater intrusion. Covariances of model parameters that can be estimated are strongly dependent on the physics. The insights gained from this type of analysis may be directly applied to field problems in the presence of data errors, using standard inverse modeling approaches to deal with uncertainty in data. Covariance analysis of the Henry problem indicates that in order to generally reduce variance of parameter estimates, the ideal places to measure pressure are as far away from the coast as possible, at any depth, and the ideal places to measure concentration are near the bottom of the aquifer between the center of the transition zone and its inland fringe. These observations are located in and near high-sensitivity regions of system parameters, which may be identified in a sensitivity analysis with respect to several parameters. However, both the form of error distribution in the observations and the observation weights impact the spatial sensitivity distributions, and different choices for error distributions or weights can result in significantly different regions of high sensitivity. Thus, in order to design effective sampling networks, the error form and weights must be carefully considered. For the Henry problem, permeability and freshwater inflow can be estimated with low estimation variance from only pressure or only concentration observations. Permeability, freshwater inflow, solute molecular diffusivity, and porosity can be estimated with roughly equivalent confidence using observations of only the logarithm of concentration. Furthermore, covariance analysis allows a logical reduction of the number of estimated parameters for ill-posed inverse seawater intrusion problems. Ill-posed problems may exhibit poor estimation convergence, have a non-unique solution, have multiple minima, or require excessive computational effort, and the condition often occurs when estimating too many or co-dependent parameters. For the Henry problem, such analysis allows selection of the two parameters that control system physics from among all possible system parameters. ?? 2005 Elsevier Ltd. All rights reserved.

Improvements in GRACE Gravity Field Determination through Stochastic Observation Modeling

NASA Astrophysics Data System (ADS)

McCullough, C.; Bettadpur, S. V.

2016-12-01

Current unconstrained Release 05 GRACE gravity field solutions from the Center for Space Research (CSR RL05) assume random observation errors following an independent multivariate Gaussian distribution. This modeling of observations, a simplifying assumption, fails to account for long period, correlated errors arising from inadequacies in the background force models. Fully modeling the errors inherent in the observation equations, through the use of a full observation covariance (modeling colored noise), enables optimal combination of GPS and inter-satellite range-rate data and obviates the need for estimating kinematic empirical parameters during the solution process. Most importantly, fully modeling the observation errors drastically improves formal error estimates of the spherical harmonic coefficients, potentially enabling improved uncertainty quantification of scientific results derived from GRACE and optimizing combinations of GRACE with independent data sets and a priori constraints.

An Upper Bound on Orbital Debris Collision Probability When Only One Object has Position Uncertainty Information

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but useful P (sub c) upper bound. There are various avenues along which an upper bound on the high speed satellite collision probability has been pursued. Typically, for the collision plane representation of the high speed collision probability problem, the predicted miss position in the collision plane is assumed fixed. Then the shape (aspect ratio of ellipse), the size (scaling of standard deviations) or the orientation (rotation of ellipse principal axes) of the combined position error ellipse is varied to obtain a maximum P (sub c). Regardless as to the exact details of the approach, previously presented methods all assume that an individual position error covariance matrix is available for each object and the two are combined into a single, relative position error covariance matrix. This combined position error covariance matrix is then modified according to the chosen scheme to arrive at a maximum P (sub c). But what if error covariance information for one of the two objects is not available? When error covariance information for one of the objects is not available the analyst has commonly defaulted to the situation in which only the relative miss position and velocity are known without any corresponding state error covariance information. The various usual methods of finding a maximum P (sub c) do no good because the analyst defaults to no knowledge of the combined, relative position error covariance matrix. It is reasonable to think, given an assumption of no covariance information, an analyst might still attempt to determine the error covariance matrix that results in an upper bound on the P (sub c). Without some guidance on limits to the shape, size and orientation of the unknown covariance matrix, the limiting case is a degenerate ellipse lying along the relative miss vector in the collision plane. Unless the miss position is exceptionally large or the at-risk object is exceptionally small, this method results in a maximum P (sub c) too large to be of practical use. For example, assuming that the miss distance is equal to the current ISS alert volume along-track (+ or -) distance of 25 kilometers and that the at-risk area has a 70 meter radius. The maximum (degenerate ellipse) P (sub c) is about 0.00136. At 40 kilometers, the maximum P (sub c) would be 0.00085 which is still almost an order of magnitude larger than the ISS maneuver threshold of 0.0001. In fact, a miss distance of almost 340 kilometers is necessary to reduce the maximum P (sub c) associated with this degenerate ellipse to the ISS maneuver threshold value. Such a result is frequently of no practical value to the analyst. Some improvement may be made with respect to this problem by realizing that while the position error covariance matrix of one of the objects (usually the debris object) may not be known the position error covariance matrix of the other object (usually the asset) is almost always available. Making use of the position error covariance information for the one object provides an improvement in finding a maximum P (sub c) which, in some cases, may offer real utility. The equations to be used are presented and their use discussed.

Estimating monthly streamflow values by cokriging

USGS Publications Warehouse

Solow, A.R.; Gorelick, S.M.

1986-01-01

Cokriging is applied to estimation of missing monthly streamflow values in three records from gaging stations in west central Virginia. Missing values are estimated from optimal consideration of the pattern of auto- and cross-correlation among standardized residual log-flow records. Investigation of the sensitivity of estimation to data configuration showed that when observations are available within two months of a missing value, estimation is improved by accounting for correlation. Concurrent and lag-one observations tend to screen the influence of other available observations. Three models of covariance structure in residual log-flow records are compared using cross-validation. Models differ in how much monthly variation they allow in covariance. Precision of estimation, reflected in mean squared error (MSE), proved to be insensitive to this choice. Cross-validation is suggested as a tool for choosing an inverse transformation when an initial nonlinear transformation is applied to flow values. ?? 1986 Plenum Publishing Corporation.

Correlation- and covariance-supported normalization method for estimating orthodontic trainer treatment for clenching activity.

PubMed

Akdenur, B; Okkesum, S; Kara, S; Günes, S

2009-11-01

In this study, electromyography signals sampled from children undergoing orthodontic treatment were used to estimate the effect of an orthodontic trainer on the anterior temporal muscle. A novel data normalization method, called the correlation- and covariance-supported normalization method (CCSNM), based on correlation and covariance between features in a data set, is proposed to provide predictive guidance to the orthodontic technique. The method was tested in two stages: first, data normalization using the CCSNM; second, prediction of normalized values of anterior temporal muscles using an artificial neural network (ANN) with a Levenberg-Marquardt learning algorithm. The data set consists of electromyography signals from right anterior temporal muscles, recorded from 20 children aged 8-13 years with class II malocclusion. The signals were recorded at the start and end of a 6-month treatment. In order to train and test the ANN, two-fold cross-validation was used. The CCSNM was compared with four normalization methods: minimum-maximum normalization, z score, decimal scaling, and line base normalization. In order to demonstrate the performance of the proposed method, prevalent performance-measuring methods, and the mean square error and mean absolute error as mathematical methods, the statistical relation factor R2 and the average deviation have been examined. The results show that the CCSNM was the best normalization method among other normalization methods for estimating the effect of the trainer.

Model dependence and its effect on ensemble projections in CMIP5

NASA Astrophysics Data System (ADS)

Abramowitz, G.; Bishop, C.

2013-12-01

Conceptually, the notion of model dependence within climate model ensembles is relatively simple - modelling groups share a literature base, parametrisations, data sets and even model code - the potential for dependence in sampling different climate futures is clear. How though can this conceptual problem inform a practical solution that demonstrably improves the ensemble mean and ensemble variance as an estimate of system uncertainty? While some research has already focused on error correlation or error covariance as a candidate to improve ensemble mean estimates, a complete definition of independence must at least implicitly subscribe to an ensemble interpretation paradigm, such as the 'truth-plus-error', 'indistinguishable', or more recently 'replicate Earth' paradigm. Using a definition of model dependence based on error covariance within the replicate Earth paradigm, this presentation will show that accounting for dependence in surface air temperature gives cooler projections in CMIP5 - by as much as 20% globally in some RCPs - although results differ significantly for each RCP, especially regionally. The fact that the change afforded by accounting for dependence across different RCPs is different is not an inconsistent result. Different numbers of submissions to each RCP by different modelling groups mean that differences in projections from different RCPs are not entirely about RCP forcing conditions - they also reflect different sampling strategies.

Q-adjusting technique applied to vertical deflections estimation in a single-axis rotation INS/GPS integrated system

NASA Astrophysics Data System (ADS)

Zhu, Jing; Wang, Xingshu; Wang, Jun; Dai, Dongkai; Xiong, Hao

2016-10-01

Former studies have proved that the attitude error in a single-axis rotation INS/GPS integrated system tracks the high frequency component of the deflections of the vertical (DOV) with a fixed delay and tracking error. This paper analyses the influence of the nominal process noise covariance matrix Q on the tracking error as well as the response delay, and proposed a Q-adjusting technique to obtain the attitude error which can track the DOV better. Simulation results show that different settings of Q lead to different response delay and tracking error; there exists optimal Q which leads to a minimum tracking error and a comparatively short response delay; for systems with different accuracy, different Q-adjusting strategy should be adopted. In this way, the DOV estimation accuracy of using the attitude error as the observation can be improved. According to the simulation results, the DOV estimation accuracy after using the Q-adjusting technique is improved by approximate 23% and 33% respectively compared to that of the Earth Model EGM2008 and the direct attitude difference method.

Double-adjustment in propensity score matching analysis: choosing a threshold for considering residual imbalance.

PubMed

Nguyen, Tri-Long; Collins, Gary S; Spence, Jessica; Daurès, Jean-Pierre; Devereaux, P J; Landais, Paul; Le Manach, Yannick

2017-04-28

Double-adjustment can be used to remove confounding if imbalance exists after propensity score (PS) matching. However, it is not always possible to include all covariates in adjustment. We aimed to find the optimal imbalance threshold for entering covariates into regression. We conducted a series of Monte Carlo simulations on virtual populations of 5,000 subjects. We performed PS 1:1 nearest-neighbor matching on each sample. We calculated standardized mean differences across groups to detect any remaining imbalance in the matched samples. We examined 25 thresholds (from 0.01 to 0.25, stepwise 0.01) for considering residual imbalance. The treatment effect was estimated using logistic regression that contained only those covariates considered to be unbalanced by these thresholds. We showed that regression adjustment could dramatically remove residual confounding bias when it included all of the covariates with a standardized difference greater than 0.10. The additional benefit was negligible when we also adjusted for covariates with less imbalance. We found that the mean squared error of the estimates was minimized under the same conditions. If covariate balance is not achieved, we recommend reiterating PS modeling until standardized differences below 0.10 are achieved on most covariates. In case of remaining imbalance, a double adjustment might be worth considering.

On-Line Identification of Simulation Examples for Forgetting Methods to Track Time Varying Parameters Using the Alternative Covariance Matrix in Matlab

NASA Astrophysics Data System (ADS)

Vachálek, Ján

2011-12-01

The paper compares the abilities of forgetting methods to track time varying parameters of two different simulated models with different types of excitation. The observed parameters in the simulations are the integral sum of the Euclidean norm, deviation of the parameter estimates from their true values and a selected band prediction error count. As supplementary information, we observe the eigenvalues of the covariance matrix. In the paper we used a modified method of Regularized Exponential Forgetting with Alternative Covariance Matrix (REFACM) along with Directional Forgetting (DF) and three standard regularized methods.

Attitude determination using vector observations: A fast optimal matrix algorithm

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1993-01-01

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function.

The Covariance Adjustment Approaches for Combining Incomparable Cox Regressions Caused by Unbalanced Covariates Adjustment: A Multivariate Meta-Analysis Study.

PubMed

Dehesh, Tania; Zare, Najaf; Ayatollahi, Seyyed Mohammad Taghi

2015-01-01

Univariate meta-analysis (UM) procedure, as a technique that provides a single overall result, has become increasingly popular. Neglecting the existence of other concomitant covariates in the models leads to loss of treatment efficiency. Our aim was proposing four new approximation approaches for the covariance matrix of the coefficients, which is not readily available for the multivariate generalized least square (MGLS) method as a multivariate meta-analysis approach. We evaluated the efficiency of four new approaches including zero correlation (ZC), common correlation (CC), estimated correlation (EC), and multivariate multilevel correlation (MMC) on the estimation bias, mean square error (MSE), and 95% probability coverage of the confidence interval (CI) in the synthesis of Cox proportional hazard models coefficients in a simulation study. Comparing the results of the simulation study on the MSE, bias, and CI of the estimated coefficients indicated that MMC approach was the most accurate procedure compared to EC, CC, and ZC procedures. The precision ranking of the four approaches according to all above settings was MMC ≥ EC ≥ CC ≥ ZC. This study highlights advantages of MGLS meta-analysis on UM approach. The results suggested the use of MMC procedure to overcome the lack of information for having a complete covariance matrix of the coefficients.

Lessons Learned from Assimilating Altimeter Data into a Coupled General Circulation Model with the GMAO Augmented Ensemble Kalman Filter

NASA Technical Reports Server (NTRS)

Keppenne, Christian; Vernieres, Guillaume; Rienecker, Michele; Jacob, Jossy; Kovach, Robin

2011-01-01

Satellite altimetry measurements have provided global, evenly distributed observations of the ocean surface since 1993. However, the difficulties introduced by the presence of model biases and the requirement that data assimilation systems extrapolate the sea surface height (SSH) information to the subsurface in order to estimate the temperature, salinity and currents make it difficult to optimally exploit these measurements. This talk investigates the potential of the altimetry data assimilation once the biases are accounted for with an ad hoc bias estimation scheme. Either steady-state or state-dependent multivariate background-error covariances from an ensemble of model integrations are used to address the problem of extrapolating the information to the sub-surface. The GMAO ocean data assimilation system applied to an ensemble of coupled model instances using the GEOS-5 AGCM coupled to MOM4 is used in the investigation. To model the background error covariances, the system relies on a hybrid ensemble approach in which a small number of dynamically evolved model trajectories is augmented on the one hand with past instances of the state vector along each trajectory and, on the other, with a steady state ensemble of error estimates from a time series of short-term model forecasts. A state-dependent adaptive error-covariance localization and inflation algorithm controls how the SSH information is extrapolated to the sub-surface. A two-step predictor corrector approach is used to assimilate future information. Independent (not-assimilated) temperature and salinity observations from Argo floats are used to validate the assimilation. A two-step projection method in which the system first calculates a SSH increment and then projects this increment vertically onto the temperature, salt and current fields is found to be most effective in reconstructing the sub-surface information. The performance of the system in reconstructing the sub-surface fields is particularly impressive for temperature, but not as satisfactory for salt.

Cluster mislocation in kinematic Sunyaev-Zel'dovich effect extraction

NASA Astrophysics Data System (ADS)

Calafut, Victoria; Bean, Rachel; Yu, Byeonghee

2017-12-01

We investigate the impact of a variety of analysis assumptions that influence cluster identification and location on the kinematic Sunyaev-Zel'dovich (kSZ) pairwise momentum signal and covariance estimation. Photometric and spectroscopic galaxy tracers from SDSS, WISE, and DECaLs, spanning redshifts 0.05

Evaluation of estimation methods and power of tests of discrete covariates in repeated time-to-event parametric models: application to Gaucher patients treated by imiglucerase.

PubMed

Vigan, Marie; Stirnemann, Jérôme; Mentré, France

2014-05-01

Analysis of repeated time-to-event data is increasingly performed in pharmacometrics using parametric frailty models. The aims of this simulation study were (1) to assess estimation performance of Stochastic Approximation Expectation Maximization (SAEM) algorithm in MONOLIX, Adaptive Gaussian Quadrature (AGQ), and Laplace algorithm in PROC NLMIXED of SAS and (2) to evaluate properties of test of a dichotomous covariate on occurrence of events. The simulation setting is inspired from an analysis of occurrence of bone events after the initiation of treatment by imiglucerase in patients with Gaucher Disease (GD). We simulated repeated events with an exponential model and various dropout rates: no, low, or high. Several values of baseline hazard model, variability, number of subject, and effect of covariate were studied. For each scenario, 100 datasets were simulated for estimation performance and 500 for test performance. We evaluated estimation performance through relative bias and relative root mean square error (RRMSE). We studied properties of Wald and likelihood ratio test (LRT). We used these methods to analyze occurrence of bone events in patients with GD after starting an enzyme replacement therapy. SAEM with three chains and AGQ algorithms provided good estimates of parameters much better than SAEM with one chain and Laplace which often provided poor estimates. Despite a small number of repeated events, SAEM with three chains and AGQ gave small biases and RRMSE. Type I errors were closed to 5%, and power varied as expected for SAEM with three chains and AGQ. Probability of having at least one event under treatment was 19.1%.

Matching on the Disease Risk Score in Comparative Effectiveness Research of New Treatments

PubMed Central

Wyss, Richard; Ellis, Alan R.; Brookhart, M. Alan; Funk, Michele Jonsson; Girman, Cynthia J.; Simpson, Ross J.; Stürmer, Til

2016-01-01

Purpose We use simulations and an empirical example to evaluate the performance of disease risk score (DRS) matching compared with propensity score (PS) matching when controlling large numbers of covariates in settings involving newly introduced treatments. Methods We simulated a dichotomous treatment, a dichotomous outcome, and 100 baseline covariates that included both continuous and dichotomous random variables. For the empirical example, we evaluated the comparative effectiveness of dabigatran versus warfarin in preventing combined ischemic stroke and all-cause mortality. We matched treatment groups on a historically estimated DRS and again on the PS. We controlled for a high-dimensional set of covariates using 20% and 1% samples of Medicare claims data from October 2010 through December 2012. Results In simulations, matching on the DRS versus the PS generally yielded matches for more treated individuals and improved precision of the effect estimate. For the empirical example, PS and DRS matching in the 20% sample resulted in similar hazard ratios (0.88 and 0.87) and standard errors (0.04 for both methods). In the 1% sample, PS matching resulted in matches for only 92.0% of the treated population and a hazard ratio and standard error of 0.89 and 0.19, respectively, while DRS matching resulted in matches for 98.5% and a hazard ratio and standard error of 0.85 and 0.16, respectively. Conclusions When PS distributions are separated, DRS matching can improve the precision of effect estimates and allow researchers to evaluate the treatment effect in a larger proportion of the treated population. However, accurately modeling the DRS can be challenging compared with the PS. PMID:26112690

Matching on the disease risk score in comparative effectiveness research of new treatments.

PubMed

Wyss, Richard; Ellis, Alan R; Brookhart, M Alan; Jonsson Funk, Michele; Girman, Cynthia J; Simpson, Ross J; Stürmer, Til

2015-09-01

We use simulations and an empirical example to evaluate the performance of disease risk score (DRS) matching compared with propensity score (PS) matching when controlling large numbers of covariates in settings involving newly introduced treatments. We simulated a dichotomous treatment, a dichotomous outcome, and 100 baseline covariates that included both continuous and dichotomous random variables. For the empirical example, we evaluated the comparative effectiveness of dabigatran versus warfarin in preventing combined ischemic stroke and all-cause mortality. We matched treatment groups on a historically estimated DRS and again on the PS. We controlled for a high-dimensional set of covariates using 20% and 1% samples of Medicare claims data from October 2010 through December 2012. In simulations, matching on the DRS versus the PS generally yielded matches for more treated individuals and improved precision of the effect estimate. For the empirical example, PS and DRS matching in the 20% sample resulted in similar hazard ratios (0.88 and 0.87) and standard errors (0.04 for both methods). In the 1% sample, PS matching resulted in matches for only 92.0% of the treated population and a hazard ratio and standard error of 0.89 and 0.19, respectively, while DRS matching resulted in matches for 98.5% and a hazard ratio and standard error of 0.85 and 0.16, respectively. When PS distributions are separated, DRS matching can improve the precision of effect estimates and allow researchers to evaluate the treatment effect in a larger proportion of the treated population. However, accurately modeling the DRS can be challenging compared with the PS. Copyright © 2015 John Wiley & Sons, Ltd.

Functional interaction-based nonlinear models with application to multiplatform genomics data.

PubMed

Davenport, Clemontina A; Maity, Arnab; Baladandayuthapani, Veerabhadran

2018-05-07

Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when a scalar exposure that interacts with the functional covariate is introduced. In this paper, we present 2 functional regression models that account for this interaction and propose 2 novel estimation procedures for the parameters in these models. These estimation methods allow for a noisy and/or sparsely observed functional covariate and are easily extended to generalized exponential family responses. We compute standard errors of our estimators, which allows for further statistical inference and hypothesis testing. We compare the performance of the proposed estimators to each other and to one found in the literature via simulation and demonstrate our methods using a real data example. Copyright © 2018 John Wiley & Sons, Ltd.

The epoch state navigation filter. [for maximum likelihood estimates of position and velocity vectors

NASA Technical Reports Server (NTRS)

Battin, R. H.; Croopnick, S. R.; Edwards, J. A.

1977-01-01

The formulation of a recursive maximum likelihood navigation system employing reference position and velocity vectors as state variables is presented. Convenient forms of the required variational equations of motion are developed together with an explicit form of the associated state transition matrix needed to refer measurement data from the measurement time to the epoch time. Computational advantages accrue from this design in that the usual forward extrapolation of the covariance matrix of estimation errors can be avoided without incurring unacceptable system errors. Simulation data for earth orbiting satellites are provided to substantiate this assertion.

Dynamic State Estimation of Power Systems With Quantization Effects: A Recursive Filter Approach.

PubMed

Hu, Liang; Wang, Zidong; Liu, Xiaohui

2016-08-01

In this paper, a recursive filter algorithm is developed to deal with the state estimation problem for power systems with quantized nonlinear measurements. The measurements from both the remote terminal units and the phasor measurement unit are subject to quantizations described by a logarithmic quantizer. Attention is focused on the design of a recursive filter such that, in the simultaneous presence of nonlinear measurements and quantization effects, an upper bound for the estimation error covariance is guaranteed and subsequently minimized. Instead of using the traditional approximation methods in nonlinear estimation that simply ignore the linearization errors, we treat both the linearization and quantization errors as norm-bounded uncertainties in the algorithm development so as to improve the performance of the estimator. For the power system with such kind of introduced uncertainties, a filter is designed in the framework of robust recursive estimation, and the developed filter algorithm is tested on the IEEE benchmark power system to demonstrate its effectiveness.

A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

NASA Technical Reports Server (NTRS)

Womble, M. E.; Potter, J. E.

1975-01-01

A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

[Theory, method and application of method R on estimation of (co)variance components].

PubMed

Liu, Wen-Zhong

2004-07-01

Theory, method and application of Method R on estimation of (co)variance components were reviewed in order to make the method be reasonably used. Estimation requires R values,which are regressions of predicted random effects that are calculated using complete dataset on predicted random effects that are calculated using random subsets of the same data. By using multivariate iteration algorithm based on a transformation matrix,and combining with the preconditioned conjugate gradient to solve the mixed model equations, the computation efficiency of Method R is much improved. Method R is computationally inexpensive,and the sampling errors and approximate credible intervals of estimates can be obtained. Disadvantages of Method R include a larger sampling variance than other methods for the same data,and biased estimates in small datasets. As an alternative method, Method R can be used in larger datasets. It is necessary to study its theoretical properties and broaden its application range further.

An Adaptive Low-Cost INS/GNSS Tightly-Coupled Integration Architecture Based on Redundant Measurement Noise Covariance Estimation.

PubMed

Li, Zheng; Zhang, Hai; Zhou, Qifan; Che, Huan

2017-09-05

The main objective of the introduced study is to design an adaptive Inertial Navigation System/Global Navigation Satellite System (INS/GNSS) tightly-coupled integration system that can provide more reliable navigation solutions by making full use of an adaptive Kalman filter (AKF) and satellite selection algorithm. To achieve this goal, we develop a novel redundant measurement noise covariance estimation (RMNCE) theorem, which adaptively estimates measurement noise properties by analyzing the difference sequences of system measurements. The proposed RMNCE approach is then applied to design both a modified weighted satellite selection algorithm and a type of adaptive unscented Kalman filter (UKF) to improve the performance of the tightly-coupled integration system. In addition, an adaptive measurement noise covariance expanding algorithm is developed to mitigate outliers when facing heavy multipath and other harsh situations. Both semi-physical simulation and field experiments were conducted to evaluate the performance of the proposed architecture and were compared with state-of-the-art algorithms. The results validate that the RMNCE provides a significant improvement in the measurement noise covariance estimation and the proposed architecture can improve the accuracy and reliability of the INS/GNSS tightly-coupled systems. The proposed architecture can effectively limit positioning errors under conditions of poor GNSS measurement quality and outperforms all the compared schemes.

An Adaptive Low-Cost INS/GNSS Tightly-Coupled Integration Architecture Based on Redundant Measurement Noise Covariance Estimation

PubMed Central

Li, Zheng; Zhang, Hai; Zhou, Qifan; Che, Huan

2017-01-01

The main objective of the introduced study is to design an adaptive Inertial Navigation System/Global Navigation Satellite System (INS/GNSS) tightly-coupled integration system that can provide more reliable navigation solutions by making full use of an adaptive Kalman filter (AKF) and satellite selection algorithm. To achieve this goal, we develop a novel redundant measurement noise covariance estimation (RMNCE) theorem, which adaptively estimates measurement noise properties by analyzing the difference sequences of system measurements. The proposed RMNCE approach is then applied to design both a modified weighted satellite selection algorithm and a type of adaptive unscented Kalman filter (UKF) to improve the performance of the tightly-coupled integration system. In addition, an adaptive measurement noise covariance expanding algorithm is developed to mitigate outliers when facing heavy multipath and other harsh situations. Both semi-physical simulation and field experiments were conducted to evaluate the performance of the proposed architecture and were compared with state-of-the-art algorithms. The results validate that the RMNCE provides a significant improvement in the measurement noise covariance estimation and the proposed architecture can improve the accuracy and reliability of the INS/GNSS tightly-coupled systems. The proposed architecture can effectively limit positioning errors under conditions of poor GNSS measurement quality and outperforms all the compared schemes. PMID:28872629

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

PubMed Central

Silva, Felipe O.; Hemerly, Elder M.; Leite Filho, Waldemar C.

2017-01-01

This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions. PMID:28241494

Weighted Optimization-Based Distributed Kalman Filter for Nonlinear Target Tracking in Collaborative Sensor Networks.

PubMed

Chen, Jie; Li, Jiahong; Yang, Shuanghua; Deng, Fang

2017-11-01

The identification of the nonlinearity and coupling is crucial in nonlinear target tracking problem in collaborative sensor networks. According to the adaptive Kalman filtering (KF) method, the nonlinearity and coupling can be regarded as the model noise covariance, and estimated by minimizing the innovation or residual errors of the states. However, the method requires large time window of data to achieve reliable covariance measurement, making it impractical for nonlinear systems which are rapidly changing. To deal with the problem, a weighted optimization-based distributed KF algorithm (WODKF) is proposed in this paper. The algorithm enlarges the data size of each sensor by the received measurements and state estimates from its connected sensors instead of the time window. A new cost function is set as the weighted sum of the bias and oscillation of the state to estimate the "best" estimate of the model noise covariance. The bias and oscillation of the state of each sensor are estimated by polynomial fitting a time window of state estimates and measurements of the sensor and its neighbors weighted by the measurement noise covariance. The best estimate of the model noise covariance is computed by minimizing the weighted cost function using the exhaustive method. The sensor selection method is in addition to the algorithm to decrease the computation load of the filter and increase the scalability of the sensor network. The existence, suboptimality and stability analysis of the algorithm are given. The local probability data association method is used in the proposed algorithm for the multitarget tracking case. The algorithm is demonstrated in simulations on tracking examples for a random signal, one nonlinear target, and four nonlinear targets. Results show the feasibility and superiority of WODKF against other filtering algorithms for a large class of systems.

A water-vapor radiometer error model. [for ionosphere in geodetic microwave techniques

NASA Technical Reports Server (NTRS)

Beckman, B.

1985-01-01

The water-vapor radiometer (WVR) is used to calibrate unpredictable delays in the wet component of the troposphere in geodetic microwave techniques such as very-long-baseline interferometry (VLBI) and Global Positioning System (GPS) tracking. Based on experience with Jet Propulsion Laboratory (JPL) instruments, the current level of accuracy in wet-troposphere calibration limits the accuracy of local vertical measurements to 5-10 cm. The goal for the near future is 1-3 cm. Although the WVR is currently the best calibration method, many instruments are prone to systematic error. In this paper, a treatment of WVR data is proposed and evaluated. This treatment reduces the effect of WVR systematic errors by estimating parameters that specify an assumed functional form for the error. The assumed form of the treatment is evaluated by comparing the results of two similar WVR's operating near each other. Finally, the observability of the error parameters is estimated by covariance analysis.

Bias Reduction and Filter Convergence for Long Range Stereo

NASA Technical Reports Server (NTRS)

Sibley, Gabe; Matthies, Larry; Sukhatme, Gaurav

2005-01-01

We are concerned here with improving long range stereo by filtering image sequences. Traditionally, measurement errors from stereo camera systems have been approximated as 3-D Gaussians, where the mean is derived by triangulation and the covariance by linearized error propagation. However, there are two problems that arise when filtering such 3-D measurements. First, stereo triangulation suffers from a range dependent statistical bias; when filtering this leads to over-estimating the true range. Second, filtering 3-D measurements derived via linearized error propagation leads to apparent filter divergence; the estimator is biased to under-estimate range. To address the first issue, we examine the statistical behavior of stereo triangulation and show how to remove the bias by series expansion. The solution to the second problem is to filter with image coordinates as measurements instead of triangulated 3-D coordinates.

A simulation for gravity fine structure recovery from low-low GRAVSAT SST data

NASA Technical Reports Server (NTRS)

Estes, R. H.; Lancaster, E. R.

1976-01-01

Covariance error analysis techniques were applied to investigate estimation strategies for the low-low SST mission for accurate local recovery of gravitational fine structure, considering the aliasing effects of unsolved for parameters. A 5 degree by 5 degree surface density block representation of the high order geopotential was utilized with the drag-free low-low GRAVSAT configuration in a circular polar orbit at 250 km altitude. Recovery of local sets of density blocks from long data arcs was found not to be feasible due to strong aliasing effects. The error analysis for the recovery of local sets of density blocks using independent short data arcs demonstrated that the estimation strategy of simultaneously estimating a local set of blocks covered by data and two "buffer layers" of blocks not covered by data greatly reduced aliasing errors.

Vast Portfolio Selection with Gross-exposure Constraints*

PubMed Central

Fan, Jianqing; Zhang, Jingjin; Yu, Ke

2012-01-01

We introduce the large portfolio selection using gross-exposure constraints. We show that with gross-exposure constraint the empirically selected optimal portfolios based on estimated covariance matrices have similar performance to the theoretical optimal ones and there is no error accumulation effect from estimation of vast covariance matrices. This gives theoretical justification to the empirical results in Jagannathan and Ma (2003). We also show that the no-short-sale portfolio can be improved by allowing some short positions. The applications to portfolio selection, tracking, and improvements are also addressed. The utility of our new approach is illustrated by simulation and empirical studies on the 100 Fama-French industrial portfolios and the 600 stocks randomly selected from Russell 3000. PMID:23293404

Accounting for independent nondifferential misclassification does not increase certainty that an observed association is in the correct direction.

PubMed

Greenland, Sander; Gustafson, Paul

2006-07-01

Researchers sometimes argue that their exposure-measurement errors are independent of other errors and are nondifferential with respect to disease, resulting in estimation bias toward the null. Among well-known problems with such arguments are that independence and nondifferentiality are harder to satisfy than ordinarily appreciated (e.g., because of correlation of errors in questionnaire items, and because of uncontrolled covariate effects on error rates); small violations of independence or nondifferentiality may lead to bias away from the null; and, if exposure is polytomous, the bias produced by independent nondifferential error is not always toward the null. The authors add to this list by showing that, in a 2 x 2 table (for which independent nondifferential error produces bias toward the null), accounting for independent nondifferential error does not reduce the p value even though it increases the point estimate. Thus, such accounting should not increase certainty that an association is present.

On using smoothing spline and residual correction to fuse rain gauge observations and remote sensing data

NASA Astrophysics Data System (ADS)

Huang, Chengcheng; Zheng, Xiaogu; Tait, Andrew; Dai, Yongjiu; Yang, Chi; Chen, Zhuoqi; Li, Tao; Wang, Zhonglei

2014-01-01

Partial thin-plate smoothing spline model is used to construct the trend surface.Correction of the spline estimated trend surface is often necessary in practice.Cressman weight is modified and applied in residual correction.The modified Cressman weight performs better than Cressman weight.A method for estimating the error covariance matrix of gridded field is provided.

Multi-subject hierarchical inverse covariance modelling improves estimation of functional brain networks.

PubMed

Colclough, Giles L; Woolrich, Mark W; Harrison, Samuel J; Rojas López, Pedro A; Valdes-Sosa, Pedro A; Smith, Stephen M

2018-05-07

A Bayesian model for sparse, hierarchical, inver-covariance estimation is presented, and applied to multi-subject functional connectivity estimation in the human brain. It enables simultaneous inference of the strength of connectivity between brain regions at both subject and population level, and is applicable to fMRI, MEG and EEG data. Two versions of the model can encourage sparse connectivity, either using continuous priors to suppress irrelevant connections, or using an explicit description of the network structure to estimate the connection probability between each pair of regions. A large evaluation of this model, and thirteen methods that represent the state of the art of inverse covariance modelling, is conducted using both simulated and resting-state functional imaging datasets. Our novel Bayesian approach has similar performance to the best extant alternative, Ng et al.'s Sparse Group Gaussian Graphical Model algorithm, which also is based on a hierarchical structure. Using data from the Human Connectome Project, we show that these hierarchical models are able to reduce the measurement error in MEG beta-band functional networks by 10%, producing concomitant increases in estimates of the genetic influence on functional connectivity. Copyright © 2018. Published by Elsevier Inc.

A Wavelet based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

NASA Technical Reports Server (NTRS)

Tangborn, Andrew; Auger, Ludovic

2003-01-01

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. This scheme projects the discretized covariance propagation equations and covariance matrix onto an orthogonal set of compactly supported wavelets. Wavelet representation is localized in both location and scale, which allows for efficient representation of the inherently anisotropic structure of the error covariances. The truncation is carried out in such a way that the resolution of the error covariance is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance size by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the constituent field. This results indicate that propagation of error covariances for a global two-dimensional data assimilation system are currently feasible. Recommendations for further reduction in computational cost are made with the goal of extending this technique to three-dimensional global assimilation systems.

EvolQG - An R package for evolutionary quantitative genetics

PubMed Central

Melo, Diogo; Garcia, Guilherme; Hubbe, Alex; Assis, Ana Paula; Marroig, Gabriel

2016-01-01

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \\textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification. PMID:27785352

Analysis of Modified SMI Method for Adaptive Array Weight Control. M.S. Thesis

NASA Technical Reports Server (NTRS)

Dilsavor, Ronald Louis

1989-01-01

An adaptive array is used to receive a desired signal in the presence of weak interference signals which need to be suppressed. A modified sample matrix inversion (SMI) algorithm controls the array weights. The modification leads to increased interference suppression by subtracting a fraction of the noise power from the diagonal elements of the covariance matrix. The modified algorithm maximizes an intuitive power ratio criterion. The expected values and variances of the array weights, output powers, and power ratios as functions of the fraction and the number of snapshots are found and compared to computer simulation and real experimental array performance. Reduced-rank covariance approximations and errors in the estimated covariance are also described.

Assessing the Impact of Pre-gpm Microwave Precipitation Observations in the Goddard WRF Ensemble Data Assimilation System

NASA Technical Reports Server (NTRS)

Chambon, Philippe; Zhang, Sara Q.; Hou, Arthur Y.; Zupanski, Milija; Cheung, Samson

2013-01-01

The forthcoming Global Precipitation Measurement (GPM) Mission will provide next generation precipitation observations from a constellation of satellites. Since precipitation by nature has large variability and low predictability at cloud-resolving scales, the impact of precipitation data on the skills of mesoscale numerical weather prediction (NWP) is largely affected by the characterization of background and observation errors and the representation of nonlinear cloud/precipitation physics in an NWP data assimilation system. We present a data impact study on the assimilation of precipitation-affected microwave (MW) radiances from a pre-GPM satellite constellation using the Goddard WRF Ensemble Data Assimilation System (Goddard WRF-EDAS). A series of assimilation experiments are carried out in a Weather Research Forecast (WRF) model domain of 9 km resolution in western Europe. Sensitivities to observation error specifications, background error covariance estimated from ensemble forecasts with different ensemble sizes, and MW channel selections are examined through single-observation assimilation experiments. An empirical bias correction for precipitation-affected MW radiances is developed based on the statistics of radiance innovations in rainy areas. The data impact is assessed by full data assimilation cycling experiments for a storm event that occurred in France in September 2010. Results show that the assimilation of MW precipitation observations from a satellite constellation mimicking GPM has a positive impact on the accumulated rain forecasts verified with surface radar rain estimates. The case-study on a convective storm also reveals that the accuracy of ensemble-based background error covariance is limited by sampling errors and model errors such as precipitation displacement and unresolved convective scale instability.

An alternative covariance estimator to investigate genetic heterogeneity in populations.

PubMed

Heslot, Nicolas; Jannink, Jean-Luc

2015-11-26

For genomic prediction and genome-wide association studies (GWAS) using mixed models, covariance between individuals is estimated using molecular markers. Based on the properties of mixed models, using available molecular data for prediction is optimal if this covariance is known. Under this assumption, adding individuals to the analysis should never be detrimental. However, some empirical studies showed that increasing training population size decreased prediction accuracy. Recently, results from theoretical models indicated that even if marker density is high and the genetic architecture of traits is controlled by many loci with small additive effects, the covariance between individuals, which depends on relationships at causal loci, is not always well estimated by the whole-genome kinship. We propose an alternative covariance estimator named K-kernel, to account for potential genetic heterogeneity between populations that is characterized by a lack of genetic correlation, and to limit the information flow between a priori unknown populations in a trait-specific manner. This is similar to a multi-trait model and parameters are estimated by REML and, in extreme cases, it can allow for an independent genetic architecture between populations. As such, K-kernel is useful to study the problem of the design of training populations. K-kernel was compared to other covariance estimators or kernels to examine its fit to the data, cross-validated accuracy and suitability for GWAS on several datasets. It provides a significantly better fit to the data than the genomic best linear unbiased prediction model and, in some cases it performs better than other kernels such as the Gaussian kernel, as shown by an empirical null distribution. In GWAS simulations, alternative kernels control type I errors as well as or better than the classical whole-genome kinship and increase statistical power. No or small gains were observed in cross-validated prediction accuracy. This alternative covariance estimator can be used to gain insight into trait-specific genetic heterogeneity by identifying relevant sub-populations that lack genetic correlation between them. Genetic correlation can be 0 between identified sub-populations by performing automatic selection of relevant sets of individuals to be included in the training population. It may also increase statistical power in GWAS.

M-estimator for the 3D symmetric Helmert coordinate transformation

NASA Astrophysics Data System (ADS)

Chang, Guobin; Xu, Tianhe; Wang, Qianxin

2018-01-01

The M-estimator for the 3D symmetric Helmert coordinate transformation problem is developed. Small-angle rotation assumption is abandoned. The direction cosine matrix or the quaternion is used to represent the rotation. The 3 × 1 multiplicative error vector is defined to represent the rotation estimation error. An analytical solution can be employed to provide the initial approximate for iteration, if the outliers are not large. The iteration is carried out using the iterative reweighted least-squares scheme. In each iteration after the first one, the measurement equation is linearized using the available parameter estimates, the reweighting matrix is constructed using the residuals obtained in the previous iteration, and then the parameter estimates with their variance-covariance matrix are calculated. The influence functions of a single pseudo-measurement on the least-squares estimator and on the M-estimator are derived to theoretically show the robustness. In the solution process, the parameter is rescaled in order to improve the numerical stability. Monte Carlo experiments are conducted to check the developed method. Different cases to investigate whether the assumed stochastic model is correct are considered. The results with the simulated data slightly deviating from the true model are used to show the developed method's statistical efficacy at the assumed stochastic model, its robustness against the deviations from the assumed stochastic model, and the validity of the estimated variance-covariance matrix no matter whether the assumed stochastic model is correct or not.

Investigating the role of background and observation error correlations in improving a model forecast of forest carbon balance using four dimensional variational data assimilation.

NASA Astrophysics Data System (ADS)

Pinnington, Ewan; Casella, Eric; Dance, Sarah; Lawless, Amos; Morison, James; Nichols, Nancy; Wilkinson, Matthew; Quaife, Tristan

2016-04-01

Forest ecosystems play an important role in sequestering human emitted carbon-dioxide from the atmosphere and therefore greatly reduce the effect of anthropogenic induced climate change. For that reason understanding their response to climate change is of great importance. Efforts to implement variational data assimilation routines with functional ecology models and land surface models have been limited, with sequential and Markov chain Monte Carlo data assimilation methods being prevalent. When data assimilation has been used with models of carbon balance, background "prior" errors and observation errors have largely been treated as independent and uncorrelated. Correlations between background errors have long been known to be a key aspect of data assimilation in numerical weather prediction. More recently, it has been shown that accounting for correlated observation errors in the assimilation algorithm can considerably improve data assimilation results and forecasts. In this paper we implement a 4D-Var scheme with a simple model of forest carbon balance, for joint parameter and state estimation and assimilate daily observations of Net Ecosystem CO2 Exchange (NEE) taken at the Alice Holt forest CO2 flux site in Hampshire, UK. We then investigate the effect of specifying correlations between parameter and state variables in background error statistics and the effect of specifying correlations in time between observation error statistics. The idea of including these correlations in time is new and has not been previously explored in carbon balance model data assimilation. In data assimilation, background and observation error statistics are often described by the background error covariance matrix and the observation error covariance matrix. We outline novel methods for creating correlated versions of these matrices, using a set of previously postulated dynamical constraints to include correlations in the background error statistics and a Gaussian correlation function to include time correlations in the observation error statistics. The methods used in this paper will allow the inclusion of time correlations between many different observation types in the assimilation algorithm, meaning that previously neglected information can be accounted for. In our experiments we compared the results using our new correlated background and observation error covariance matrices and those using diagonal covariance matrices. We found that using the new correlated matrices reduced the root mean square error in the 14 year forecast of daily NEE by 44 % decreasing from 4.22 g C m-2 day-1 to 2.38 g C m-2 day-1.

Goodness-Of-Fit Test for Nonparametric Regression Models: Smoothing Spline ANOVA Models as Example.

PubMed

Teran Hidalgo, Sebastian J; Wu, Michael C; Engel, Stephanie M; Kosorok, Michael R

2018-06-01

Nonparametric regression models do not require the specification of the functional form between the outcome and the covariates. Despite their popularity, the amount of diagnostic statistics, in comparison to their parametric counter-parts, is small. We propose a goodness-of-fit test for nonparametric regression models with linear smoother form. In particular, we apply this testing framework to smoothing spline ANOVA models. The test can consider two sources of lack-of-fit: whether covariates that are not currently in the model need to be included, and whether the current model fits the data well. The proposed method derives estimated residuals from the model. Then, statistical dependence is assessed between the estimated residuals and the covariates using the HSIC. If dependence exists, the model does not capture all the variability in the outcome associated with the covariates, otherwise the model fits the data well. The bootstrap is used to obtain p-values. Application of the method is demonstrated with a neonatal mental development data analysis. We demonstrate correct type I error as well as power performance through simulations.

Statistics of the epoch of reionization 21-cm signal - I. Power spectrum error-covariance

NASA Astrophysics Data System (ADS)

Mondal, Rajesh; Bharadwaj, Somnath; Majumdar, Suman

2016-02-01

The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a significant impact on the error variance of its power spectrum P(k). We have used a large ensemble of seminumerical simulations and an analytical model to estimate the effect of this non-Gaussianity on the entire error-covariance matrix {C}ij. Our analytical model shows that {C}ij has contributions from two sources. One is the usual variance for a Gaussian random field which scales inversely of the number of modes that goes into the estimation of P(k). The other is the trispectrum of the signal. Using the simulated 21-cm Signal Ensemble, an ensemble of the Randomized Signal and Ensembles of Gaussian Random Ensembles we have quantified the effect of the trispectrum on the error variance {C}II. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the k range 0.3 ≤ k ≤ 1.0 Mpc-1, and can be even ˜200 times larger at k ˜ 5 Mpc-1. We also establish that the off-diagonal terms of {C}ij have statistically significant non-zero values which arise purely from the trispectrum. This further signifies that the error in different k modes are not independent. We find a strong correlation between the errors at large k values (≥0.5 Mpc-1), and a weak correlation between the smallest and largest k values. There is also a small anticorrelation between the errors in the smallest and intermediate k values. These results are relevant for the k range that will be probed by the current and upcoming EoR 21-cm experiments.

Application of a single-objective, hybrid genetic algorithm approach to pharmacokinetic model building.

PubMed

Sherer, Eric A; Sale, Mark E; Pollock, Bruce G; Belani, Chandra P; Egorin, Merrill J; Ivy, Percy S; Lieberman, Jeffrey A; Manuck, Stephen B; Marder, Stephen R; Muldoon, Matthew F; Scher, Howard I; Solit, David B; Bies, Robert R

2012-08-01

A limitation in traditional stepwise population pharmacokinetic model building is the difficulty in handling interactions between model components. To address this issue, a method was previously introduced which couples NONMEM parameter estimation and model fitness evaluation to a single-objective, hybrid genetic algorithm for global optimization of the model structure. In this study, the generalizability of this approach for pharmacokinetic model building is evaluated by comparing (1) correct and spurious covariate relationships in a simulated dataset resulting from automated stepwise covariate modeling, Lasso methods, and single-objective hybrid genetic algorithm approaches to covariate identification and (2) information criteria values, model structures, convergence, and model parameter values resulting from manual stepwise versus single-objective, hybrid genetic algorithm approaches to model building for seven compounds. Both manual stepwise and single-objective, hybrid genetic algorithm approaches to model building were applied, blinded to the results of the other approach, for selection of the compartment structure as well as inclusion and model form of inter-individual and inter-occasion variability, residual error, and covariates from a common set of model options. For the simulated dataset, stepwise covariate modeling identified three of four true covariates and two spurious covariates; Lasso identified two of four true and 0 spurious covariates; and the single-objective, hybrid genetic algorithm identified three of four true covariates and one spurious covariate. For the clinical datasets, the Akaike information criterion was a median of 22.3 points lower (range of 470.5 point decrease to 0.1 point decrease) for the best single-objective hybrid genetic-algorithm candidate model versus the final manual stepwise model: the Akaike information criterion was lower by greater than 10 points for four compounds and differed by less than 10 points for three compounds. The root mean squared error and absolute mean prediction error of the best single-objective hybrid genetic algorithm candidates were a median of 0.2 points higher (range of 38.9 point decrease to 27.3 point increase) and 0.02 points lower (range of 0.98 point decrease to 0.74 point increase), respectively, than that of the final stepwise models. In addition, the best single-objective, hybrid genetic algorithm candidate models had successful convergence and covariance steps for each compound, used the same compartment structure as the manual stepwise approach for 6 of 7 (86 %) compounds, and identified 54 % (7 of 13) of covariates included by the manual stepwise approach and 16 covariate relationships not included by manual stepwise models. The model parameter values between the final manual stepwise and best single-objective, hybrid genetic algorithm models differed by a median of 26.7 % (q₁ = 4.9 % and q₃ = 57.1 %). Finally, the single-objective, hybrid genetic algorithm approach was able to identify models capable of estimating absorption rate parameters for four compounds that the manual stepwise approach did not identify. The single-objective, hybrid genetic algorithm represents a general pharmacokinetic model building methodology whose ability to rapidly search the feasible solution space leads to nearly equivalent or superior model fits to pharmacokinetic data.

Submillimeter, millimeter, and microwave spectral line catalogue

NASA Technical Reports Server (NTRS)

Poynter, R. L.; Pickett, H. M.

1980-01-01

A computer accessible catalogue of submillimeter, millimeter, and microwave spectral lines in the frequency range between O and 3000 GHz (such as; wavelengths longer than 100 m) is discussed. The catalogue was used as a planning guide and as an aid in the identification and analysis of observed spectral lines. The information listed for each spectral line includes the frequency and its estimated error, the intensity, lower state energy, and quantum number assignment. The catalogue was constructed by using theoretical least squares fits of published spectral lines to accepted molecular models. The associated predictions and their estimated errors are based upon the resultant fitted parameters and their covariances.

Comparing nocturnal eddy covariance measurements to estimates of ecosystem respiration made by scaling chamber measurements at six coniferous boreal sites

USGS Publications Warehouse

Lavigne, M.B.; Ryan, M.G.; Anderson, D.E.; Baldocchi, D.D.; Crill, P.M.; Fitzjarrald, D.R.; Goulden, M.L.; Gower, S.T.; Massheder, J.M.; McCaughey, J.H.; Rayment, M.; Striegl, Robert G.

1997-01-01

During the growing season, nighttime ecosystem respiration emits 30–100% of the daytime net photosynthetic uptake of carbon, and therefore measurements of rates and understanding of its control by the environment are important for understanding net ecosystem exchange. Ecosystem respiration can be measured at night by eddy covariance methods, but the data may not be reliable because of low turbulence or other methodological problems. We used relationships between woody tissue, foliage, and soil respiration rates and temperature, with temperature records collected on site to estimate ecosystem respiration rates at six coniferous BOREAS sites at half-hour or 1-hour intervals, and then compared these estimates to nocturnal measurements of CO2 exchange by eddy covariance. Soil surface respiration was the largest source of CO2 at all sites (48–71%), and foliar respiration made a large contribution to ecosystem respiration at all sites (25–43%). Woody tissue respiration contributed only 5–15% to ecosystem respiration. We estimated error for the scaled chamber predictions of ecosystem respiration by using the uncertainty associated with each respiration parameter and respiring biomass value. There was substantial uncertainty in estimates of foliar and soil respiration because of the spatial variability of specific respiration rates. In addition, more attention needs to be paid to estimating foliar respiration during the early part of the growing season, when new foliage is growing, and to determining seasonal trends of soil surface respiration. Nocturnal eddy covariance measurements were poorly correlated to scaled chamber estimates of ecosystem respiration (r2=0.06–0.27) and were consistently lower than scaled chamber predictions (by 27% on average for the six sites). The bias in eddy covariance estimates of ecosystem respiration will alter estimates of gross assimilation in the light and of net ecosystem exchange rates over extended periods.

Position Error Covariance Matrix Validation and Correction

NASA Technical Reports Server (NTRS)

Frisbee, Joe, Jr.

2016-01-01

In order to calculate operationally accurate collision probabilities, the position error covariance matrices predicted at times of closest approach must be sufficiently accurate representations of the position uncertainties. This presentation will discuss why the Gaussian distribution is a reasonable expectation for the position uncertainty and how this assumed distribution type is used in the validation and correction of position error covariance matrices.

Fuzzy Neural Network-Based Interacting Multiple Model for Multi-Node Target Tracking Algorithm

PubMed Central

Sun, Baoliang; Jiang, Chunlan; Li, Ming

2016-01-01

An interacting multiple model for multi-node target tracking algorithm was proposed based on a fuzzy neural network (FNN) to solve the multi-node target tracking problem of wireless sensor networks (WSNs). Measured error variance was adaptively adjusted during the multiple model interacting output stage using the difference between the theoretical and estimated values of the measured error covariance matrix. The FNN fusion system was established during multi-node fusion to integrate with the target state estimated data from different nodes and consequently obtain network target state estimation. The feasibility of the algorithm was verified based on a network of nine detection nodes. Experimental results indicated that the proposed algorithm could trace the maneuvering target effectively under sensor failure and unknown system measurement errors. The proposed algorithm exhibited great practicability in the multi-node target tracking of WSNs. PMID:27809271

TLE uncertainty estimation using robust weighted differencing

NASA Astrophysics Data System (ADS)

Geul, Jacco; Mooij, Erwin; Noomen, Ron

2017-05-01

Accurate knowledge of satellite orbit errors is essential for many types of analyses. Unfortunately, for two-line elements (TLEs) this is not available. This paper presents a weighted differencing method using robust least-squares regression for estimating many important error characteristics. The method is applied to both classic and enhanced TLEs, compared to previous implementations, and validated using Global Positioning System (GPS) solutions for the GOCE satellite in Low-Earth Orbit (LEO), prior to its re-entry. The method is found to be more accurate than previous TLE differencing efforts in estimating initial uncertainty, as well as error growth. The method also proves more reliable and requires no data filtering (such as outlier removal). Sensitivity analysis shows a strong relationship between argument of latitude and covariance (standard deviations and correlations), which the method is able to approximate. Overall, the method proves accurate, computationally fast, and robust, and is applicable to any object in the satellite catalogue (SATCAT).

A multi-pixel InSAR time series analysis method: Simultaneous estimation of atmospheric noise, orbital errors and deformation

NASA Astrophysics Data System (ADS)

Jolivet, R.; Simons, M.

2016-12-01

InSAR time series analysis allows reconstruction of ground deformation with meter-scale spatial resolution and high temporal sampling. For instance, the ESA Sentinel-1 Constellation is capable of providing 6-day temporal sampling, thereby opening a new window on the spatio-temporal behavior of tectonic processes. However, due to computational limitations, most time series methods rely on a pixel-by-pixel approach. This limitation is a concern because (1) accounting for orbital errors requires referencing all interferograms to a common set of pixels before reconstruction of the time series and (2) spatially correlated atmospheric noise due to tropospheric turbulence is ignored. Decomposing interferograms into statistically independent wavelets will mitigate issues of correlated noise, but prior estimation of orbital uncertainties will still be required. Here, we explore a method that considers all pixels simultaneously when solving for the spatio-temporal evolution of interferometric phase Our method is based on a massively parallel implementation of a conjugate direction solver. We consider an interferogram as the sum of the phase difference between 2 SAR acquisitions and the corresponding orbital errors. In addition, we fit the temporal evolution with a physically parameterized function while accounting for spatially correlated noise in the data covariance. We assume noise is isotropic for any given InSAR pair with a covariance described by an exponential function that decays with increasing separation distance between pixels. We regularize our solution in space using a similar exponential function as model covariance. Given the problem size, we avoid matrix multiplications of the full covariances by computing convolutions in the Fourier domain. We first solve the unregularized least squares problem using the LSQR algorithm to approach the final solution, then run our conjugate direction solver to account for data and model covariances. We present synthetic tests showing the efficiency of our method. We then reconstruct a 20-year continuous time series covering Northern Chile. Without input from any additional GNSS data, we recover the secular deformation rate, seasonal oscillations and the deformation fields from the 2005 Mw 7.8 Tarapaca and 2007 Mw 7.7 Tocopilla earthquakes.

Cocaine Dependence Treatment Data: Methods for Measurement Error Problems With Predictors Derived From Stationary Stochastic Processes

PubMed Central

Guan, Yongtao; Li, Yehua; Sinha, Rajita

2011-01-01

In a cocaine dependence treatment study, we use linear and nonlinear regression models to model posttreatment cocaine craving scores and first cocaine relapse time. A subset of the covariates are summary statistics derived from baseline daily cocaine use trajectories, such as baseline cocaine use frequency and average daily use amount. These summary statistics are subject to estimation error and can therefore cause biased estimators for the regression coefficients. Unlike classical measurement error problems, the error we encounter here is heteroscedastic with an unknown distribution, and there are no replicates for the error-prone variables or instrumental variables. We propose two robust methods to correct for the bias: a computationally efficient method-of-moments-based method for linear regression models and a subsampling extrapolation method that is generally applicable to both linear and nonlinear regression models. Simulations and an application to the cocaine dependence treatment data are used to illustrate the efficacy of the proposed methods. Asymptotic theory and variance estimation for the proposed subsampling extrapolation method and some additional simulation results are described in the online supplementary material. PMID:21984854

Trans-dimensional matched-field geoacoustic inversion with hierarchical error models and interacting Markov chains.

PubMed

Dettmer, Jan; Dosso, Stan E

2012-10-01

This paper develops a trans-dimensional approach to matched-field geoacoustic inversion, including interacting Markov chains to improve efficiency and an autoregressive model to account for correlated errors. The trans-dimensional approach and hierarchical seabed model allows inversion without assuming any particular parametrization by relaxing model specification to a range of plausible seabed models (e.g., in this case, the number of sediment layers is an unknown parameter). Data errors are addressed by sampling statistical error-distribution parameters, including correlated errors (covariance), by applying a hierarchical autoregressive error model. The well-known difficulty of low acceptance rates for trans-dimensional jumps is addressed with interacting Markov chains, resulting in a substantial increase in efficiency. The trans-dimensional seabed model and the hierarchical error model relax the degree of prior assumptions required in the inversion, resulting in substantially improved (more realistic) uncertainty estimates and a more automated algorithm. In particular, the approach gives seabed parameter uncertainty estimates that account for uncertainty due to prior model choice (layering and data error statistics). The approach is applied to data measured on a vertical array in the Mediterranean Sea.

Further Evaluation of Covariate Analysis using Empirical Bayes Estimates in Population Pharmacokinetics: the Perception of Shrinkage and Likelihood Ratio Test.

PubMed

Xu, Xu Steven; Yuan, Min; Yang, Haitao; Feng, Yan; Xu, Jinfeng; Pinheiro, Jose

2017-01-01

Covariate analysis based on population pharmacokinetics (PPK) is used to identify clinically relevant factors. The likelihood ratio test (LRT) based on nonlinear mixed effect model fits is currently recommended for covariate identification, whereas individual empirical Bayesian estimates (EBEs) are considered unreliable due to the presence of shrinkage. The objectives of this research were to investigate the type I error for LRT and EBE approaches, to confirm the similarity of power between the LRT and EBE approaches from a previous report and to explore the influence of shrinkage on LRT and EBE inferences. Using an oral one-compartment PK model with a single covariate impacting on clearance, we conducted a wide range of simulations according to a two-way factorial design. The results revealed that the EBE-based regression not only provided almost identical power for detecting a covariate effect, but also controlled the false positive rate better than the LRT approach. Shrinkage of EBEs is likely not the root cause for decrease in power or inflated false positive rate although the size of the covariate effect tends to be underestimated at high shrinkage. In summary, contrary to the current recommendations, EBEs may be a better choice for statistical tests in PPK covariate analysis compared to LRT. We proposed a three-step covariate modeling approach for population PK analysis to utilize the advantages of EBEs while overcoming their shortcomings, which allows not only markedly reducing the run time for population PK analysis, but also providing more accurate covariate tests.

The effect of the dynamic wet troposphere on radio interferometric measurements

NASA Technical Reports Server (NTRS)

Treuhaft, R. N.; Lanyi, G. E.

1987-01-01

A statistical model of water vapor fluctuations is used to describe the effect of the dynamic wet troposphere on radio interferometric measurements. It is assumed that the spatial structure of refractivity is approximated by Kolmogorov turbulence theory, and that the temporal fluctuations are caused by spatial patterns moved over a site by the wind, and these assumptions are examined for the VLBI delay and delay rate observables. The results suggest that the delay rate measurement error is usually dominated by water vapor fluctuations, and water vapor induced VLBI parameter errors and correlations are determined as a function of the delay observable errors. A method is proposed for including the water vapor fluctuations in the parameter estimation method to obtain improved parameter estimates and parameter covariances.

Massively Parallel Assimilation of TOGA/TAO and Topex/Poseidon Measurements into a Quasi Isopycnal Ocean General Circulation Model Using an Ensemble Kalman Filter

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele; Borovikov, Anna Y.; Suarez, Max

1999-01-01

A massively parallel ensemble Kalman filter (EnKF)is used to assimilate temperature data from the TOGA/TAO array and altimetry from TOPEX/POSEIDON into a Pacific basin version of the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. The EnKF is an approximate Kalman filter in which the error-covariance propagation step is modeled by the integration of multiple instances of a numerical model. An estimate of the true error covariances is then inferred from the distribution of the ensemble of model state vectors. This inplementation of the filter takes advantage of the inherent parallelism in the EnKF algorithm by running all the model instances concurrently. The Kalman filter update step also occurs in parallel by having each processor process the observations that occur in the region of physical space for which it is responsible. The massively parallel data assimilation system is validated by withholding some of the data and then quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The distributions of the forecast and analysis error covariances predicted by the ENKF are also examined.

Error estimation in multitemporal InSAR deformation time series, with application to Lanzarote, Canary Islands

NASA Astrophysics Data System (ADS)

GonzáLez, Pablo J.; FernáNdez, José

2011-10-01

Interferometric Synthetic Aperture Radar (InSAR) is a reliable technique for measuring crustal deformation. However, despite its long application in geophysical problems, its error estimation has been largely overlooked. Currently, the largest problem with InSAR is still the atmospheric propagation errors, which is why multitemporal interferometric techniques have been successfully developed using a series of interferograms. However, none of the standard multitemporal interferometric techniques, namely PS or SB (Persistent Scatterers and Small Baselines, respectively) provide an estimate of their precision. Here, we present a method to compute reliable estimates of the precision of the deformation time series. We implement it for the SB multitemporal interferometric technique (a favorable technique for natural terrains, the most usual target of geophysical applications). We describe the method that uses a properly weighted scheme that allows us to compute estimates for all interferogram pixels, enhanced by a Montecarlo resampling technique that properly propagates the interferogram errors (variance-covariances) into the unknown parameters (estimated errors for the displacements). We apply the multitemporal error estimation method to Lanzarote Island (Canary Islands), where no active magmatic activity has been reported in the last decades. We detect deformation around Timanfaya volcano (lengthening of line-of-sight ˜ subsidence), where the last eruption in 1730-1736 occurred. Deformation closely follows the surface temperature anomalies indicating that magma crystallization (cooling and contraction) of the 300-year shallow magmatic body under Timanfaya volcano is still ongoing.

A New Approach to Extract Forest Water Use Efficiency from Eddy Covariance Data

NASA Astrophysics Data System (ADS)

Scanlon, T. M.; Sulman, B. N.

2016-12-01

Determination of forest water use efficiency (WUE) from eddy covariance data typically involves the following steps: (a) estimating gross primary productivity (GPP) from direct measurements of net ecosystem exchange (NEE) by extrapolating nighttime ecosystem respiration (ER) to daytime conditions, and (b) assuming direct evaporation (E) is minimal several days after rainfall, meaning that direct measurements of evapotranspiration (ET) are identical to transpiration (T). Both of these steps could lead to errors in the estimation of forest WUE. Here, we present a theoretical approach for estimating WUE through the analysis of standard eddy covariance data, which circumvents these steps. Only five statistics are needed from the high-frequency time series to extract WUE: CO2 flux, water vapor flux, standard deviation in CO2 concentration, standard deviation in water vapor concentration, and the correlation coefficient between CO2 and water vapor concentration for each half-hour period. The approach is based on the assumption that stomatal fluxes (i.e. photosynthesis and transpiration) lead to perfectly negative correlations and non-stomatal fluxes (i.e. ecosystem respiration and direct evaporation) lead to perfectly positive correlations within the CO2 and water vapor high frequency time series measured above forest canopies. A mathematical framework is presented, followed by a proof of concept using eddy covariance data and leaf-level measurements of WUE.

Study of continuous blood pressure estimation based on pulse transit time, heart rate and photoplethysmography-derived hemodynamic covariates.

PubMed

Feng, Jingjie; Huang, Zhongyi; Zhou, Congcong; Ye, Xuesong

2018-06-01

It is widely recognized that pulse transit time (PTT) can track blood pressure (BP) over short periods of time, and hemodynamic covariates such as heart rate, stiffness index may also contribute to BP monitoring. In this paper, we derived a proportional relationship between BP and PPT -2 and proposed an improved method adopting hemodynamic covariates in addition to PTT for continuous BP estimation. We divided 28 subjects from the Multi-parameter Intelligent Monitoring for Intensive Care database into two groups (with/without cardiovascular diseases) and utilized a machine learning strategy based on regularized linear regression (RLR) to construct BP models with different covariates for corresponding groups. RLR was performed for individuals as the initial calibration, while recursive least square algorithm was employed for the re-calibration. The results showed that errors of BP estimation by our method stayed within the Association of Advancement of Medical Instrumentation limits (- 0.98 ± 6.00 mmHg @ SBP, 0.02 ± 4.98 mmHg @ DBP) when the calibration interval extended to 1200-beat cardiac cycles. In comparison with other two representative studies, Chen's method kept accurate (0.32 ± 6.74 mmHg @ SBP, 0.94 ± 5.37 mmHg @ DBP) using a 400-beat calibration interval, while Poon's failed (- 1.97 ± 10.59 mmHg @ SBP, 0.70 ± 4.10 mmHg @ DBP) when using a 200-beat calibration interval. With additional hemodynamic covariates utilized, our method improved the accuracy of PTT-based BP estimation, decreased the calibration frequency and had the potential for better continuous BP estimation.

Simplification of the Kalman filter for meteorological data assimilation

NASA Technical Reports Server (NTRS)

Dee, Dick P.

1991-01-01

The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

Analyzing Multivariate Repeated Measures Designs: A Comparison of Two Approximate Degrees of Freedom Procedures

ERIC Educational Resources Information Center

Lix, Lisa M.; Algina, James; Keselman, H. J.

2003-01-01

The approximate degrees of freedom Welch-James (WJ) and Brown-Forsythe (BF) procedures for testing within-subjects effects in multivariate groups by trials repeated measures designs were investigated under departures from covariance homogeneity and normality. Empirical Type I error and power rates were obtained for least-squares estimators and…

Comparison of ArcGIS and SAS Geostatistical Analyst to Estimate Population-Weighted Monthly Temperature for US Counties.

PubMed

Xiaopeng, Q I; Liang, Wei; Barker, Laurie; Lekiachvili, Akaki; Xingyou, Zhang

Temperature changes are known to have significant impacts on human health. Accurate estimates of population-weighted average monthly air temperature for US counties are needed to evaluate temperature's association with health behaviours and disease, which are sampled or reported at the county level and measured on a monthly-or 30-day-basis. Most reported temperature estimates were calculated using ArcGIS, relatively few used SAS. We compared the performance of geostatistical models to estimate population-weighted average temperature in each month for counties in 48 states using ArcGIS v9.3 and SAS v 9.2 on a CITGO platform. Monthly average temperature for Jan-Dec 2007 and elevation from 5435 weather stations were used to estimate the temperature at county population centroids. County estimates were produced with elevation as a covariate. Performance of models was assessed by comparing adjusted R 2 , mean squared error, root mean squared error, and processing time. Prediction accuracy for split validation was above 90% for 11 months in ArcGIS and all 12 months in SAS. Cokriging in SAS achieved higher prediction accuracy and lower estimation bias as compared to cokriging in ArcGIS. County-level estimates produced by both packages were positively correlated (adjusted R 2 range=0.95 to 0.99); accuracy and precision improved with elevation as a covariate. Both methods from ArcGIS and SAS are reliable for U.S. county-level temperature estimates; However, ArcGIS's merits in spatial data pre-processing and processing time may be important considerations for software selection, especially for multi-year or multi-state projects.

A Closed-Form Error Model of Straight Lines for Improved Data Association and Sensor Fusing

PubMed Central

2018-01-01

Linear regression is a basic tool in mobile robotics, since it enables accurate estimation of straight lines from range-bearing scans or in digital images, which is a prerequisite for reliable data association and sensor fusing in the context of feature-based SLAM. This paper discusses, extends and compares existing algorithms for line fitting applicable also in the case of strong covariances between the coordinates at each single data point, which must not be neglected if range-bearing sensors are used. Besides, in particular, the determination of the covariance matrix is considered, which is required for stochastic modeling. The main contribution is a new error model of straight lines in closed form for calculating quickly and reliably the covariance matrix dependent on just a few comprehensible and easily-obtainable parameters. The model can be applied widely in any case when a line is fitted from a number of distinct points also without a priori knowledge of the specific measurement noise. By means of extensive simulations, the performance and robustness of the new model in comparison to existing approaches is shown. PMID:29673205

Observations of geographically correlated orbit errors for TOPEX/Poseidon using the global positioning system

NASA Technical Reports Server (NTRS)

Christensen, E. J.; Haines, B. J.; Mccoll, K. C.; Nerem, R. S.

1994-01-01

We have compared Global Positioning System (GPS)-based dynamic and reduced-dynamic TOPEX/Poseidon orbits over three 10-day repeat cycles of the ground-track. The results suggest that the prelaunch joint gravity model (JGM-1) introduces geographically correlated errors (GCEs) which have a strong meridional dependence. The global distribution and magnitude of these GCEs are consistent with a prelaunch covariance analysis, with estimated and predicted global rms error statistics of 2.3 and 2.4 cm rms, respectively. Repeating the analysis with the post-launch joint gravity model (JGM-2) suggests that a portion of the meridional dependence observed in JGM-1 still remains, with global rms error of 1.2 cm.

Multivariate localization methods for ensemble Kalman filtering

NASA Astrophysics Data System (ADS)

Roh, S.; Jun, M.; Szunyogh, I.; Genton, M. G.

2015-05-01

In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (entry-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help.

New estimates of the CMB angular power spectra from the WMAP 5 year low-resolution data

NASA Astrophysics Data System (ADS)

Gruppuso, A.; de Rosa, A.; Cabella, P.; Paci, F.; Finelli, F.; Natoli, P.; de Gasperis, G.; Mandolesi, N.

2009-11-01

A quadratic maximum likelihood (QML) estimator is applied to the Wilkinson Microwave Anisotropy Probe (WMAP) 5 year low-resolution maps to compute the cosmic microwave background angular power spectra (APS) at large scales for both temperature and polarization. Estimates and error bars for the six APS are provided up to l = 32 and compared, when possible, to those obtained by the WMAP team, without finding any inconsistency. The conditional likelihood slices are also computed for the Cl of all the six power spectra from l = 2 to 10 through a pixel-based likelihood code. Both the codes treat the covariance for (T, Q, U) in a single matrix without employing any approximation. The inputs of both the codes (foreground-reduced maps, related covariances and masks) are provided by the WMAP team. The peaks of the likelihood slices are always consistent with the QML estimates within the error bars; however, an excellent agreement occurs when the QML estimates are used as a fiducial power spectrum instead of the best-fitting theoretical power spectrum. By the full computation of the conditional likelihood on the estimated spectra, the value of the temperature quadrupole CTTl=2 is found to be less than 2σ away from the WMAP 5 year Λ cold dark matter best-fitting value. The BB spectrum is found to be well consistent with zero, and upper limits on the B modes are provided. The parity odd signals TB and EB are found to be consistent with zero.

The use of a covariate reduces experimental error in nutrient digestion studies in growing pigs

USDA-ARS?s Scientific Manuscript database

Covariance analysis limits error, the degree of nuisance variation, and overparameterizing factors to accurately measure treatment effects. Data dealing with growth, carcass composition, and genetics often utilize covariates in data analysis. In contrast, nutritional studies typically do not. The ob...

The Space-Wise Global Gravity Model from GOCE Nominal Mission Data

NASA Astrophysics Data System (ADS)

Gatti, A.; Migliaccio, F.; Reguzzoni, M.; Sampietro, D.; Sanso, F.

2011-12-01

In the framework of the GOCE data analysis, the space-wise approach implements a multi-step collocation solution for the estimation of a global geopotential model in terms of spherical harmonic coefficients and their error covariance matrix. The main idea is to use the collocation technique to exploit the spatial correlation of the gravity field in the GOCE data reduction. In particular the method consists of an along-track Wiener filter, a collocation gridding at satellite altitude and a spherical harmonic analysis by integration. All these steps are iterated, also to account for the rotation between local orbital and gradiometer reference frame. Error covariances are computed by Montecarlo simulations. The first release of the space-wise approach was presented at the ESA Living Planet Symposium in July 2010. This model was based on only two months of GOCE data and partially contained a priori information coming from other existing gravity models, especially at low degrees and low orders. A second release was distributed after the 4th International GOCE User Workshop in May 2011. In this solution, based on eight months of GOCE data, all the dependencies from external gravity information were removed thus giving rise to a GOCE-only space-wise model. However this model showed an over-regularization at the highest degrees of the spherical harmonic expansion due to the combination technique of intermediate solutions (based on about two months of data). In this work a new space-wise solution is presented. It is based on all nominal mission data from November 2009 to mid April 2011, and its main novelty is that the intermediate solutions are now computed in such a way to avoid over-regularization in the final solution. Beyond the spherical harmonic coefficients of the global model and their error covariance matrix, the space-wise approach is able to deliver as by-products a set of spherical grids of potential and of its second derivatives at mean satellite altitude. These grids have an information content that is very similar to the original along-orbit data, but they are much easier to handle. In addition they are estimated by local least-squares collocation and therefore, although computed by a unique global covariance function, they could yield more information at local level than the spherical harmonic coefficients of the global model. For this reason these grids seem to be useful for local geophysical investigations. The estimated grids with their estimated errors are presented in this work together with proposals on possible future improvements. A test to compare the different information contents of the along-orbit data, the gridded data and the spherical harmonic coefficients is also shown.

Ice Cores Dating With a New Inverse Method Taking Account of the Flow Modeling Errors

NASA Astrophysics Data System (ADS)

Lemieux-Dudon, B.; Parrenin, F.; Blayo, E.

2007-12-01

Deep ice cores extracted from Antarctica or Greenland recorded a wide range of past climatic events. In order to contribute to the Quaternary climate system understanding, the calculation of an accurate depth-age relationship is a crucial point. Up to now ice chronologies for deep ice cores estimated with inverse approaches are based on quite simplified ice-flow models that fail to reproduce flow irregularities and consequently to respect all available set of age markers. We describe in this paper, a new inverse method that takes into account the model uncertainty in order to circumvent the restrictions linked to the use of simplified flow models. This method uses first guesses on two flow physical entities, the ice thinning function and the accumulation rate and then identifies correction functions on both flow entities. We highlight two major benefits brought by this new method: first of all the ability to respect large set of observations and as a consequence, the feasibility to estimate a synchronized common ice chronology for several cores at the same time. This inverse approach relies on a bayesian framework. To respect the positive constraint on the searched correction functions, we assume lognormal probability distribution on one hand for the background errors, but also for one particular set of the observation errors. We test this new inversion method on three cores simultaneously (the two EPICA cores : DC and DML and the Vostok core) and we assimilate more than 150 observations (e.g.: age markers, stratigraphic links,...). We analyze the sensitivity of the solution with respect to the background information, especially the prior error covariance matrix. The confidence intervals based on the posterior covariance matrix calculation, are estimated on the correction functions and for the first time on the overall output chronologies.

A simulation study to quantify the impacts of exposure measurement error on air pollution health risk estimates in copollutant time-series models.

PubMed

Dionisio, Kathie L; Chang, Howard H; Baxter, Lisa K

2016-11-25

Exposure measurement error in copollutant epidemiologic models has the potential to introduce bias in relative risk (RR) estimates. A simulation study was conducted using empirical data to quantify the impact of correlated measurement errors in time-series analyses of air pollution and health. ZIP-code level estimates of exposure for six pollutants (CO, NO x , EC, PM 2.5 , SO 4 , O 3 ) from 1999 to 2002 in the Atlanta metropolitan area were used to calculate spatial, population (i.e. ambient versus personal), and total exposure measurement error. Empirically determined covariance of pollutant concentration pairs and the associated measurement errors were used to simulate true exposure (exposure without error) from observed exposure. Daily emergency department visits for respiratory diseases were simulated using a Poisson time-series model with a main pollutant RR = 1.05 per interquartile range, and a null association for the copollutant (RR = 1). Monte Carlo experiments were used to evaluate the impacts of correlated exposure errors of different copollutant pairs. Substantial attenuation of RRs due to exposure error was evident in nearly all copollutant pairs studied, ranging from 10 to 40% attenuation for spatial error, 3-85% for population error, and 31-85% for total error. When CO, NO x or EC is the main pollutant, we demonstrated the possibility of false positives, specifically identifying significant, positive associations for copollutants based on the estimated type I error rate. The impact of exposure error must be considered when interpreting results of copollutant epidemiologic models, due to the possibility of attenuation of main pollutant RRs and the increased probability of false positives when measurement error is present.

MIXREG: a computer program for mixed-effects regression analysis with autocorrelated errors.

PubMed

Hedeker, D; Gibbons, R D

1996-05-01

MIXREG is a program that provides estimates for a mixed-effects regression model (MRM) for normally-distributed response data including autocorrelated errors. This model can be used for analysis of unbalanced longitudinal data, where individuals may be measured at a different number of timepoints, or even at different timepoints. Autocorrelated errors of a general form or following an AR(1), MA(1), or ARMA(1,1) form are allowable. This model can also be used for analysis of clustered data, where the mixed-effects model assumes data within clusters are dependent. The degree of dependency is estimated jointly with estimates of the usual model parameters, thus adjusting for clustering. MIXREG uses maximum marginal likelihood estimation, utilizing both the EM algorithm and a Fisher-scoring solution. For the scoring solution, the covariance matrix of the random effects is expressed in its Gaussian decomposition, and the diagonal matrix reparameterized using the exponential transformation. Estimation of the individual random effects is accomplished using an empirical Bayes approach. Examples illustrating usage and features of MIXREG are provided.

Multiple Flux Footprints, Flux Divergences and Boundary Layer Mixing Ratios: Studies of Ecosystem-Atmosphere CO2 Exchange Using the WLEF Tall Tower.

NASA Astrophysics Data System (ADS)

Davis, K. J.; Bakwin, P. S.; Yi, C.; Cook, B. D.; Wang, W.; Denning, A. S.; Teclaw, R.; Isebrands, J. G.

2001-05-01

Long-term, tower-based measurements using the eddy-covariance method have revealed a wealth of detail about the temporal dynamics of netecosystem-atmosphere exchange (NEE) of CO2. The data also provide a measure of the annual net CO2 exchange. The area represented by these flux measurements, however, is limited, and doubts remain about possible systematic errors that may bias the annual net exchange measurements. Flux and mixing ratio measurements conducted at the WLEF tall tower as part of the Chequamegon Ecosystem-Atmosphere Study (ChEAS) allow for unique assessment of the uncertainties in NEE of CO2. The synergy between flux and mixing ratio observations shows the potential for comparing inverse and eddy-covariance methods of estimating NEE of CO2. Such comparisons may strengthen confidence in both results and begin to bridge the huge gap in spatial scales (at least 3 orders of magnitude) between continental or hemispheric scale inverse studies and kilometer-scale eddy covariance flux measurements. Data from WLEF and Willow Creek, another ChEAS tower, are used to estimate random and systematic errors in NEE of CO2. Random uncertainty in seasonal exchange rates and the annual integrated NEE, including both turbulent sampling errors and variability in enviromental conditions, is small. Systematic errors are identified by examining changes in flux as a function of atmospheric stability and wind direction, and by comparing the multiple level flux measurements on the WLEF tower. Nighttime drainage is modest but evident. Systematic horizontal advection occurs during the morning turbulence transition. The potential total systematic error appears to be larger than random uncertainty, but still modest. The total systematic error, however, is difficult to assess. It appears that the WLEF region ecosystems were a small net sink of CO2 in 1997. It is clear that the summer uptake rate at WLEF is much smaller than that at most deciduous forest sites, including the nearby Willow Creek site. The WLEF tower also allows us to study the potential for monitoring continental CO2 mixing ratios from tower sites. Despite concerns about the proximity to ecosystem sources and sinks, it is clear that boundary layer CO2 mixing ratios can be monitored using typical surface layer towers. Seasonal and annual land-ocean mixing ratio gradients are readily detectable, providing the motivation for a flux-tower based mixing ratio observation network that could greatly improve the accuracy of inversion-based estimates of NEE of CO2, and enable inversions to be applied on smaller temporal and spatial scales. Results from the WLEF tower illustrate the degree to which local flux measurements represent interannual, seasonal and synoptic CO2 mixing ratio trends. This coherence between fluxes and mixing ratios serves to "regionalize" the eddy-covariance based local NEE observations.

Error Covariance Penalized Regression: A novel multivariate model combining penalized regression with multivariate error structure.

PubMed

Allegrini, Franco; Braga, Jez W B; Moreira, Alessandro C O; Olivieri, Alejandro C

2018-06-29

A new multivariate regression model, named Error Covariance Penalized Regression (ECPR) is presented. Following a penalized regression strategy, the proposed model incorporates information about the measurement error structure of the system, using the error covariance matrix (ECM) as a penalization term. Results are reported from both simulations and experimental data based on replicate mid and near infrared (MIR and NIR) spectral measurements. The results for ECPR are better under non-iid conditions when compared with traditional first-order multivariate methods such as ridge regression (RR), principal component regression (PCR) and partial least-squares regression (PLS). Copyright © 2018 Elsevier B.V. All rights reserved.

Spatial Statistical Data Fusion (SSDF)

NASA Technical Reports Server (NTRS)

Braverman, Amy J.; Nguyen, Hai M.; Cressie, Noel

2013-01-01

As remote sensing for scientific purposes has transitioned from an experimental technology to an operational one, the selection of instruments has become more coordinated, so that the scientific community can exploit complementary measurements. However, tech nological and scientific heterogeneity across devices means that the statistical characteristics of the data they collect are different. The challenge addressed here is how to combine heterogeneous remote sensing data sets in a way that yields optimal statistical estimates of the underlying geophysical field, and provides rigorous uncertainty measures for those estimates. Different remote sensing data sets may have different spatial resolutions, different measurement error biases and variances, and other disparate characteristics. A state-of-the-art spatial statistical model was used to relate the true, but not directly observed, geophysical field to noisy, spatial aggregates observed by remote sensing instruments. The spatial covariances of the true field and the covariances of the true field with the observations were modeled. The observations are spatial averages of the true field values, over pixels, with different measurement noise superimposed. A kriging framework is used to infer optimal (minimum mean squared error and unbiased) estimates of the true field at point locations from pixel-level, noisy observations. A key feature of the spatial statistical model is the spatial mixed effects model that underlies it. The approach models the spatial covariance function of the underlying field using linear combinations of basis functions of fixed size. Approaches based on kriging require the inversion of very large spatial covariance matrices, and this is usually done by making simplifying assumptions about spatial covariance structure that simply do not hold for geophysical variables. In contrast, this method does not require these assumptions, and is also computationally much faster. This method is fundamentally different than other approaches to data fusion for remote sensing data because it is inferential rather than merely descriptive. All approaches combine data in a way that minimizes some specified loss function. Most of these are more or less ad hoc criteria based on what looks good to the eye, or some criteria that relate only to the data at hand.

Precise estimation of tropospheric path delays with GPS techniques

NASA Technical Reports Server (NTRS)

Lichten, S. M.

1990-01-01

Tropospheric path delays are a major source of error in deep space tracking. However, the tropospheric-induced delay at tracking sites can be calibrated using measurements of Global Positioning System (GPS) satellites. A series of experiments has demonstrated the high sensitivity of GPS to tropospheric delays. A variety of tests and comparisons indicates that current accuracy of the GPS zenith tropospheric delay estimates is better than 1-cm root-mean-square over many hours, sampled continuously at intervals of six minutes. These results are consistent with expectations from covariance analyses. The covariance analyses also indicate that by the mid-1990s, when the GPS constellation is complete and the Deep Space Network is equipped with advanced GPS receivers, zenith tropospheric delay accuracy with GPS will improve further to 0.5 cm or better.

CoCoa: a software tool for estimating the coefficient of coancestry from multilocus genotype data.

PubMed

Maenhout, Steven; De Baets, Bernard; Haesaert, Geert

2009-10-15

Phenotypic data collected in breeding programs and marker-trait association studies are often analyzed by means of linear mixed models. In these models, the covariance between the genetic background effects of all genotypes under study is modeled by means of pairwise coefficients of coancestry. Several marker-based coancestry estimation procedures allow to estimate this covariance matrix, but generally introduce a certain amount of bias when the examined genotypes are part of a breeding program. CoCoa implements the most commonly used marker-based coancestry estimation procedures and as such, allows to select the best fitting covariance structure for the phenotypic data at hand. This better model fit translates into an increased power and improved type I error control in association studies and an improved accuracy in phenotypic prediction studies. The presented software package also provides an implementation of the new Weighted Alikeness in State (WAIS) estimator for use in hybrid breeding programs. Besides several matrix manipulation tools, CoCoa implements two different bending heuristics, in case the inverse of an ill-conditioned coancestry matrix estimate is needed. The software package CoCoa is freely available at http://webs.hogent.be/cocoa. Source code, manual, binaries for 32 and 64-bit Linux systems and an installer for Microsoft Windows are provided. The core components of CoCoa are written in C++, while the graphical user interface is written in Java.

Uncertainty analysis of the Operational Simplified Surface Energy Balance (SSEBop) model at multiple flux tower sites

USGS Publications Warehouse

Chen, Mingshi; Senay, Gabriel B.; Singh, Ramesh K.; Verdin, James P.

2016-01-01

Evapotranspiration (ET) is an important component of the water cycle – ET from the land surface returns approximately 60% of the global precipitation back to the atmosphere. ET also plays an important role in energy transport among the biosphere, atmosphere, and hydrosphere. Current regional to global and daily to annual ET estimation relies mainly on surface energy balance (SEB) ET models or statistical and empirical methods driven by remote sensing data and various climatological databases. These models have uncertainties due to inevitable input errors, poorly defined parameters, and inadequate model structures. The eddy covariance measurements on water, energy, and carbon fluxes at the AmeriFlux tower sites provide an opportunity to assess the ET modeling uncertainties. In this study, we focused on uncertainty analysis of the Operational Simplified Surface Energy Balance (SSEBop) model for ET estimation at multiple AmeriFlux tower sites with diverse land cover characteristics and climatic conditions. The 8-day composite 1-km MODerate resolution Imaging Spectroradiometer (MODIS) land surface temperature (LST) was used as input land surface temperature for the SSEBop algorithms. The other input data were taken from the AmeriFlux database. Results of statistical analysis indicated that the SSEBop model performed well in estimating ET with an R2 of 0.86 between estimated ET and eddy covariance measurements at 42 AmeriFlux tower sites during 2001–2007. It was encouraging to see that the best performance was observed for croplands, where R2 was 0.92 with a root mean square error of 13 mm/month. The uncertainties or random errors from input variables and parameters of the SSEBop model led to monthly ET estimates with relative errors less than 20% across multiple flux tower sites distributed across different biomes. This uncertainty of the SSEBop model lies within the error range of other SEB models, suggesting systematic error or bias of the SSEBop model is within the normal range. This finding implies that the simplified parameterization of the SSEBop model did not significantly affect the accuracy of the ET estimate while increasing the ease of model setup for operational applications. The sensitivity analysis indicated that the SSEBop model is most sensitive to input variables, land surface temperature (LST) and reference ET (ETo); and parameters, differential temperature (dT), and maximum ET scalar (Kmax), particularly during the non-growing season and in dry areas. In summary, the uncertainty assessment verifies that the SSEBop model is a reliable and robust method for large-area ET estimation. The SSEBop model estimates can be further improved by reducing errors in two input variables (ETo and LST) and two key parameters (Kmax and dT).

Bias and heteroscedastic memory error in self-reported health behavior: an investigation using covariance structure analysis

PubMed Central

Kupek, Emil

2002-01-01

Background Frequent use of self-reports for investigating recent and past behavior in medical research requires statistical techniques capable of analyzing complex sources of bias associated with this methodology. In particular, although decreasing accuracy of recalling more distant past events is commonplace, the bias due to differential in memory errors resulting from it has rarely been modeled statistically. Methods Covariance structure analysis was used to estimate the recall error of self-reported number of sexual partners for past periods of varying duration and its implication for the bias. Results Results indicated increasing levels of inaccuracy for reports about more distant past. Considerable positive bias was found for a small fraction of respondents who reported ten or more partners in the last year, last two years and last five years. This is consistent with the effect of heteroscedastic random error where the majority of partners had been acquired in the more distant past and therefore were recalled less accurately than the partners acquired more recently to the time of interviewing. Conclusions Memory errors of this type depend on the salience of the events recalled and are likely to be present in many areas of health research based on self-reported behavior. PMID:12435276

Suboptimal schemes for atmospheric data assimilation based on the Kalman filter

NASA Technical Reports Server (NTRS)

Todling, Ricardo; Cohn, Stephen E.

1994-01-01

This work is directed toward approximating the evolution of forecast error covariances for data assimilation. The performance of different algorithms based on simplification of the standard Kalman filter (KF) is studied. These are suboptimal schemes (SOSs) when compared to the KF, which is optimal for linear problems with known statistics. The SOSs considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. To employ a methodology for exact comparison among these schemes, a linear environment is maintained, in which a beta-plane shallow-water model linearized about a constant zonal flow is chosen for the test-bed dynamics. The results show that constructing dynamically balanced forecast error covariances rather than using conventional geostrophically balanced ones is essential for successful performance of any SOS. A posteriori initialization of SOSs to compensate for model - data imbalance sometimes results in poor performance. Instead, properly constructed dynamically balanced forecast error covariances eliminate the need for initialization. When the SOSs studied here make use of dynamically balanced forecast error covariances, the difference among their performances progresses naturally from conventional OI to the KF. In fact, the results suggest that even modest enhancements of OI, such as including an approximate dynamical equation for height error variances while leaving height error correlation structure homogeneous, go a long way toward achieving the performance of the KF, provided that dynamically balanced cross-covariances are constructed and that model errors are accounted for properly. The results indicate that such enhancements are necessary if unconventional data are to have a positive impact.

Considerations for analysis of time-to-event outcomes measured with error: Bias and correction with SIMEX.

PubMed

Oh, Eric J; Shepherd, Bryan E; Lumley, Thomas; Shaw, Pamela A

2018-04-15

For time-to-event outcomes, a rich literature exists on the bias introduced by covariate measurement error in regression models, such as the Cox model, and methods of analysis to address this bias. By comparison, less attention has been given to understanding the impact or addressing errors in the failure time outcome. For many diseases, the timing of an event of interest (such as progression-free survival or time to AIDS progression) can be difficult to assess or reliant on self-report and therefore prone to measurement error. For linear models, it is well known that random errors in the outcome variable do not bias regression estimates. With nonlinear models, however, even random error or misclassification can introduce bias into estimated parameters. We compare the performance of 2 common regression models, the Cox and Weibull models, in the setting of measurement error in the failure time outcome. We introduce an extension of the SIMEX method to correct for bias in hazard ratio estimates from the Cox model and discuss other analysis options to address measurement error in the response. A formula to estimate the bias induced into the hazard ratio by classical measurement error in the event time for a log-linear survival model is presented. Detailed numerical studies are presented to examine the performance of the proposed SIMEX method under varying levels and parametric forms of the error in the outcome. We further illustrate the method with observational data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic. Copyright © 2017 John Wiley & Sons, Ltd.

Multisensor Parallel Largest Ellipsoid Distributed Data Fusion with Unknown Cross-Covariances

PubMed Central

Liu, Baoyu; Zhan, Xingqun; Zhu, Zheng H.

2017-01-01

As the largest ellipsoid (LE) data fusion algorithm can only be applied to two-sensor system, in this contribution, parallel fusion structure is proposed to introduce the LE algorithm into a multisensor system with unknown cross-covariances, and three parallel fusion structures based on different estimate pairing methods are presented and analyzed. In order to assess the influence of fusion structure on fusion performance, two fusion performance assessment parameters are defined as Fusion Distance and Fusion Index. Moreover, the formula for calculating the upper bounds of actual fused error covariances of the presented multisensor LE fusers is also provided. Demonstrated with simulation examples, the Fusion Index indicates fuser’s actual fused accuracy and its sensitivity to the sensor orders, as well as its robustness to the accuracy of newly added sensors. Compared to the LE fuser with sequential structure, the LE fusers with proposed parallel structures not only significantly improve their properties in these aspects, but also embrace better performances in consistency and computation efficiency. The presented multisensor LE fusers generally have better accuracies than covariance intersection (CI) fusion algorithm and are consistent when the local estimates are weakly correlated. PMID:28661442

Statistical Field Estimation and Scale Estimation for Complex Coastal Regions and Archipelagos

DTIC Science & Technology

2009-05-01

instruments applied to mode-73. Deep-Sea Research, 23:559–582. Brown , R. G. and Hwang , P. Y. C. (1997). Introduction to Random Signals and Applied Kalman ...the covariance matrix becomes neg- ative due to numerical issues ( Brown and Hwang , 1997). Some useful techniques to counter these divergence problems...equations ( Brown and Hwang , 1997). If the number of observations is large, divergence problems can arise under certain con- ditions due to truncation errors

Effects of Covariance Heterogeneity on Three Procedures for Analyzing Multivariate Repeated Measures Designs.

ERIC Educational Resources Information Center

Vallejo, Guillermo; Fidalgo, Angel; Fernandez, Paula

2001-01-01

Estimated empirical Type I error rate and power rate for three procedures for analyzing multivariate repeated measures designs: (1) the doubly multivariate model; (2) the Welch-James multivariate solution (H. Keselman, M. Carriere, a nd L. Lix, 1993); and (3) the multivariate version of the modified Brown-Forsythe procedure (M. Brown and A.…

A Note on Sample Size and Solution Propriety for Confirmatory Factor Analytic Models

ERIC Educational Resources Information Center

Jackson, Dennis L.; Voth, Jennifer; Frey, Marc P.

2013-01-01

Determining an appropriate sample size for use in latent variable modeling techniques has presented ongoing challenges to researchers. In particular, small sample sizes are known to present concerns over sampling error for the variances and covariances on which model estimation is based, as well as for fit indexes and convergence failures. The…

Estimation of Phytoplankton Accessory Pigments From Hyperspectral Reflectance Spectra: Toward a Global Algorithm

NASA Astrophysics Data System (ADS)

Chase, A. P.; Boss, E.; Cetinić, I.; Slade, W.

2017-12-01

Phytoplankton community composition in the ocean is complex and highly variable over a wide range of space and time scales. Able to cover these scales, remote-sensing reflectance spectra can be measured both by satellite and by in situ radiometers. The spectral shape of reflectance in the open ocean is influenced by the particles in the water, mainly phytoplankton and covarying nonalgal particles. We investigate the utility of in situ hyperspectral remote-sensing reflectance measurements to detect phytoplankton pigments by using an inversion algorithm that defines phytoplankton pigment absorption as a sum of Gaussian functions. The inverted amplitudes of the Gaussian functions representing pigment absorption are compared to coincident High Performance Liquid Chromatography measurements of pigment concentration. We determined strong predictive capability for chlorophylls a, b, c1+c2, and the photoprotective carotenoids. We also tested the estimation of pigment concentrations from reflectance-derived chlorophyll a using global relationships of covariation between chlorophyll a and the accessory pigments. We found similar errors in pigment estimation based on the relationships of covariation versus the inversion algorithm. An investigation of spectral residuals in reflectance data after removal of chlorophyll-based average absorption spectra showed no strong relationship between spectral residuals and pigments. Ultimately, we are able to estimate concentrations of three chlorophylls and the photoprotective carotenoid pigments, noting that further work is necessary to address the challenge of extracting information from hyperspectral reflectance beyond the information that can be determined from chlorophyll a and its covariation with other pigments.

Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model.

PubMed

Merlé, Y; Mentré, F

1995-02-01

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the pre-posterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and the Emax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for the Emax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for the Emax model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.

A Sequential Multiplicative Extended Kalman Filter for Attitude Estimation Using Vector Observations.

PubMed

Qin, Fangjun; Chang, Lubin; Jiang, Sai; Zha, Feng

2018-05-03

In this paper, a sequential multiplicative extended Kalman filter (SMEKF) is proposed for attitude estimation using vector observations. In the proposed SMEKF, each of the vector observations is processed sequentially to update the attitude, which can make the measurement model linearization more accurate for the next vector observation. This is the main difference to Murrell’s variation of the MEKF, which does not update the attitude estimate during the sequential procedure. Meanwhile, the covariance is updated after all the vector observations have been processed, which is used to account for the special characteristics of the reset operation necessary for the attitude update. This is the main difference to the traditional sequential EKF, which updates the state covariance at each step of the sequential procedure. The numerical simulation study demonstrates that the proposed SMEKF has more consistent and accurate performance in a wide range of initial estimate errors compared to the MEKF and its traditional sequential forms.

A Sequential Multiplicative Extended Kalman Filter for Attitude Estimation Using Vector Observations

PubMed Central

Qin, Fangjun; Jiang, Sai; Zha, Feng

2018-01-01

In this paper, a sequential multiplicative extended Kalman filter (SMEKF) is proposed for attitude estimation using vector observations. In the proposed SMEKF, each of the vector observations is processed sequentially to update the attitude, which can make the measurement model linearization more accurate for the next vector observation. This is the main difference to Murrell’s variation of the MEKF, which does not update the attitude estimate during the sequential procedure. Meanwhile, the covariance is updated after all the vector observations have been processed, which is used to account for the special characteristics of the reset operation necessary for the attitude update. This is the main difference to the traditional sequential EKF, which updates the state covariance at each step of the sequential procedure. The numerical simulation study demonstrates that the proposed SMEKF has more consistent and accurate performance in a wide range of initial estimate errors compared to the MEKF and its traditional sequential forms. PMID:29751538

A stochastic multiple imputation algorithm for missing covariate data in tree-structured survival analysis.

PubMed

Wallace, Meredith L; Anderson, Stewart J; Mazumdar, Sati

2010-12-20

Missing covariate data present a challenge to tree-structured methodology due to the fact that a single tree model, as opposed to an estimated parameter value, may be desired for use in a clinical setting. To address this problem, we suggest a multiple imputation algorithm that adds draws of stochastic error to a tree-based single imputation method presented by Conversano and Siciliano (Technical Report, University of Naples, 2003). Unlike previously proposed techniques for accommodating missing covariate data in tree-structured analyses, our methodology allows the modeling of complex and nonlinear covariate structures while still resulting in a single tree model. We perform a simulation study to evaluate our stochastic multiple imputation algorithm when covariate data are missing at random and compare it to other currently used methods. Our algorithm is advantageous for identifying the true underlying covariate structure when complex data and larger percentages of missing covariate observations are present. It is competitive with other current methods with respect to prediction accuracy. To illustrate our algorithm, we create a tree-structured survival model for predicting time to treatment response in older, depressed adults. Copyright © 2010 John Wiley & Sons, Ltd.

Using SAS PROC CALIS to fit Level-1 error covariance structures of latent growth models.

PubMed

Ding, Cherng G; Jane, Ten-Der

2012-09-01

In the present article, we demonstrates the use of SAS PROC CALIS to fit various types of Level-1 error covariance structures of latent growth models (LGM). Advantages of the SEM approach, on which PROC CALIS is based, include the capabilities of modeling the change over time for latent constructs, measured by multiple indicators; embedding LGM into a larger latent variable model; incorporating measurement models for latent predictors; and better assessing model fit and the flexibility in specifying error covariance structures. The strength of PROC CALIS is always accompanied with technical coding work, which needs to be specifically addressed. We provide a tutorial on the SAS syntax for modeling the growth of a manifest variable and the growth of a latent construct, focusing the documentation on the specification of Level-1 error covariance structures. Illustrations are conducted with the data generated from two given latent growth models. The coding provided is helpful when the growth model has been well determined and the Level-1 error covariance structure is to be identified.

Using CO2:CO Correlations to Improve Inverse Analyses of Carbon Fluxes

NASA Technical Reports Server (NTRS)

Palmer, Paul I.; Suntharalingam, Parvadha; Jones, Dylan B. A.; Jacob, Daniel J.; Streets, David G.; Fu, Qingyan; Vay, Stephanie A.; Sachse, Glen W.

2006-01-01

Observed correlations between atmospheric concentrations of CO2 and CO represent potentially powerful information for improving CO2 surface flux estimates through coupled CO2-CO inverse analyses. We explore the value of these correlations in improving estimates of regional CO2 fluxes in east Asia by using aircraft observations of CO2 and CO from the TRACE-P campaign over the NW Pacific in March 2001. Our inverse model uses regional CO2 and CO surface fluxes as the state vector, separating biospheric and combustion contributions to CO2. CO2-CO error correlation coefficients are included in the inversion as off-diagonal entries in the a priori and observation error covariance matrices. We derive error correlations in a priori combustion source estimates of CO2 and CO by propagating error estimates of fuel consumption rates and emission factors. However, we find that these correlations are weak because CO source uncertainties are mostly determined by emission factors. Observed correlations between atmospheric CO2 and CO concentrations imply corresponding error correlations in the chemical transport model used as the forward model for the inversion. These error correlations in excess of 0.7, as derived from the TRACE-P data, enable a coupled CO2-CO inversion to achieve significant improvement over a CO2-only inversion for quantifying regional fluxes of CO2.

A comparison of entropy balance and probability weighting methods to generalize observational cohorts to a population: a simulation and empirical example.

PubMed

Harvey, Raymond A; Hayden, Jennifer D; Kamble, Pravin S; Bouchard, Jonathan R; Huang, Joanna C

2017-04-01

We compared methods to control bias and confounding in observational studies including inverse probability weighting (IPW) and stabilized IPW (sIPW). These methods often require iteration and post-calibration to achieve covariate balance. In comparison, entropy balance (EB) optimizes covariate balance a priori by calibrating weights using the target's moments as constraints. We measured covariate balance empirically and by simulation by using absolute standardized mean difference (ASMD), absolute bias (AB), and root mean square error (RMSE), investigating two scenarios: the size of the observed (exposed) cohort exceeds the target (unexposed) cohort and vice versa. The empirical application weighted a commercial health plan cohort to a nationally representative National Health and Nutrition Examination Survey target on the same covariates and compared average total health care cost estimates across methods. Entropy balance alone achieved balance (ASMD ≤ 0.10) on all covariates in simulation and empirically. In simulation scenario I, EB achieved the lowest AB and RMSE (13.64, 31.19) compared with IPW (263.05, 263.99) and sIPW (319.91, 320.71). In scenario II, EB outperformed IPW and sIPW with smaller AB and RMSE. In scenarios I and II, EB achieved the lowest mean estimate difference from the simulated population outcome ($490.05, $487.62) compared with IPW and sIPW, respectively. Empirically, only EB differed from the unweighted mean cost indicating IPW, and sIPW weighting was ineffective. Entropy balance demonstrated the bias-variance tradeoff achieving higher estimate accuracy, yet lower estimate precision, compared with IPW methods. EB weighting required no post-processing and effectively mitigated observed bias and confounding. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Survival analysis with error-prone time-varying covariates: a risk set calibration approach

PubMed Central

Liao, Xiaomei; Zucker, David M.; Li, Yi; Spiegelman, Donna

2010-01-01

Summary Occupational, environmental, and nutritional epidemiologists are often interested in estimating the prospective effect of time-varying exposure variables such as cumulative exposure or cumulative updated average exposure, in relation to chronic disease endpoints such as cancer incidence and mortality. From exposure validation studies, it is apparent that many of the variables of interest are measured with moderate to substantial error. Although the ordinary regression calibration approach is approximately valid and efficient for measurement error correction of relative risk estimates from the Cox model with time-independent point exposures when the disease is rare, it is not adaptable for use with time-varying exposures. By re-calibrating the measurement error model within each risk set, a risk set regression calibration method is proposed for this setting. An algorithm for a bias-corrected point estimate of the relative risk using an RRC approach is presented, followed by the derivation of an estimate of its variance, resulting in a sandwich estimator. Emphasis is on methods applicable to the main study/external validation study design, which arises in important applications. Simulation studies under several assumptions about the error model were carried out, which demonstrated the validity and efficiency of the method in finite samples. The method was applied to a study of diet and cancer from Harvard’s Health Professionals Follow-up Study (HPFS). PMID:20486928

Parametric analysis for matched pair survival data.

PubMed

Manatunga, A K; Oakes, D

1999-12-01

Hougaard's (1986) bivariate Weibull distribution with positive stable frailties is applied to matched pairs survival data when either or both components of the pair may be censored and covariate vectors may be of arbitrary fixed length. When there is no censoring, we quantify the corresponding gain in Fisher information over a fixed-effects analysis. With the appropriate parameterization, the results take a simple algebraic form. An alternative marginal ("independence working model") approach to estimation is also considered. This method ignores the correlation between the two survival times in the derivation of the estimator, but provides a valid estimate of standard error. It is shown that when both the correlation between the two survival times is high, and the ratio of the within-pair variability to the between-pair variability of the covariates is high, the fixed-effects analysis captures most of the information about the regression coefficient but the independence working model does badly. When the correlation is low, and/or most of the variability of the covariates occurs between pairs, the reverse is true. The random effects model is applied to data on skin grafts, and on loss of visual acuity among diabetics. In conclusion some extensions of the methods are indicated and they are placed in a wider context of Generalized Estimation Equation methodology.

Broad-band Lg Attenuation Tomography in Eastern Eurasia and The Resolution, Uncertainty and Data Predication

NASA Astrophysics Data System (ADS)

Chen, Y.; Xu, X.

2017-12-01

The broad band Lg 1/Q tomographic models in eastern Eurasia are inverted from source- and site-corrected path 1/Q data. The path 1/Q are measured between stations (or events) by the two-station (TS), reverse two-station (RTS) and reverse two-event (RTE) methods, respectively. Because path 1/Q are computed using logarithm of the product of observed spectral ratios and simplified 1D geometrical spreading correction, they are subject to "modeling errors" dominated by uncompensated 3D structural effects. We have found in Chen and Xie [2017] that these errors closely follow normal distribution after the long-tailed outliers are screened out (similar to teleseismic travel time residuals). We thus rigorously analyze the statistics of these errors collected from repeated samplings of station (and event) pairs from 1.0 to 10.0Hz and reject about 15% outliers at each frequency band. The resultant variance of Δ/Q decreases with frequency as 1/f2. The 1/Q tomography using screened data is now a stochastic inverse problem with solutions approximate the means of Gaussian random variables and the model covariance matrix is that of Gaussian variables with well-known statistical behavior. We adopt a new SVD based tomographic method to solve for 2D Q image together with its resolution and covariance matrices. The RTS and RTE yield the most reliable 1/Q data free of source and site effects, but the path coverage is rather sparse due to very strict recording geometry. The TS absorbs the effects of non-unit site response ratios into 1/Q data. The RTS also yields site responses, which can then be corrected from the path 1/Q of TS to make them also free of site effect. The site corrected TS data substantially improve path coverage, allowing able to solve for 1/Q tomography up to 6.0Hz. The model resolution and uncertainty are first quantitively accessed by spread functions (fulfilled by resolution matrix) and covariance matrix. The reliably retrieved Q models correlate well with the distinct tectonic blocks featured by the most recent major deformations and vary with frequencies. With the 1/Q tomographic model and its covariance matrix, we can formally estimate the uncertainty of any path-specific Lg 1/Q prediction. This new capability significantly benefits source estimation for which reliable uncertainty estimate is especially important.

Comparison of ArcGIS and SAS Geostatistical Analyst to Estimate Population-Weighted Monthly Temperature for US Counties

PubMed Central

Xiaopeng, QI; Liang, WEI; BARKER, Laurie; LEKIACHVILI, Akaki; Xingyou, ZHANG

2015-01-01

Temperature changes are known to have significant impacts on human health. Accurate estimates of population-weighted average monthly air temperature for US counties are needed to evaluate temperature’s association with health behaviours and disease, which are sampled or reported at the county level and measured on a monthly—or 30-day—basis. Most reported temperature estimates were calculated using ArcGIS, relatively few used SAS. We compared the performance of geostatistical models to estimate population-weighted average temperature in each month for counties in 48 states using ArcGIS v9.3 and SAS v 9.2 on a CITGO platform. Monthly average temperature for Jan-Dec 2007 and elevation from 5435 weather stations were used to estimate the temperature at county population centroids. County estimates were produced with elevation as a covariate. Performance of models was assessed by comparing adjusted R2, mean squared error, root mean squared error, and processing time. Prediction accuracy for split validation was above 90% for 11 months in ArcGIS and all 12 months in SAS. Cokriging in SAS achieved higher prediction accuracy and lower estimation bias as compared to cokriging in ArcGIS. County-level estimates produced by both packages were positively correlated (adjusted R2 range=0.95 to 0.99); accuracy and precision improved with elevation as a covariate. Both methods from ArcGIS and SAS are reliable for U.S. county-level temperature estimates; However, ArcGIS’s merits in spatial data pre-processing and processing time may be important considerations for software selection, especially for multi-year or multi-state projects. PMID:26167169

On the Likely Utility of Hybrid Weights Optimized for Variances in Hybrid Error Covariance Models

NASA Astrophysics Data System (ADS)

Satterfield, E.; Hodyss, D.; Kuhl, D.; Bishop, C. H.

2017-12-01

Because of imperfections in ensemble data assimilation schemes, one cannot assume that the ensemble covariance is equal to the true error covariance of a forecast. Previous work demonstrated how information about the distribution of true error variances given an ensemble sample variance can be revealed from an archive of (observation-minus-forecast, ensemble-variance) data pairs. Here, we derive a simple and intuitively compelling formula to obtain the mean of this distribution of true error variances given an ensemble sample variance from (observation-minus-forecast, ensemble-variance) data pairs produced by a single run of a data assimilation system. This formula takes the form of a Hybrid weighted average of the climatological forecast error variance and the ensemble sample variance. Here, we test the extent to which these readily obtainable weights can be used to rapidly optimize the covariance weights used in Hybrid data assimilation systems that employ weighted averages of static covariance models and flow-dependent ensemble based covariance models. Univariate data assimilation and multi-variate cycling ensemble data assimilation are considered. In both cases, it is found that our computationally efficient formula gives Hybrid weights that closely approximate the optimal weights found through the simple but computationally expensive process of testing every plausible combination of weights.

Modeling workplace contact networks: The effects of organizational structure, architecture, and reporting errors on epidemic predictions.

PubMed

Potter, Gail E; Smieszek, Timo; Sailer, Kerstin

2015-09-01

Face-to-face social contacts are potentially important transmission routes for acute respiratory infections, and understanding the contact network can improve our ability to predict, contain, and control epidemics. Although workplaces are important settings for infectious disease transmission, few studies have collected workplace contact data and estimated workplace contact networks. We use contact diaries, architectural distance measures, and institutional structures to estimate social contact networks within a Swiss research institute. Some contact reports were inconsistent, indicating reporting errors. We adjust for this with a latent variable model, jointly estimating the true (unobserved) network of contacts and duration-specific reporting probabilities. We find that contact probability decreases with distance, and that research group membership, role, and shared projects are strongly predictive of contact patterns. Estimated reporting probabilities were low only for 0-5 min contacts. Adjusting for reporting error changed the estimate of the duration distribution, but did not change the estimates of covariate effects and had little effect on epidemic predictions. Our epidemic simulation study indicates that inclusion of network structure based on architectural and organizational structure data can improve the accuracy of epidemic forecasting models.

Modeling workplace contact networks: The effects of organizational structure, architecture, and reporting errors on epidemic predictions

PubMed Central

Potter, Gail E.; Smieszek, Timo; Sailer, Kerstin

2015-01-01

Face-to-face social contacts are potentially important transmission routes for acute respiratory infections, and understanding the contact network can improve our ability to predict, contain, and control epidemics. Although workplaces are important settings for infectious disease transmission, few studies have collected workplace contact data and estimated workplace contact networks. We use contact diaries, architectural distance measures, and institutional structures to estimate social contact networks within a Swiss research institute. Some contact reports were inconsistent, indicating reporting errors. We adjust for this with a latent variable model, jointly estimating the true (unobserved) network of contacts and duration-specific reporting probabilities. We find that contact probability decreases with distance, and that research group membership, role, and shared projects are strongly predictive of contact patterns. Estimated reporting probabilities were low only for 0–5 min contacts. Adjusting for reporting error changed the estimate of the duration distribution, but did not change the estimates of covariate effects and had little effect on epidemic predictions. Our epidemic simulation study indicates that inclusion of network structure based on architectural and organizational structure data can improve the accuracy of epidemic forecasting models. PMID:26634122

A semiempirical error estimation technique for PWV derived from atmospheric radiosonde data

NASA Astrophysics Data System (ADS)

Castro-Almazán, Julio A.; Pérez-Jordán, Gabriel; Muñoz-Tuñón, Casiana

2016-09-01

A semiempirical method for estimating the error and optimum number of sampled levels in precipitable water vapour (PWV) determinations from atmospheric radiosoundings is proposed. Two terms have been considered: the uncertainties in the measurements and the sampling error. Also, the uncertainty has been separated in the variance and covariance components. The sampling and covariance components have been modelled from an empirical dataset of 205 high-vertical-resolution radiosounding profiles, equipped with Vaisala RS80 and RS92 sondes at four different locations: Güímar (GUI) in Tenerife, at sea level, and the astronomical observatory at Roque de los Muchachos (ORM, 2300 m a.s.l.) on La Palma (both on the Canary Islands, Spain), Lindenberg (LIN) in continental Germany, and Ny-Ålesund (NYA) in the Svalbard Islands, within the Arctic Circle. The balloons at the ORM were launched during intensive and unique site-testing runs carried out in 1990 and 1995, while the data for the other sites were obtained from radiosounding stations operating for a period of 1 year (2013-2014). The PWV values ranged between ˜ 0.9 and ˜ 41 mm. The method sub-samples the profile for error minimization. The result is the minimum error and the optimum number of levels. The results obtained in the four sites studied showed that the ORM is the driest of the four locations and the one with the fastest vertical decay of PWV. The exponential autocorrelation pressure lags ranged from 175 hPa (ORM) to 500 hPa (LIN). The results show a coherent behaviour with no biases as a function of the profile. The final error is roughly proportional to PWV whereas the optimum number of levels (N0) is the reverse. The value of N0 is less than 400 for 77 % of the profiles and the absolute errors are always < 0.6 mm. The median relative error is 2.0 ± 0.7 % and the 90th percentile P90 = 4.6 %. Therefore, whereas a radiosounding samples at least N0 uniform vertical levels, depending on the water vapour content and distribution of the atmosphere, the error in the PWV estimate is likely to stay below ≈ 3 %, even for dry conditions.

Structured pedigree information for distributed fusion systems

NASA Astrophysics Data System (ADS)

Arambel, Pablo O.

2008-04-01

One of the most critical challenges in distributed data fusion is the avoidance of information double counting (also called "data incest" or "rumor propagation"). This occurs when a node in a network incorporates information into an estimate - e.g. the position of an object - and the estimate is injected into the network. Other nodes fuse this estimate with their own estimates, and continue to propagate estimates through the network. When the first node receives a fused estimate from the network, it does not know if it already contains its own contributions or not. Since the correlation between its own estimate and the estimate received from the network is not known, the node can not fuse the estimates in an optimal way. If it assumes that both estimates are independent from each other, it unknowingly double counts the information that has already being used to obtain the two estimates. This leads to overoptimistic error covariance matrices. If the double-counting is not kept under control, it may lead to serious performance degradation. Double counting can be avoided by propagating uniquely tagged raw measurements; however, that forces each node to process all the measurements and precludes the propagation of derived information. Another approach is to fuse the information using the Covariance Intersection (CI) equations, which maintain consistent estimates irrespective of the cross-correlation among estimates. However, CI does not exploit pedigree information of any kind. In this paper we present an approach that propagates multiple covariance matrices, one for each uncorrelated source in the network. This is a way to compress the pedigree information and avoids the need to propagate raw measurements. The approach uses a generalized version of the Split CI to fuse different estimates with appropriate weights to guarantee the consistency of the estimates.

A Wavelet Based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

NASA Technical Reports Server (NTRS)

Auger, Ludovic; Tangborn, Andrew; Atlas, Robert (Technical Monitor)

2002-01-01

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. The truncation is carried out in such a way that the resolution of the error covariance, is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance, by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and a growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the tracer field.

A Systematic Approach for Identifying Level-1 Error Covariance Structures in Latent Growth Modeling

ERIC Educational Resources Information Center

Ding, Cherng G.; Jane, Ten-Der; Wu, Chiu-Hui; Lin, Hang-Rung; Shen, Chih-Kang

2017-01-01

It has been pointed out in the literature that misspecification of the level-1 error covariance structure in latent growth modeling (LGM) has detrimental impacts on the inferences about growth parameters. Since correct covariance structure is difficult to specify by theory, the identification needs to rely on a specification search, which,…

On the error in crop acreage estimation using satellite (LANDSAT) data

NASA Technical Reports Server (NTRS)

Chhikara, R. (Principal Investigator)

1983-01-01

The problem of crop acreage estimation using satellite data is discussed. Bias and variance of a crop proportion estimate in an area segment obtained from the classification of its multispectral sensor data are derived as functions of the means, variances, and covariance of error rates. The linear discriminant analysis and the class proportion estimation for the two class case are extended to include a third class of measurement units, where these units are mixed on ground. Special attention is given to the investigation of mislabeling in training samples and its effect on crop proportion estimation. It is shown that the bias and variance of the estimate of a specific crop acreage proportion increase as the disparity in mislabeling rates between two classes increases. Some interaction is shown to take place, causing the bias and the variance to decrease at first and then to increase, as the mixed unit class varies in size from 0 to 50 percent of the total area segment.

Estimation of sensible and latent heat flux from natural sparse vegetation surfaces using surface renewal

NASA Astrophysics Data System (ADS)

Zapata, N.; Martínez-Cob, A.

2001-12-01

This paper reports a study undertaken to evaluate the feasibility of the surface renewal method to accurately estimate long-term evaporation from the playa and margins of an endorreic salty lagoon (Gallocanta lagoon, Spain) under semiarid conditions. High-frequency temperature readings were taken for two time lags ( r) and three measurement heights ( z) in order to get surface renewal sensible heat flux ( HSR) values. These values were compared against eddy covariance sensible heat flux ( HEC) values for a calibration period (25-30 July 2000). Error analysis statistics (index of agreement, IA; root mean square error, RMSE; and systematic mean square error, MSEs) showed that the agreement between HSR and HEC improved as measurement height decreased and time lag increased. Calibration factors α were obtained for all analyzed cases. The best results were obtained for the z=0.9 m ( r=0.75 s) case for which α=1.0 was observed. In this case, uncertainty was about 10% in terms of relative error ( RE). Latent heat flux values were obtained by solving the energy balance equation for both the surface renewal ( LESR) and the eddy covariance ( LEEC) methods, using HSR and HEC, respectively, and measurements of net radiation and soil heat flux. For the calibration period, error analysis statistics for LESR were quite similar to those for HSR, although errors were mostly at random. LESR uncertainty was less than 9%. Calibration factors were applied for a validation data subset (30 July-4 August 2000) for which meteorological conditions were somewhat different (higher temperatures and wind speed and lower solar and net radiation). Error analysis statistics for both HSR and LESR were quite good for all cases showing the goodness of the calibration factors. Nevertheless, the results obtained for the z=0.9 m ( r=0.75 s) case were still the best ones.

Data Fusion of Gridded Snow Products Enhanced with Terrain Covariates and a Simple Snow Model

NASA Astrophysics Data System (ADS)

Snauffer, A. M.; Hsieh, W. W.; Cannon, A. J.

2017-12-01

Hydrologic planning requires accurate estimates of regional snow water equivalent (SWE), particularly areas with hydrologic regimes dominated by spring melt. While numerous gridded data products provide such estimates, accurate representations are particularly challenging under conditions of mountainous terrain, heavy forest cover and large snow accumulations, contexts which in many ways define the province of British Columbia (BC), Canada. One promising avenue of improving SWE estimates is a data fusion approach which combines field observations with gridded SWE products and relevant covariates. A base artificial neural network (ANN) was constructed using three of the best performing gridded SWE products over BC (ERA-Interim/Land, MERRA and GLDAS-2) and simple location and time covariates. This base ANN was then enhanced to include terrain covariates (slope, aspect and Terrain Roughness Index, TRI) as well as a simple 1-layer energy balance snow model driven by gridded bias-corrected ANUSPLIN temperature and precipitation values. The ANN enhanced with all aforementioned covariates performed better than the base ANN, but most of the skill improvement was attributable to the snow model with very little contribution from the terrain covariates. The enhanced ANN improved station mean absolute error (MAE) by an average of 53% relative to the composing gridded products over the province. Interannual peak SWE correlation coefficient was found to be 0.78, an improvement of 0.05 to 0.18 over the composing products. This nonlinear approach outperformed a comparable multiple linear regression (MLR) model by 22% in MAE and 0.04 in interannual correlation. The enhanced ANN has also been shown to estimate better than the Variable Infiltration Capacity (VIC) hydrologic model calibrated and run for four BC watersheds, improving MAE by 22% and correlation by 0.05. The performance improvements of the enhanced ANN are statistically significant at the 5% level across the province and in four out of five physiographic regions.

Uncertainty information in climate data records from Earth observation

NASA Astrophysics Data System (ADS)

Merchant, C. J.

2017-12-01

How to derive and present uncertainty in climate data records (CDRs) has been debated within the European Space Agency Climate Change Initiative, in search of common principles applicable across a range of essential climate variables. Various points of consensus have been reached, including the importance of improving provision of uncertainty information and the benefit of adopting international norms of metrology for language around the distinct concepts of uncertainty and error. Providing an estimate of standard uncertainty per datum (or the means to readily calculate it) emerged as baseline good practice, and should be highly relevant to users of CDRs when the uncertainty in data is variable (the usual case). Given this baseline, the role of quality flags is clarified as being complementary to and not repetitive of uncertainty information. Data with high uncertainty are not poor quality if a valid estimate of the uncertainty is available. For CDRs and their applications, the error correlation properties across spatio-temporal scales present important challenges that are not fully solved. Error effects that are negligible in the uncertainty of a single pixel may dominate uncertainty in the large-scale and long-term. A further principle is that uncertainty estimates should themselves be validated. The concepts of estimating and propagating uncertainty are generally acknowledged in geophysical sciences, but less widely practised in Earth observation and development of CDRs. Uncertainty in a CDR depends in part (and usually significantly) on the error covariance of the radiances and auxiliary data used in the retrieval. Typically, error covariance information is not available in the fundamental CDR (FCDR) (i.e., with the level-1 radiances), since provision of adequate level-1 uncertainty information is not yet standard practice. Those deriving CDRs thus cannot propagate the radiance uncertainty to their geophysical products. The FIDUCEO project (www.fiduceo.eu) is demonstrating metrologically sound methodologies addressing this problem for four key historical CDRs. FIDUCEO methods of uncertainty analysis (which also tend to lead to improved FCDRs and CDRs) could support coherent treatment of uncertainty across FCDRs to CDRs and higher level products for a wide range of essential climate variables.

Tutorial on Biostatistics: Linear Regression Analysis of Continuous Correlated Eye Data.

PubMed

Ying, Gui-Shuang; Maguire, Maureen G; Glynn, Robert; Rosner, Bernard

2017-04-01

To describe and demonstrate appropriate linear regression methods for analyzing correlated continuous eye data. We describe several approaches to regression analysis involving both eyes, including mixed effects and marginal models under various covariance structures to account for inter-eye correlation. We demonstrate, with SAS statistical software, applications in a study comparing baseline refractive error between one eye with choroidal neovascularization (CNV) and the unaffected fellow eye, and in a study determining factors associated with visual field in the elderly. When refractive error from both eyes were analyzed with standard linear regression without accounting for inter-eye correlation (adjusting for demographic and ocular covariates), the difference between eyes with CNV and fellow eyes was 0.15 diopters (D; 95% confidence interval, CI -0.03 to 0.32D, p = 0.10). Using a mixed effects model or a marginal model, the estimated difference was the same but with narrower 95% CI (0.01 to 0.28D, p = 0.03). Standard regression for visual field data from both eyes provided biased estimates of standard error (generally underestimated) and smaller p-values, while analysis of the worse eye provided larger p-values than mixed effects models and marginal models. In research involving both eyes, ignoring inter-eye correlation can lead to invalid inferences. Analysis using only right or left eyes is valid, but decreases power. Worse-eye analysis can provide less power and biased estimates of effect. Mixed effects or marginal models using the eye as the unit of analysis should be used to appropriately account for inter-eye correlation and maximize power and precision.

Dynamic statistical optimization of GNSS radio occultation bending angles: advanced algorithm and performance analysis

NASA Astrophysics Data System (ADS)

Li, Y.; Kirchengast, G.; Scherllin-Pirscher, B.; Norman, R.; Yuan, Y. B.; Fritzer, J.; Schwaerz, M.; Zhang, K.

2015-08-01

We introduce a new dynamic statistical optimization algorithm to initialize ionosphere-corrected bending angles of Global Navigation Satellite System (GNSS)-based radio occultation (RO) measurements. The new algorithm estimates background and observation error covariance matrices with geographically varying uncertainty profiles and realistic global-mean correlation matrices. The error covariance matrices estimated by the new approach are more accurate and realistic than in simplified existing approaches and can therefore be used in statistical optimization to provide optimal bending angle profiles for high-altitude initialization of the subsequent Abel transform retrieval of refractivity. The new algorithm is evaluated against the existing Wegener Center Occultation Processing System version 5.6 (OPSv5.6) algorithm, using simulated data on two test days from January and July 2008 and real observed CHAllenging Minisatellite Payload (CHAMP) and Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) measurements from the complete months of January and July 2008. The following is achieved for the new method's performance compared to OPSv5.6: (1) significant reduction of random errors (standard deviations) of optimized bending angles down to about half of their size or more; (2) reduction of the systematic differences in optimized bending angles for simulated MetOp data; (3) improved retrieval of refractivity and temperature profiles; and (4) realistically estimated global-mean correlation matrices and realistic uncertainty fields for the background and observations. Overall the results indicate high suitability for employing the new dynamic approach in the processing of long-term RO data into a reference climate record, leading to well-characterized and high-quality atmospheric profiles over the entire stratosphere.

POWERLIB: SAS/IML Software for Computing Power in Multivariate Linear Models

PubMed Central

Johnson, Jacqueline L.; Muller, Keith E.; Slaughter, James C.; Gurka, Matthew J.; Gribbin, Matthew J.; Simpson, Sean L.

2014-01-01

The POWERLIB SAS/IML software provides convenient power calculations for a wide range of multivariate linear models with Gaussian errors. The software includes the Box, Geisser-Greenhouse, Huynh-Feldt, and uncorrected tests in the “univariate” approach to repeated measures (UNIREP), the Hotelling Lawley Trace, Pillai-Bartlett Trace, and Wilks Lambda tests in “multivariate” approach (MULTIREP), as well as a limited but useful range of mixed models. The familiar univariate linear model with Gaussian errors is an important special case. For estimated covariance, the software provides confidence limits for the resulting estimated power. All power and confidence limits values can be output to a SAS dataset, which can be used to easily produce plots and tables for manuscripts. PMID:25400516

On the Use, the Misuse, and the Very Limited Usefulness of Cronbach's Alpha

ERIC Educational Resources Information Center

Sijtsma, Klaas

2009-01-01

This discussion paper argues that both the use of Cronbach's alpha as a reliability estimate and as a measure of internal consistency suffer from major problems. First, alpha always has a value, which cannot be equal to the test score's reliability given the inter-item covariance matrix and the usual assumptions about measurement error. Second, in…

Using Propensity Score Matching Methods to Improve Generalization from Randomized Experiments

ERIC Educational Resources Information Center

Tipton, Elizabeth

2011-01-01

The main result of an experiment is typically an estimate of the average treatment effect (ATE) and its standard error. In most experiments, the number of covariates that may be moderators is large. One way this issue is typically skirted is by interpreting the ATE as the average effect for "some" population. Cornfield and Tukey (1956)…

Resampling-based Methods in Single and Multiple Testing for Equality of Covariance/Correlation Matrices

PubMed Central

Yang, Yang; DeGruttola, Victor

2016-01-01

Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by group sample means and standardized by group sample covariance matrices. This approach, however, has been observed to inflate type I error when sample size is small or data are generated from heavy-tailed distributions. We propose to improve this approach by using robust estimation for the first and second moments. We discuss two statistics: the Bartlett statistic and a statistic based on eigen-decomposition of sample covariance matrices. Both statistics can be expressed in terms of standardized errors under the null hypothesis. These methods are extended to test homogeneity in correlation matrices. Using simulation studies, we demonstrate that the robust resampling approach provides comparable or superior performance, relative to traditional approaches, for single testing and reasonable performance for multiple testing. The proposed methods are applied to data collected in an HIV vaccine trial to investigate possible determinants, including vaccine status, vaccine-induced immune response level and viral genotype, of unusual correlation pattern between HIV viral load and CD4 count in newly infected patients. PMID:22740584

Resampling-based methods in single and multiple testing for equality of covariance/correlation matrices.

PubMed

Yang, Yang; DeGruttola, Victor

2012-06-22

Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by group sample means and standardized by group sample covariance matrices. This approach, however, has been observed to inflate type I error when sample size is small or data are generated from heavy-tailed distributions. We propose to improve this approach by using robust estimation for the first and second moments. We discuss two statistics: the Bartlett statistic and a statistic based on eigen-decomposition of sample covariance matrices. Both statistics can be expressed in terms of standardized errors under the null hypothesis. These methods are extended to test homogeneity in correlation matrices. Using simulation studies, we demonstrate that the robust resampling approach provides comparable or superior performance, relative to traditional approaches, for single testing and reasonable performance for multiple testing. The proposed methods are applied to data collected in an HIV vaccine trial to investigate possible determinants, including vaccine status, vaccine-induced immune response level and viral genotype, of unusual correlation pattern between HIV viral load and CD4 count in newly infected patients.

Statistics of the residual refraction errors in laser ranging data

NASA Technical Reports Server (NTRS)

Gardner, C. S.

1977-01-01

A theoretical model for the range error covariance was derived by assuming that the residual refraction errors are due entirely to errors in the meteorological data which are used to calculate the atmospheric correction. The properties of the covariance function are illustrated by evaluating the theoretical model for the special case of a dense network of weather stations uniformly distributed within a circle.

Sensitivity of regression calibration to non-perfect validation data with application to the Norwegian Women and Cancer Study.

PubMed

Buonaccorsi, John P; Dalen, Ingvild; Laake, Petter; Hjartåker, Anette; Engeset, Dagrun; Thoresen, Magne

2015-04-15

Measurement error occurs when we observe error-prone surrogates, rather than true values. It is common in observational studies and especially so in epidemiology, in nutritional epidemiology in particular. Correcting for measurement error has become common, and regression calibration is the most popular way to account for measurement error in continuous covariates. We consider its use in the context where there are validation data, which are used to calibrate the true values given the observed covariates. We allow for the case that the true value itself may not be observed in the validation data, but instead, a so-called reference measure is observed. The regression calibration method relies on certain assumptions.This paper examines possible biases in regression calibration estimators when some of these assumptions are violated. More specifically, we allow for the fact that (i) the reference measure may not necessarily be an 'alloyed gold standard' (i.e., unbiased) for the true value; (ii) there may be correlated random subject effects contributing to the surrogate and reference measures in the validation data; and (iii) the calibration model itself may not be the same in the validation study as in the main study; that is, it is not transportable. We expand on previous work to provide a general result, which characterizes potential bias in the regression calibration estimators as a result of any combination of the violations aforementioned. We then illustrate some of the general results with data from the Norwegian Women and Cancer Study. Copyright © 2015 John Wiley & Sons, Ltd.

Causal Inference for fMRI Time Series Data with Systematic Errors of Measurement in a Balanced On/Off Study of Social Evaluative Threat.

PubMed

Sobel, Michael E; Lindquist, Martin A

2014-07-01

Functional magnetic resonance imaging (fMRI) has facilitated major advances in understanding human brain function. Neuroscientists are interested in using fMRI to study the effects of external stimuli on brain activity and causal relationships among brain regions, but have not stated what is meant by causation or defined the effects they purport to estimate. Building on Rubin's causal model, we construct a framework for causal inference using blood oxygenation level dependent (BOLD) fMRI time series data. In the usual statistical literature on causal inference, potential outcomes, assumed to be measured without systematic error, are used to define unit and average causal effects. However, in general the potential BOLD responses are measured with stimulus dependent systematic error. Thus we define unit and average causal effects that are free of systematic error. In contrast to the usual case of a randomized experiment where adjustment for intermediate outcomes leads to biased estimates of treatment effects (Rosenbaum, 1984), here the failure to adjust for task dependent systematic error leads to biased estimates. We therefore adjust for systematic error using measured "noise covariates" , using a linear mixed model to estimate the effects and the systematic error. Our results are important for neuroscientists, who typically do not adjust for systematic error. They should also prove useful to researchers in other areas where responses are measured with error and in fields where large amounts of data are collected on relatively few subjects. To illustrate our approach, we re-analyze data from a social evaluative threat task, comparing the findings with results that ignore systematic error.

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

PubMed Central

Cohen, E. A. K.; Ober, R. J.

2014-01-01

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data. PMID:24634573

Accounting for the measurement error of spectroscopically inferred soil carbon data for improved precision of spatial predictions.

PubMed

Somarathna, P D S N; Minasny, Budiman; Malone, Brendan P; Stockmann, Uta; McBratney, Alex B

2018-08-01

Spatial modelling of environmental data commonly only considers spatial variability as the single source of uncertainty. In reality however, the measurement errors should also be accounted for. In recent years, infrared spectroscopy has been shown to offer low cost, yet invaluable information needed for digital soil mapping at meaningful spatial scales for land management. However, spectrally inferred soil carbon data are known to be less accurate compared to laboratory analysed measurements. This study establishes a methodology to filter out the measurement error variability by incorporating the measurement error variance in the spatial covariance structure of the model. The study was carried out in the Lower Hunter Valley, New South Wales, Australia where a combination of laboratory measured, and vis-NIR and MIR inferred topsoil and subsoil soil carbon data are available. We investigated the applicability of residual maximum likelihood (REML) and Markov Chain Monte Carlo (MCMC) simulation methods to generate parameters of the Matérn covariance function directly from the data in the presence of measurement error. The results revealed that the measurement error can be effectively filtered-out through the proposed technique. When the measurement error was filtered from the data, the prediction variance almost halved, which ultimately yielded a greater certainty in spatial predictions of soil carbon. Further, the MCMC technique was successfully used to define the posterior distribution of measurement error. This is an important outcome, as the MCMC technique can be used to estimate the measurement error if it is not explicitly quantified. Although this study dealt with soil carbon data, this method is amenable for filtering the measurement error of any kind of continuous spatial environmental data. Copyright © 2018 Elsevier B.V. All rights reserved.

A Semiparametric Change-Point Regression Model for Longitudinal Observations.

PubMed

Xing, Haipeng; Ying, Zhiliang

2012-12-01

Many longitudinal studies involve relating an outcome process to a set of possibly time-varying covariates, giving rise to the usual regression models for longitudinal data. When the purpose of the study is to investigate the covariate effects when experimental environment undergoes abrupt changes or to locate the periods with different levels of covariate effects, a simple and easy-to-interpret approach is to introduce change-points in regression coefficients. In this connection, we propose a semiparametric change-point regression model, in which the error process (stochastic component) is nonparametric and the baseline mean function (functional part) is completely unspecified, the observation times are allowed to be subject-specific, and the number, locations and magnitudes of change-points are unknown and need to be estimated. We further develop an estimation procedure which combines the recent advance in semiparametric analysis based on counting process argument and multiple change-points inference, and discuss its large sample properties, including consistency and asymptotic normality, under suitable regularity conditions. Simulation results show that the proposed methods work well under a variety of scenarios. An application to a real data set is also given.

Multivariate localization methods for ensemble Kalman filtering

NASA Astrophysics Data System (ADS)

Roh, S.; Jun, M.; Szunyogh, I.; Genton, M. G.

2015-12-01

In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (element-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables that exist at the same locations has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help.

Maximum likelihood techniques applied to quasi-elastic light scattering

NASA Technical Reports Server (NTRS)

Edwards, Robert V.

1992-01-01

There is a necessity of having an automatic procedure for reliable estimation of the quality of the measurement of particle size from QELS (Quasi-Elastic Light Scattering). Getting the measurement itself, before any error estimates can be made, is a problem because it is obtained by a very indirect measurement of a signal derived from the motion of particles in the system and requires the solution of an inverse problem. The eigenvalue structure of the transform that generates the signal is such that an arbitrarily small amount of noise can obliterate parts of any practical inversion spectrum. This project uses the Maximum Likelihood Estimation (MLE) as a framework to generate a theory and a functioning set of software to oversee the measurement process and extract the particle size information, while at the same time providing error estimates for those measurements. The theory involved verifying a correct form of the covariance matrix for the noise on the measurement and then estimating particle size parameters using a modified histogram approach.

The ITSG-Grace2014 Gravity Field Model

NASA Astrophysics Data System (ADS)

Kvas, Andreas; Mayer-Gürr, Torsten; Zehenter, Norbert; Klinger, Beate

2015-04-01

The ITSG-Grace2014 GRACE-only gravity field model consists of a high resolution unconstrained static model (up to degree 200) with trend and annual signal, monthly unconstrained solutions with different spatial resolutions as well as daily snapshots derived by using a Kalman smoother. Apart from the estimated spherical harmonic coefficients, full variance-covariance matrices for the monthly solutions and the static gravity field component are provided. Compared to the previous release, multiple improvements in the processing chain are implemented: updated background models, better ionospheric modeling for GPS observations, an improved satellite attitude by combination of star camera and angular accelerations, estimation of K-band antenna center variations within the gravity field recovery process as well as error covariance function determination. Furthermore, daily gravity field variations have been modeled in the adjustment process to reduce errors caused by temporal leakage. This combined estimation of daily gravity variations field variations together with the static gravity field component represents a computational challenge due to the significantly increased parameter count. The modeling of daily variations up to a spherical harmonic degree of 40 for the whole GRACE observation period results in a system of linear equations with over 6 million unknown gravity field parameters. A least squares adjustment of this size is not solvable in a sensible time frame, therefore measures to reduce the problem size have to be taken. The ITSG-Grace2014 release is presented and selected parts of the processing chain and their effect on the estimated gravity field solutions are discussed.

Highlights of TOMS Version 9 Total Ozone Algorithm

NASA Technical Reports Server (NTRS)

Bhartia, Pawan; Haffner, David

2012-01-01

The fundamental basis of TOMS total ozone algorithm was developed some 45 years ago by Dave and Mateer. It was designed to estimate total ozone from satellite measurements of the backscattered UV radiances at few discrete wavelengths in the Huggins ozone absorption band (310-340 nm). Over the years, as the need for higher accuracy in measuring total ozone from space has increased, several improvements to the basic algorithms have been made. They include: better correction for the effects of aerosols and clouds, an improved method to account for the variation in shape of ozone profiles with season, latitude, and total ozone, and a multi-wavelength correction for remaining profile shape errors. These improvements have made it possible to retrieve total ozone with just 3 spectral channels of moderate spectral resolution (approx. 1 nm) with accuracy comparable to state-of-the-art spectral fitting algorithms like DOAS that require high spectral resolution measurements at large number of wavelengths. One of the deficiencies of the TOMS algorithm has been that it doesn't provide an error estimate. This is a particular problem in high latitudes when the profile shape errors become significant and vary with latitude, season, total ozone, and instrument viewing geometry. The primary objective of the TOMS V9 algorithm is to account for these effects in estimating the error bars. This is done by a straightforward implementation of the Rodgers optimum estimation method using a priori ozone profiles and their error covariances matrices constructed using Aura MLS and ozonesonde data. The algorithm produces a vertical ozone profile that contains 1-2.5 pieces of information (degrees of freedom of signal) depending upon solar zenith angle (SZA). The profile is integrated to obtain the total column. We provide information that shows the altitude range in which the profile is best determined by the measurements. One can use this information in data assimilation and analysis. A side benefit of this algorithm is that it is considerably simpler than the present algorithm that uses a database of 1512 profiles to retrieve total ozone. These profiles are tedious to construct and modify. Though conceptually similar to the SBUV V8 algorithm that was developed about a decade ago, the SBUV and TOMS V9 algorithms differ in detail. The TOMS algorithm uses 3 wavelengths to retrieve the profile while the SBUV algorithm uses 6-9 wavelengths, so TOMS provides less profile information. However both algorithms have comparable total ozone information and TOMS V9 can be easily adapted to use additional wavelengths from instruments like GOME, OMI and OMPS to provide better profile information at smaller SZAs. The other significant difference between the two algorithms is that while the SBUV algorithm has been optimized for deriving monthly zonal means by making an appropriate choice of the a priori error covariance matrix, the TOMS algorithm has been optimized for tracking short-term variability using month and latitude dependent covariance matrices.

Iowa radon leukaemia study: a hierarchical population risk model for spatially correlated exposure measured with error.

PubMed

Smith, Brian J; Zhang, Lixun; Field, R William

2007-11-10

This paper presents a Bayesian model that allows for the joint prediction of county-average radon levels and estimation of the associated leukaemia risk. The methods are motivated by radon data from an epidemiologic study of residential radon in Iowa that include 2726 outdoor and indoor measurements. Prediction of county-average radon is based on a geostatistical model for the radon data which assumes an underlying continuous spatial process. In the radon model, we account for uncertainties due to incomplete spatial coverage, spatial variability, characteristic differences between homes, and detector measurement error. The predicted radon averages are, in turn, included as a covariate in Poisson models for incident cases of acute lymphocytic (ALL), acute myelogenous (AML), chronic lymphocytic (CLL), and chronic myelogenous (CML) leukaemias reported to the Iowa cancer registry from 1973 to 2002. Since radon and leukaemia risk are modelled simultaneously in our approach, the resulting risk estimates accurately reflect uncertainties in the predicted radon exposure covariate. Posterior mean (95 per cent Bayesian credible interval) estimates of the relative risk associated with a 1 pCi/L increase in radon for ALL, AML, CLL, and CML are 0.91 (0.78-1.03), 1.01 (0.92-1.12), 1.06 (0.96-1.16), and 1.12 (0.98-1.27), respectively. Copyright 2007 John Wiley & Sons, Ltd.

An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model

NASA Technical Reports Server (NTRS)

Fukumori, Ichiro; Malanotte-Rizzoli, Paola

1995-01-01

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximation of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

Spatial measurement error and correction by spatial SIMEX in linear regression models when using predicted air pollution exposures.

PubMed

Alexeeff, Stacey E; Carroll, Raymond J; Coull, Brent

2016-04-01

Spatial modeling of air pollution exposures is widespread in air pollution epidemiology research as a way to improve exposure assessment. However, there are key sources of exposure model uncertainty when air pollution is modeled, including estimation error and model misspecification. We examine the use of predicted air pollution levels in linear health effect models under a measurement error framework. For the prediction of air pollution exposures, we consider a universal Kriging framework, which may include land-use regression terms in the mean function and a spatial covariance structure for the residuals. We derive the bias induced by estimation error and by model misspecification in the exposure model, and we find that a misspecified exposure model can induce asymptotic bias in the effect estimate of air pollution on health. We propose a new spatial simulation extrapolation (SIMEX) procedure, and we demonstrate that the procedure has good performance in correcting this asymptotic bias. We illustrate spatial SIMEX in a study of air pollution and birthweight in Massachusetts. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model

NASA Astrophysics Data System (ADS)

Fukumori, Ichiro; Malanotte-Rizzoli, Paola

1995-04-01

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kaiman filter based on approximations of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

Optimal interpolation schemes to constrain pmPM2.5 in regional modeling over the United States

NASA Astrophysics Data System (ADS)

Sousan, Sinan Dhia Jameel

This thesis presents the use of data assimilation with optimal interpolation (OI) to develop atmospheric aerosol concentration estimates for the United States at high spatial and temporal resolutions. Concentration estimates are highly desirable for a wide range of applications, including visibility, climate, and human health. OI is a viable data assimilation method that can be used to improve Community Multiscale Air Quality (CMAQ) model fine particulate matter (PM2.5) estimates. PM2.5 is the mass of solid and liquid particles with diameters less than or equal to 2.5 µm suspended in the gas phase. OI was employed by combining model estimates with satellite and surface measurements. The satellite data assimilation combined 36 x 36 km aerosol concentrations from CMAQ with aerosol optical depth (AOD) measured by MODIS and AERONET over the continental United States for 2002. Posterior model concentrations generated by the OI algorithm were compared with surface PM2.5 measurements to evaluate a number of possible data assimilation parameters, including model error, observation error, and temporal averaging assumptions. Evaluation was conducted separately for six geographic U.S. regions in 2002. Variability in model error and MODIS biases limited the effectiveness of a single data assimilation system for the entire continental domain. The best combinations of four settings and three averaging schemes led to a domain-averaged improvement in fractional error from 1.2 to 0.97 and from 0.99 to 0.89 at respective IMPROVE and STN monitoring sites. For 38% of OI results, MODIS OI degraded the forward model skill due to biases and outliers in MODIS AOD. Surface data assimilation combined 36 × 36 km aerosol concentrations from the CMAQ model with surface PM2.5 measurements over the continental United States for 2002. The model error covariance matrix was constructed by using the observational method. The observation error covariance matrix included site representation that scaled the observation error by land use (i.e. urban or rural locations). In theory, urban locations should have less effect on surrounding areas than rural sites, which can be controlled using site representation error. The annual evaluations showed substantial improvements in model performance with increases in the correlation coefficient from 0.36 (prior) to 0.76 (posterior), and decreases in the fractional error from 0.43 (prior) to 0.15 (posterior). In addition, the normalized mean error decreased from 0.36 (prior) to 0.13 (posterior), and the RMSE decreased from 5.39 µg m-3 (prior) to 2.32 µg m-3 (posterior). OI decreased model bias for both large spatial areas and point locations, and could be extended to more advanced data assimilation methods. The current work will be applied to a five year (2000-2004) CMAQ simulation aimed at improving aerosol model estimates. The posterior model concentrations will be used to inform exposure studies over the U.S. that relate aerosol exposure to mortality and morbidity rates. Future improvements for the OI techniques used in the current study will include combining both surface and satellite data to improve posterior model estimates. Satellite data have high spatial and temporal resolutions in comparison to surface measurements, which are scarce but more accurate than model estimates. The satellite data are subject to noise affected by location and season of retrieval. The implementation of OI to combine satellite and surface data sets has the potential to improve posterior model estimates for locations that have no direct measurements.

Evaluation of subset matching methods and forms of covariate balance.

PubMed

de Los Angeles Resa, María; Zubizarreta, José R

2016-11-30

This paper conducts a Monte Carlo simulation study to evaluate the performance of multivariate matching methods that select a subset of treatment and control observations. The matching methods studied are the widely used nearest neighbor matching with propensity score calipers and the more recently proposed methods, optimal matching of an optimally chosen subset and optimal cardinality matching. The main findings are: (i) covariate balance, as measured by differences in means, variance ratios, Kolmogorov-Smirnov distances, and cross-match test statistics, is better with cardinality matching because by construction it satisfies balance requirements; (ii) for given levels of covariate balance, the matched samples are larger with cardinality matching than with the other methods; (iii) in terms of covariate distances, optimal subset matching performs best; (iv) treatment effect estimates from cardinality matching have lower root-mean-square errors, provided strong requirements for balance, specifically, fine balance, or strength-k balance, plus close mean balance. In standard practice, a matched sample is considered to be balanced if the absolute differences in means of the covariates across treatment groups are smaller than 0.1 standard deviations. However, the simulation results suggest that stronger forms of balance should be pursued in order to remove systematic biases due to observed covariates when a difference in means treatment effect estimator is used. In particular, if the true outcome model is additive, then marginal distributions should be balanced, and if the true outcome model is additive with interactions, then low-dimensional joints should be balanced. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Addressing data privacy in matched studies via virtual pooling.

PubMed

Saha-Chaudhuri, P; Weinberg, C R

2017-09-07

Data confidentiality and shared use of research data are two desirable but sometimes conflicting goals in research with multi-center studies and distributed data. While ideal for straightforward analysis, confidentiality restrictions forbid creation of a single dataset that includes covariate information of all participants. Current approaches such as aggregate data sharing, distributed regression, meta-analysis and score-based methods can have important limitations. We propose a novel application of an existing epidemiologic tool, specimen pooling, to enable confidentiality-preserving analysis of data arising from a matched case-control, multi-center design. Instead of pooling specimens prior to assay, we apply the methodology to virtually pool (aggregate) covariates within nodes. Such virtual pooling retains most of the information used in an analysis with individual data and since individual participant data is not shared externally, within-node virtual pooling preserves data confidentiality. We show that aggregated covariate levels can be used in a conditional logistic regression model to estimate individual-level odds ratios of interest. The parameter estimates from the standard conditional logistic regression are compared to the estimates based on a conditional logistic regression model with aggregated data. The parameter estimates are shown to be similar to those without pooling and to have comparable standard errors and confidence interval coverage. Virtual data pooling can be used to maintain confidentiality of data from multi-center study and can be particularly useful in research with large-scale distributed data.

Optimal Estimation of Clock Values and Trends from Finite Data

NASA Technical Reports Server (NTRS)

Greenhall, Charles

2005-01-01

We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.

Hyper-X Post-Flight Trajectory Reconstruction

NASA Technical Reports Server (NTRS)

Karlgaard, Christopher D.; Tartabini, Paul V.; Blanchard, RobertC.; Kirsch, Michael; Toniolo, Matthew D.

2004-01-01

This paper discusses the formulation and development of a trajectory reconstruction tool for the NASA X{43A/Hyper{X high speed research vehicle, and its implementation for the reconstruction and analysis of ight test data. Extended Kalman ltering techniques are employed to reconstruct the trajectory of the vehicle, based upon numerical integration of inertial measurement data along with redundant measurements of the vehicle state. The equations of motion are formulated in order to include the effects of several systematic error sources, whose values may also be estimated by the ltering routines. Additionally, smoothing algorithms have been implemented in which the nal value of the state (or an augmented state that includes other systematic error parameters to be estimated) and covariance are propagated back to the initial time to generate the best-estimated trajectory, based upon all available data. The methods are applied to the problem of reconstructing the trajectory of the Hyper-X vehicle from ight data.

A simulation study to quantify the impacts of exposure ...

EPA Pesticide Factsheets

BackgroundExposure measurement error in copollutant epidemiologic models has the potential to introduce bias in relative risk (RR) estimates. A simulation study was conducted using empirical data to quantify the impact of correlated measurement errors in time-series analyses of air pollution and health.MethodsZIP-code level estimates of exposure for six pollutants (CO, NOx, EC, PM2.5, SO4, O3) from 1999 to 2002 in the Atlanta metropolitan area were used to calculate spatial, population (i.e. ambient versus personal), and total exposure measurement error.Empirically determined covariance of pollutant concentration pairs and the associated measurement errors were used to simulate true exposure (exposure without error) from observed exposure. Daily emergency department visits for respiratory diseases were simulated using a Poisson time-series model with a main pollutant RR = 1.05 per interquartile range, and a null association for the copollutant (RR = 1). Monte Carlo experiments were used to evaluate the impacts of correlated exposure errors of different copollutant pairs.ResultsSubstantial attenuation of RRs due to exposure error was evident in nearly all copollutant pairs studied, ranging from 10 to 40% attenuation for spatial error, 3–85% for population error, and 31–85% for total error. When CO, NOx or EC is the main pollutant, we demonstrated the possibility of false positives, specifically identifying significant, positive associations for copoll

Algorithm for pose estimation based on objective function with uncertainty-weighted measuring error of feature point cling to the curved surface.

PubMed

Huo, Ju; Zhang, Guiyang; Yang, Ming

2018-04-20

This paper is concerned with the anisotropic and non-identical gray distribution of feature points clinging to the curved surface, upon which a high precision and uncertainty-resistance algorithm for pose estimation is proposed. Weighted contribution of uncertainty to the objective function of feature points measuring error is analyzed. Then a novel error objective function based on the spatial collinear error is constructed by transforming the uncertainty into a covariance-weighted matrix, which is suitable for the practical applications. Further, the optimized generalized orthogonal iterative (GOI) algorithm is utilized for iterative solutions such that it avoids the poor convergence and significantly resists the uncertainty. Hence, the optimized GOI algorithm extends the field-of-view applications and improves the accuracy and robustness of the measuring results by the redundant information. Finally, simulation and practical experiments show that the maximum error of re-projection image coordinates of the target is less than 0.110 pixels. Within the space 3000  mm×3000  mm×4000  mm, the maximum estimation errors of static and dynamic measurement for rocket nozzle motion are superior to 0.065° and 0.128°, respectively. Results verify the high accuracy and uncertainty attenuation performance of the proposed approach and should therefore have potential for engineering applications.

An iteratively reweighted least-squares approach to adaptive robust adjustment of parameters in linear regression models with autoregressive and t-distributed deviations

NASA Astrophysics Data System (ADS)

Kargoll, Boris; Omidalizarandi, Mohammad; Loth, Ina; Paffenholz, Jens-André; Alkhatib, Hamza

2018-03-01

In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student's) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.

Cooperative Robot Localization Using Event-Triggered Estimation

NASA Astrophysics Data System (ADS)

Iglesias Echevarria, David I.

It is known that multiple robot systems that need to cooperate to perform certain activities or tasks incur in high energy costs that hinder their autonomous functioning and limit the benefits provided to humans by these kinds of platforms. This work presents a communications-based method for cooperative robot localization. Implementing concepts from event-triggered estimation, used with success in the field of wireless sensor networks but rarely to do robot localization, agents are able to only send measurements to their neighbors when the expected novelty in this information is high. Since all agents know the condition that triggers a measurement to be sent or not, the lack of a measurement is therefore informative and fused into state estimates. In the case agents do not receive either direct nor indirect measurements of all others, the agents employ a covariance intersection fusion rule in order to keep the local covariance error metric bounded. A comprehensive analysis of the proposed algorithm and its estimation performance in a variety of scenarios is performed, and the algorithm is compared to similar cooperative localization approaches. Extensive simulations are performed that illustrate the effectiveness of this method.

Outcome modelling strategies in epidemiology: traditional methods and basic alternatives

PubMed Central

Greenland, Sander; Daniel, Rhian; Pearce, Neil

2016-01-01

Abstract Controlling for too many potential confounders can lead to or aggravate problems of data sparsity or multicollinearity, particularly when the number of covariates is large in relation to the study size. As a result, methods to reduce the number of modelled covariates are often deployed. We review several traditional modelling strategies, including stepwise regression and the ‘change-in-estimate’ (CIE) approach to deciding which potential confounders to include in an outcome-regression model for estimating effects of a targeted exposure. We discuss their shortcomings, and then provide some basic alternatives and refinements that do not require special macros or programming. Throughout, we assume the main goal is to derive the most accurate effect estimates obtainable from the data and commercial software. Allowing that most users must stay within standard software packages, this goal can be roughly approximated using basic methods to assess, and thereby minimize, mean squared error (MSE). PMID:27097747

A minimalist approach to bias estimation for passive sensor measurements with targets of opportunity

NASA Astrophysics Data System (ADS)

Belfadel, Djedjiga; Osborne, Richard W.; Bar-Shalom, Yaakov

2013-09-01

In order to carry out data fusion, registration error correction is crucial in multisensor systems. This requires estimation of the sensor measurement biases. It is important to correct for these bias errors so that the multiple sensor measurements and/or tracks can be referenced as accurately as possible to a common tracking coordinate system. This paper provides a solution for bias estimation for the minimum number of passive sensors (two), when only targets of opportunity are available. The sensor measurements are assumed time-coincident (synchronous) and perfectly associated. Since these sensors provide only line of sight (LOS) measurements, the formation of a single composite Cartesian measurement obtained from fusing the LOS measurements from different sensors is needed to avoid the need for nonlinear filtering. We evaluate the Cramer-Rao Lower Bound (CRLB) on the covariance of the bias estimate, i.e., the quantification of the available information about the biases. Statistical tests on the results of simulations show that this method is statistically efficient, even for small sample sizes (as few as two sensors and six points on the trajectory of a single target of opportunity). We also show that the RMS position error is significantly improved with bias estimation compared with the target position estimation using the original biased measurements.

Evaluating uses of data mining techniques in propensity score estimation: a simulation study.

PubMed

Setoguchi, Soko; Schneeweiss, Sebastian; Brookhart, M Alan; Glynn, Robert J; Cook, E Francis

2008-06-01

In propensity score modeling, it is a standard practice to optimize the prediction of exposure status based on the covariate information. In a simulation study, we examined in what situations analyses based on various types of exposure propensity score (EPS) models using data mining techniques such as recursive partitioning (RP) and neural networks (NN) produce unbiased and/or efficient results. We simulated data for a hypothetical cohort study (n = 2000) with a binary exposure/outcome and 10 binary/continuous covariates with seven scenarios differing by non-linear and/or non-additive associations between exposure and covariates. EPS models used logistic regression (LR) (all possible main effects), RP1 (without pruning), RP2 (with pruning), and NN. We calculated c-statistics (C), standard errors (SE), and bias of exposure-effect estimates from outcome models for the PS-matched dataset. Data mining techniques yielded higher C than LR (mean: NN, 0.86; RPI, 0.79; RP2, 0.72; and LR, 0.76). SE tended to be greater in models with higher C. Overall bias was small for each strategy, although NN estimates tended to be the least biased. C was not correlated with the magnitude of bias (correlation coefficient [COR] = -0.3, p = 0.1) but increased SE (COR = 0.7, p < 0.001). Effect estimates from EPS models by simple LR were generally robust. NN models generally provided the least numerically biased estimates. C was not associated with the magnitude of bias but was with the increased SE.

Mixtures of Berkson and classical covariate measurement error in the linear mixed model: Bias analysis and application to a study on ultrafine particles.

PubMed

Deffner, Veronika; Küchenhoff, Helmut; Breitner, Susanne; Schneider, Alexandra; Cyrys, Josef; Peters, Annette

2018-05-01

The ultrafine particle measurements in the Augsburger Umweltstudie, a panel study conducted in Augsburg, Germany, exhibit measurement error from various sources. Measurements of mobile devices show classical possibly individual-specific measurement error; Berkson-type error, which may also vary individually, occurs, if measurements of fixed monitoring stations are used. The combination of fixed site and individual exposure measurements results in a mixture of the two error types. We extended existing bias analysis approaches to linear mixed models with a complex error structure including individual-specific error components, autocorrelated errors, and a mixture of classical and Berkson error. Theoretical considerations and simulation results show, that autocorrelation may severely change the attenuation of the effect estimations. Furthermore, unbalanced designs and the inclusion of confounding variables influence the degree of attenuation. Bias correction with the method of moments using data with mixture measurement error partially yielded better results compared to the usage of incomplete data with classical error. Confidence intervals (CIs) based on the delta method achieved better coverage probabilities than those based on Bootstrap samples. Moreover, we present the application of these new methods to heart rate measurements within the Augsburger Umweltstudie: the corrected effect estimates were slightly higher than their naive equivalents. The substantial measurement error of ultrafine particle measurements has little impact on the results. The developed methodology is generally applicable to longitudinal data with measurement error. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Tutorial on Biostatistics: Linear Regression Analysis of Continuous Correlated Eye Data

PubMed Central

Ying, Gui-shuang; Maguire, Maureen G; Glynn, Robert; Rosner, Bernard

2017-01-01

Purpose To describe and demonstrate appropriate linear regression methods for analyzing correlated continuous eye data. Methods We describe several approaches to regression analysis involving both eyes, including mixed effects and marginal models under various covariance structures to account for inter-eye correlation. We demonstrate, with SAS statistical software, applications in a study comparing baseline refractive error between one eye with choroidal neovascularization (CNV) and the unaffected fellow eye, and in a study determining factors associated with visual field data in the elderly. Results When refractive error from both eyes were analyzed with standard linear regression without accounting for inter-eye correlation (adjusting for demographic and ocular covariates), the difference between eyes with CNV and fellow eyes was 0.15 diopters (D; 95% confidence interval, CI −0.03 to 0.32D, P=0.10). Using a mixed effects model or a marginal model, the estimated difference was the same but with narrower 95% CI (0.01 to 0.28D, P=0.03). Standard regression for visual field data from both eyes provided biased estimates of standard error (generally underestimated) and smaller P-values, while analysis of the worse eye provided larger P-values than mixed effects models and marginal models. Conclusion In research involving both eyes, ignoring inter-eye correlation can lead to invalid inferences. Analysis using only right or left eyes is valid, but decreases power. Worse-eye analysis can provide less power and biased estimates of effect. Mixed effects or marginal models using the eye as the unit of analysis should be used to appropriately account for inter-eye correlation and maximize power and precision. PMID:28102741

How large are the consequences of covariate imbalance in cluster randomized trials: a simulation study with a continuous outcome and a binary covariate at the cluster level.

PubMed

Moerbeek, Mirjam; van Schie, Sander

2016-07-11

The number of clusters in a cluster randomized trial is often low. It is therefore likely random assignment of clusters to treatment conditions results in covariate imbalance. There are no studies that quantify the consequences of covariate imbalance in cluster randomized trials on parameter and standard error bias and on power to detect treatment effects. The consequences of covariance imbalance in unadjusted and adjusted linear mixed models are investigated by means of a simulation study. The factors in this study are the degree of imbalance, the covariate effect size, the cluster size and the intraclass correlation coefficient. The covariate is binary and measured at the cluster level; the outcome is continuous and measured at the individual level. The results show covariate imbalance results in negligible parameter bias and small standard error bias in adjusted linear mixed models. Ignoring the possibility of covariate imbalance while calculating the sample size at the cluster level may result in a loss in power of at most 25 % in the adjusted linear mixed model. The results are more severe for the unadjusted linear mixed model: parameter biases up to 100 % and standard error biases up to 200 % may be observed. Power levels based on the unadjusted linear mixed model are often too low. The consequences are most severe for large clusters and/or small intraclass correlation coefficients since then the required number of clusters to achieve a desired power level is smallest. The possibility of covariate imbalance should be taken into account while calculating the sample size of a cluster randomized trial. Otherwise more sophisticated methods to randomize clusters to treatments should be used, such as stratification or balance algorithms. All relevant covariates should be carefully identified, be actually measured and included in the statistical model to avoid severe levels of parameter and standard error bias and insufficient power levels.

Benefits Derived From Laser Ranging Measurements for Orbit Determination of the GPS Satellite Orbit

NASA Technical Reports Server (NTRS)

Welch, Bryan W.

2007-01-01

While navigation systems for the determination of the orbit of the Global Position System (GPS) have proven to be very effective, the current research is examining methods to lower the error in the GPS satellite ephemerides below their current level. Two GPS satellites that are currently in orbit carry retro-reflectors onboard. One notion to reduce the error in the satellite ephemerides is to utilize the retro-reflectors via laser ranging measurements taken from multiple Earth ground stations. Analysis has been performed to determine the level of reduction in the semi-major axis covariance of the GPS satellites, when laser ranging measurements are supplemented to the radiometric station keeping, which the satellites undergo. Six ground tracking systems are studied to estimate the performance of the satellite. The first system is the baseline current system approach which provides pseudo-range and integrated Doppler measurements from six ground stations. The remaining five ground tracking systems utilize all measurements from the current system and laser ranging measurements from the additional ground stations utilized within those systems. Station locations for the additional ground sites were taken from a listing of laser ranging ground stations from the International Laser Ranging Service. Results show reductions in state covariance estimates when utilizing laser ranging measurements to solve for the satellite s position component of the state vector. Results also show dependency on the number of ground stations providing laser ranging measurements, orientation of the satellite to the ground stations, and the initial covariance of the satellite's state vector.

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

NASA Technical Reports Server (NTRS)

Garrison, James L.; Axelrod, Penina; Kasdin, N. Jeremy

1997-01-01

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Mars approach navigation using Doppler and range measurements to surface beacons and orbiting spacecraft

NASA Technical Reports Server (NTRS)

Thurman, Sam W.; Estefan, Jeffrey A.

1991-01-01

Approximate analytical models are developed and used to construct an error covariance analysis for investigating the range of orbit determination accuracies which might be achieved for typical Mars approach trajectories. The sensitivity or orbit determination accuracy to beacon/orbiter position errors and to small spacecraft force modeling errors is also investigated. The results indicate that the orbit determination performance obtained from both Doppler and range data is a strong function of the inclination of the approach trajectory to the Martian equator, for surface beacons, and for orbiters, the inclination relative to the orbital plane. Large variations in performance were also observed for different approach velocity magnitudes; Doppler data in particular were found to perform poorly in determining the downtrack (along the direction of flight) component of spacecraft position. In addition, it was found that small spacecraft acceleration modeling errors can induce large errors in the Doppler-derived downtrack position estimate.

Linear error analysis of slope-area discharge determinations

USGS Publications Warehouse

Kirby, W.H.

1987-01-01

The slope-area method can be used to calculate peak flood discharges when current-meter measurements are not possible. This calculation depends on several quantities, such as water-surface fall, that are subject to large measurement errors. Other critical quantities, such as Manning's n, are not even amenable to direct measurement but can only be estimated. Finally, scour and fill may cause gross discrepancies between the observed condition of the channel and the hydraulic conditions during the flood peak. The effects of these potential errors on the accuracy of the computed discharge have been estimated by statistical error analysis using a Taylor-series approximation of the discharge formula and the well-known formula for the variance of a sum of correlated random variates. The resultant error variance of the computed discharge is a weighted sum of covariances of the various observational errors. The weights depend on the hydraulic and geometric configuration of the channel. The mathematical analysis confirms the rule of thumb that relative errors in computed discharge increase rapidly when velocity heads exceed the water-surface fall, when the flow field is expanding and when lateral velocity variation (alpha) is large. It also confirms the extreme importance of accurately assessing the presence of scour or fill. ?? 1987.

Statistical inference for template aging

NASA Astrophysics Data System (ADS)

Schuckers, Michael E.

2006-04-01

A change in classification error rates for a biometric device is often referred to as template aging. Here we offer two methods for determining whether the effect of time is statistically significant. The first of these is the use of a generalized linear model to determine if these error rates change linearly over time. This approach generalizes previous work assessing the impact of covariates using generalized linear models. The second approach uses of likelihood ratio tests methodology. The focus here is on statistical methods for estimation not the underlying cause of the change in error rates over time. These methodologies are applied to data from the National Institutes of Standards and Technology Biometric Score Set Release 1. The results of these applications are discussed.

Using Analysis of Covariance (ANCOVA) with Fallible Covariates

ERIC Educational Resources Information Center

Culpepper, Steven Andrew; Aguinis, Herman

2011-01-01

Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e., measured with error), which is the norm, researchers must choose from among 3 inadequate courses of action: (a) know that the assumption that covariates are perfectly reliable is violated but…

Quantifying uncertainty in geoacoustic inversion. II. Application to broadband, shallow-water data.

PubMed

Dosso, Stan E; Nielsen, Peter L

2002-01-01

This paper applies the new method of fast Gibbs sampling (FGS) to estimate the uncertainties of seabed geoacoustic parameters in a broadband, shallow-water acoustic survey, with the goal of interpreting the survey results and validating the method for experimental data. FGS applies a Bayesian approach to geoacoustic inversion based on sampling the posterior probability density to estimate marginal probability distributions and parameter covariances. This requires knowledge of the statistical distribution of the data errors, including both measurement and theory errors, which is generally not available. Invoking the simplifying assumption of independent, identically distributed Gaussian errors allows a maximum-likelihood estimate of the data variance and leads to a practical inversion algorithm. However, it is necessary to validate these assumptions, i.e., to verify that the parameter uncertainties obtained represent meaningful estimates. To this end, FGS is applied to a geoacoustic experiment carried out at a site off the west coast of Italy where previous acoustic and geophysical studies have been performed. The parameter uncertainties estimated via FGS are validated by comparison with: (i) the variability in the results of inverting multiple independent data sets collected during the experiment; (ii) the results of FGS inversion of synthetic test cases designed to simulate the experiment and data errors; and (iii) the available geophysical ground truth. Comparisons are carried out for a number of different source bandwidths, ranges, and levels of prior information, and indicate that FGS provides reliable and stable uncertainty estimates for the geoacoustic inverse problem.

Lunar gravitational field estimation and the effects of mismodeling upon lunar satellite orbit prediction. M.S. Thesis

NASA Technical Reports Server (NTRS)

Davis, John H.

1993-01-01

Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based nearside observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two different lunar spacecraft mission phases are simulated to evaluate the estimated fit models. Results for predicting state covariances one orbit ahead are presented along with the state errors resulting from the mismodeled gravity field. The position errors from planning a lunar landing maneuver with a mismodeled gravity field are also presented. These simulations clearly demonstrate the need to include observations of satellite motion over the far side in estimating the lunar gravity field. The simulations also illustrate that the eighth degree and order expansions used in the simulated fits were unable to adequately model lunar mascons.

A Comprehensive review of group level model performance in the presence of heteroscedasticity: Can a single model control Type I errors in the presence of outliers?

PubMed Central

Mumford, Jeanette A.

2017-01-01

Even after thorough preprocessing and a careful time series analysis of functional magnetic resonance imaging (fMRI) data, artifact and other issues can lead to violations of the assumption that the variance is constant across subjects in the group level model. This is especially concerning when modeling a continuous covariate at the group level, as the slope is easily biased by outliers. Various models have been proposed to deal with outliers including models that use the first level variance or that use the group level residual magnitude to differentially weight subjects. The most typically used robust regression, implementing a robust estimator of the regression slope, has been previously studied in the context of fMRI studies and was found to perform well in some scenarios, but a loss of Type I error control can occur for some outlier settings. A second type of robust regression using a heteroscedastic autocorrelation consistent (HAC) estimator, which produces robust slope and variance estimates has been shown to perform well, with better Type I error control, but with large sample sizes (500–1000 subjects). The Type I error control with smaller sample sizes has not been studied in this model and has not been compared to other modeling approaches that handle outliers such as FSL’s Flame 1 and FSL’s outlier de-weighting. Focusing on group level inference with a continuous covariate over a range of sample sizes and degree of heteroscedasticity, which can be driven either by the within- or between-subject variability, both styles of robust regression are compared to ordinary least squares (OLS), FSL’s Flame 1, Flame 1 with outlier de-weighting algorithm and Kendall’s Tau. Additionally, subject omission using the Cook’s Distance measure with OLS and nonparametric inference with the OLS statistic are studied. Pros and cons of these models as well as general strategies for detecting outliers in data and taking precaution to avoid inflated Type I error rates are discussed. PMID:28030782

How well can we measure the vertical wind speed? Implications for fluxes of energy and mass

Treesearch

John Kochendorfer; Tilden P. Meyers; John Frank; William J. Massman; Mark W. Heuer

2012-01-01

Sonic anemometers are capable of measuring the wind speed in all three dimensions at high frequencies (10­50 Hz), and are relied upon to estimate eddy-covariance-based fluxes of mass and energy over a wide variety of surfaces and ecosystems. In this study, wind-velocity measurement errors from a three-dimensional sonic anemometer with a nonorthogonal transducer...

Treating Sample Covariances for Use in Strongly Coupled Atmosphere-Ocean Data Assimilation

NASA Astrophysics Data System (ADS)

Smith, Polly J.; Lawless, Amos S.; Nichols, Nancy K.

2018-01-01

Strongly coupled data assimilation requires cross-domain forecast error covariances; information from ensembles can be used, but limited sampling means that ensemble derived error covariances are routinely rank deficient and/or ill-conditioned and marred by noise. Thus, they require modification before they can be incorporated into a standard assimilation framework. Here we compare methods for improving the rank and conditioning of multivariate sample error covariance matrices for coupled atmosphere-ocean data assimilation. The first method, reconditioning, alters the matrix eigenvalues directly; this preserves the correlation structures but does not remove sampling noise. We show that it is better to recondition the correlation matrix rather than the covariance matrix as this prevents small but dynamically important modes from being lost. The second method, model state-space localization via the Schur product, effectively removes sample noise but can dampen small cross-correlation signals. A combination that exploits the merits of each is found to offer an effective alternative.

Estimating the State of Aerodynamic Flows in the Presence of Modeling Errors

NASA Astrophysics Data System (ADS)

da Silva, Andre F. C.; Colonius, Tim

2017-11-01

The ensemble Kalman filter (EnKF) has been proven to be successful in fields such as meteorology, in which high-dimensional nonlinear systems render classical estimation techniques impractical. When the model used to forecast state evolution misrepresents important aspects of the true dynamics, estimator performance may degrade. In this work, parametrization and state augmentation are used to track misspecified boundary conditions (e.g., free stream perturbations). The resolution error is modeled as a Gaussian-distributed random variable with the mean (bias) and variance to be determined. The dynamics of the flow past a NACA 0009 airfoil at high angles of attack and moderate Reynolds number is represented by a Navier-Stokes equations solver with immersed boundaries capabilities. The pressure distribution on the airfoil or the velocity field in the wake, both randomized by synthetic noise, are sampled as measurement data and incorporated into the estimated state and bias following Kalman's analysis scheme. Insights about how to specify the modeling error covariance matrix and its impact on the estimator performance are conveyed. This work has been supported in part by a Grant from AFOSR (FA9550-14-1-0328) with Dr. Douglas Smith as program manager, and by a Science without Borders scholarship from the Ministry of Education of Brazil (Capes Foundation - BEX 12966/13-4).

Assessment and Selection of Competing Models for Zero-Inflated Microbiome Data

PubMed Central

Xu, Lizhen; Paterson, Andrew D.; Turpin, Williams; Xu, Wei

2015-01-01

Typical data in a microbiome study consist of the operational taxonomic unit (OTU) counts that have the characteristic of excess zeros, which are often ignored by investigators. In this paper, we compare the performance of different competing methods to model data with zero inflated features through extensive simulations and application to a microbiome study. These methods include standard parametric and non-parametric models, hurdle models, and zero inflated models. We examine varying degrees of zero inflation, with or without dispersion in the count component, as well as different magnitude and direction of the covariate effect on structural zeros and the count components. We focus on the assessment of type I error, power to detect the overall covariate effect, measures of model fit, and bias and effectiveness of parameter estimations. We also evaluate the abilities of model selection strategies using Akaike information criterion (AIC) or Vuong test to identify the correct model. The simulation studies show that hurdle and zero inflated models have well controlled type I errors, higher power, better goodness of fit measures, and are more accurate and efficient in the parameter estimation. Besides that, the hurdle models have similar goodness of fit and parameter estimation for the count component as their corresponding zero inflated models. However, the estimation and interpretation of the parameters for the zero components differs, and hurdle models are more stable when structural zeros are absent. We then discuss the model selection strategy for zero inflated data and implement it in a gut microbiome study of > 400 independent subjects. PMID:26148172

Assessment and Selection of Competing Models for Zero-Inflated Microbiome Data.

PubMed

Xu, Lizhen; Paterson, Andrew D; Turpin, Williams; Xu, Wei

2015-01-01

Typical data in a microbiome study consist of the operational taxonomic unit (OTU) counts that have the characteristic of excess zeros, which are often ignored by investigators. In this paper, we compare the performance of different competing methods to model data with zero inflated features through extensive simulations and application to a microbiome study. These methods include standard parametric and non-parametric models, hurdle models, and zero inflated models. We examine varying degrees of zero inflation, with or without dispersion in the count component, as well as different magnitude and direction of the covariate effect on structural zeros and the count components. We focus on the assessment of type I error, power to detect the overall covariate effect, measures of model fit, and bias and effectiveness of parameter estimations. We also evaluate the abilities of model selection strategies using Akaike information criterion (AIC) or Vuong test to identify the correct model. The simulation studies show that hurdle and zero inflated models have well controlled type I errors, higher power, better goodness of fit measures, and are more accurate and efficient in the parameter estimation. Besides that, the hurdle models have similar goodness of fit and parameter estimation for the count component as their corresponding zero inflated models. However, the estimation and interpretation of the parameters for the zero components differs, and hurdle models are more stable when structural zeros are absent. We then discuss the model selection strategy for zero inflated data and implement it in a gut microbiome study of > 400 independent subjects.

The linear transformation model with frailties for the analysis of item response times.

PubMed

Wang, Chun; Chang, Hua-Hua; Douglas, Jeffrey A

2013-02-01

The item response times (RTs) collected from computerized testing represent an underutilized source of information about items and examinees. In addition to knowing the examinees' responses to each item, we can investigate the amount of time examinees spend on each item. In this paper, we propose a semi-parametric model for RTs, the linear transformation model with a latent speed covariate, which combines the flexibility of non-parametric modelling and the brevity as well as interpretability of parametric modelling. In this new model, the RTs, after some non-parametric monotone transformation, become a linear model with latent speed as covariate plus an error term. The distribution of the error term implicitly defines the relationship between the RT and examinees' latent speeds; whereas the non-parametric transformation is able to describe various shapes of RT distributions. The linear transformation model represents a rich family of models that includes the Cox proportional hazards model, the Box-Cox normal model, and many other models as special cases. This new model is embedded in a hierarchical framework so that both RTs and responses are modelled simultaneously. A two-stage estimation method is proposed. In the first stage, the Markov chain Monte Carlo method is employed to estimate the parametric part of the model. In the second stage, an estimating equation method with a recursive algorithm is adopted to estimate the non-parametric transformation. Applicability of the new model is demonstrated with a simulation study and a real data application. Finally, methods to evaluate the model fit are suggested. © 2012 The British Psychological Society.

THE IMPACT OF POINT-SOURCE SUBTRACTION RESIDUALS ON 21 cm EPOCH OF REIONIZATION ESTIMATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trott, Cathryn M.; Wayth, Randall B.; Tingay, Steven J., E-mail: cathryn.trott@curtin.edu.au

Precise subtraction of foreground sources is crucial for detecting and estimating 21 cm H I signals from the Epoch of Reionization (EoR). We quantify how imperfect point-source subtraction due to limitations of the measurement data set yields structured residual signal in the data set. We use the Cramer-Rao lower bound, as a metric for quantifying the precision with which a parameter may be measured, to estimate the residual signal in a visibility data set due to imperfect point-source subtraction. We then propagate these residuals into two metrics of interest for 21 cm EoR experiments-the angular power spectrum and two-dimensional powermore » spectrum-using a combination of full analytic covariant derivation, analytic variant derivation, and covariant Monte Carlo simulations. This methodology differs from previous work in two ways: (1) it uses information theory to set the point-source position error, rather than assuming a global rms error, and (2) it describes a method for propagating the errors analytically, thereby obtaining the full correlation structure of the power spectra. The methods are applied to two upcoming low-frequency instruments that are proposing to perform statistical EoR experiments: the Murchison Widefield Array and the Precision Array for Probing the Epoch of Reionization. In addition to the actual antenna configurations, we apply the methods to minimally redundant and maximally redundant configurations. We find that for peeling sources above 1 Jy, the amplitude of the residual signal, and its variance, will be smaller than the contribution from thermal noise for the observing parameters proposed for upcoming EoR experiments, and that optimal subtraction of bright point sources will not be a limiting factor for EoR parameter estimation. We then use the formalism to provide an ab initio analytic derivation motivating the 'wedge' feature in the two-dimensional power spectrum, complementing previous discussion in the literature.« less

Analyses of global sea surface temperature 1856-1991

NASA Astrophysics Data System (ADS)

Kaplan, Alexey; Cane, Mark A.; Kushnir, Yochanan; Clement, Amy C.; Blumenthal, M. Benno; Rajagopalan, Balaji

1998-08-01

Global analyses of monthly sea surface temperature (SST) anomalies from 1856 to 1991 are produced using three statistically based methods: optimal smoothing (OS), the Kaiman filter (KF) and optimal interpolation (OI). Each of these is accompanied by estimates of the error covariance of the analyzed fields. The spatial covariance function these methods require is estimated from the available data; the timemarching model is a first-order autoregressive model again estimated from data. The data input for the analyses are monthly anomalies from the United Kingdom Meteorological Office historical sea surface temperature data set (MOHSST5) [Parker et al., 1994] of the Global Ocean Surface Temperature Atlas (GOSTA) [Bottomley et al., 1990]. These analyses are compared with each other, with GOSTA, and with an analysis generated by projection (P) onto a set of empirical orthogonal functions (as in Smith et al. [1996]). In theory, the quality of the analyses should rank in the order OS, KF, OI, P, and GOSTA. It is found that the first four give comparable results in the data-rich periods (1951-1991), but at times when data is sparse the first three differ significantly from P and GOSTA. At these times the latter two often have extreme and fluctuating values, prima facie evidence of error. The statistical schemes are also verified against data not used in any of the analyses (proxy records derived from corals and air temperature records from coastal and island stations). We also present evidence that the analysis error estimates are indeed indicative of the quality of the products. At most times the OS and KF products are close to the OI product, but at times of especially poor coverage their use of information from other times is advantageous. The methods appear to reconstruct the major features of the global SST field from very sparse data. Comparison with other indications of the El Niño-Southern Oscillation cycle show that the analyses provide usable information on interannual variability as far back as the 1860s.

Stable and verifiable state estimation methods and systems with spacecraft applications

NASA Technical Reports Server (NTRS)

Li, Rongsheng (Inventor); Wu, Yeong-Wei Andy (Inventor)

2001-01-01

The stability of a recursive estimator process (e.g., a Kalman filter is assured for long time periods by periodically resetting an error covariance P(t.sub.n) of the system to a predetermined reset value P.sub.r. The recursive process is thus repetitively forced to start from a selected covariance and continue for a time period that is short compared to the system's total operational time period. The time period in which the process must maintain its numerical stability is significantly reduced as is the demand on the system's numerical stability. The process stability for an extended operational time period T.sub.o is verified by performing the resetting step at the end of at least one reset time period T.sub.r whose duration is less than the operational time period T.sub.o and then confirming stability of the process over the reset time period T.sub.r. Because the recursive process starts from a selected covariance at the beginning of each reset time period T.sub.r, confirming stability of the process over at least one reset time period substantially confirms stability over the longer operational time period T.sub.o.

The choice of prior distribution for a covariance matrix in multivariate meta-analysis: a simulation study.

PubMed

Hurtado Rúa, Sandra M; Mazumdar, Madhu; Strawderman, Robert L

2015-12-30

Bayesian meta-analysis is an increasingly important component of clinical research, with multivariate meta-analysis a promising tool for studies with multiple endpoints. Model assumptions, including the choice of priors, are crucial aspects of multivariate Bayesian meta-analysis (MBMA) models. In a given model, two different prior distributions can lead to different inferences about a particular parameter. A simulation study was performed in which the impact of families of prior distributions for the covariance matrix of a multivariate normal random effects MBMA model was analyzed. Inferences about effect sizes were not particularly sensitive to prior choice, but the related covariance estimates were. A few families of prior distributions with small relative biases, tight mean squared errors, and close to nominal coverage for the effect size estimates were identified. Our results demonstrate the need for sensitivity analysis and suggest some guidelines for choosing prior distributions in this class of problems. The MBMA models proposed here are illustrated in a small meta-analysis example from the periodontal field and a medium meta-analysis from the study of stroke. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Asteroid approach covariance analysis for the Clementine mission

NASA Technical Reports Server (NTRS)

Ionasescu, Rodica; Sonnabend, David

1993-01-01

The Clementine mission is designed to test Strategic Defense Initiative Organization (SDIO) technology, the Brilliant Pebbles and Brilliant Eyes sensors, by mapping the moon surface and flying by the asteroid Geographos. The capability of two of the instruments available on board the spacecraft, the lidar (laser radar) and the UV/Visible camera is used in the covariance analysis to obtain the spacecraft delivery uncertainties at the asteroid. These uncertainties are due primarily to asteroid ephemeris uncertainties. On board optical navigation reduces the uncertainty in the knowledge of the spacecraft position in the direction perpendicular to the incoming asymptote to a one-sigma value of under 1 km, at the closest approach distance of 100 km. The uncertainty in the knowledge of the encounter time is about 0.1 seconds for a flyby velocity of 10.85 km/s. The magnitude of these uncertainties is due largely to Center Finding Errors (CFE). These systematic errors represent the accuracy expected in locating the center of the asteroid in the optical navigation images, in the absence of a topographic model for the asteroid. The direction of the incoming asymptote cannot be estimated accurately until minutes before the asteroid flyby, and correcting for it would require autonomous navigation. Orbit determination errors dominate over maneuver execution errors, and the final delivery accuracy attained is basically the orbit determination uncertainty before the final maneuver.

"A space-time ensemble Kalman filter for state and parameter estimation of groundwater transport models"

NASA Astrophysics Data System (ADS)

Briseño, Jessica; Herrera, Graciela S.

2010-05-01

Herrera (1998) proposed a method for the optimal design of groundwater quality monitoring networks that involves space and time in a combined form. The method was applied later by Herrera et al (2001) and by Herrera and Pinder (2005). To get the estimates of the contaminant concentration being analyzed, this method uses a space-time ensemble Kalman filter, based on a stochastic flow and transport model. When the method is applied, it is important that the characteristics of the stochastic model be congruent with field data, but, in general, it is laborious to manually achieve a good match between them. For this reason, the main objective of this work is to extend the space-time ensemble Kalman filter proposed by Herrera, to estimate the hydraulic conductivity, together with hydraulic head and contaminant concentration, and its application in a synthetic example. The method has three steps: 1) Given the mean and the semivariogram of the natural logarithm of hydraulic conductivity (ln K), random realizations of this parameter are obtained through two alternatives: Gaussian simulation (SGSim) and Latin Hypercube Sampling method (LHC). 2) The stochastic model is used to produce hydraulic head (h) and contaminant (C) realizations, for each one of the conductivity realizations. With these realization the mean of ln K, h and C are obtained, for h and C, the mean is calculated in space and time, and also the cross covariance matrix h-ln K-C in space and time. The covariance matrix is obtained averaging products of the ln K, h and C realizations on the estimation points and times, and the positions and times with data of the analyzed variables. The estimation points are the positions at which estimates of ln K, h or C are gathered. In an analogous way, the estimation times are those at which estimates of any of the three variables are gathered. 3) Finally the ln K, h and C estimate are obtained using the space-time ensemble Kalman filter. The realization mean for each one of the variables is used as the prior space-time estimate for the Kalman filter, and the space-time cross-covariance matrix of h-ln K-C as the prior estimate-error covariance-matrix. The synthetic example has a modeling area of 700 x 700 square meters; a triangular mesh model with 702 nodes and 1306 elements is used. A pumping well located in the central part of the study area is considered. For the contaminant transport model, a contaminant source area is present in the western part of the study area. The estimation points for hydraulic conductivity, hydraulic head and contaminant concentrations are located on a submesh of the model mesh (same location for h, ln K and c), composed by 48 nodes spread throughout the study area, with an approximately separation of 90 meters between nodes. The results analysis was done through the mean error, root mean square error, initial and final estimation maps of h, ln K and C at each time, and the initial and final variance maps of h, ln K and C. To obtain model convergence, 3000 realizations of ln K were required using SGSim, and only 1000 with LHC. The results show that for both alternatives, the Kalman filter estimates for h, ln K and C using h and C data, have errors which magnitudes decrease as data is added. HERRERA, G. S.(1998), Cost Effective Groundwater Quality Sampling Network Design. Ph. D. thesis, University of Vermont, Burlington, Vermont, 172 pp. HERRERA G., GUARNACCIA J., PINDER G. Y SIMUTA R.(2001),"Diseño de redes de monitoreo de la calidad del agua subterránea eficientes", Proceedings of the 2001 International Symposium on Environmental Hydraulics, Arizona, U.S.A. HERRERA G. S. and PINDER G.F. (2005), Space-time optimization of groundwater quality sampling networks Water Resour. Res., Vol. 41, No. 12, W12407, 10.1029/2004WR003626.

Decentralized state estimation for a large-scale spatially interconnected system.

PubMed

Liu, Huabo; Yu, Haisheng

2018-03-01

A decentralized state estimator is derived for the spatially interconnected systems composed of many subsystems with arbitrary connection relations. An optimization problem on the basis of linear matrix inequality (LMI) is constructed for the computations of improved subsystem parameter matrices. Several computationally effective approaches are derived which efficiently utilize the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, this decentralized state estimator is proved to converge to a stable system and obtain a bounded covariance matrix of estimation errors under certain conditions. Numerical simulations show that the obtained decentralized state estimator is attractive in the synthesis of a large-scale networked system. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Vehicle Lateral State Estimation Based on Measured Tyre Forces

PubMed Central

Tuononen, Ari J.

2009-01-01

Future active safety systems need more accurate information about the state of vehicles. This article proposes a method to evaluate the lateral state of a vehicle based on measured tyre forces. The tyre forces of two tyres are estimated from optically measured tyre carcass deflections and transmitted wirelessly to the vehicle body. The two remaining tyres are so-called virtual tyre sensors, the forces of which are calculated from the real tyre sensor estimates. The Kalman filter estimator for lateral vehicle state based on measured tyre forces is presented, together with a simple method to define adaptive measurement error covariance depending on the driving condition of the vehicle. The estimated yaw rate and lateral velocity are compared with the validation sensor measurements. PMID:22291535

Solution of the weighted symmetric similarity transformations based on quaternions

NASA Astrophysics Data System (ADS)

Mercan, H.; Akyilmaz, O.; Aydin, C.

2017-12-01

A new method through Gauss-Helmert model of adjustment is presented for the solution of the similarity transformations, either 3D or 2D, in the frame of errors-in-variables (EIV) model. EIV model assumes that all the variables in the mathematical model are contaminated by random errors. Total least squares estimation technique may be used to solve the EIV model. Accounting for the heteroscedastic uncertainty both in the target and the source coordinates, that is the more common and general case in practice, leads to a more realistic estimation of the transformation parameters. The presented algorithm can handle the heteroscedastic transformation problems, i.e., positions of the both target and the source points may have full covariance matrices. Therefore, there is no limitation such as the isotropic or the homogenous accuracy for the reference point coordinates. The developed algorithm takes the advantage of the quaternion definition which uniquely represents a 3D rotation matrix. The transformation parameters: scale, translations, and the quaternion (so that the rotation matrix) along with their covariances, are iteratively estimated with rapid convergence. Moreover, prior least squares (LS) estimation of the unknown transformation parameters is not required to start the iterations. We also show that the developed method can also be used to estimate the 2D similarity transformation parameters by simply treating the problem as a 3D transformation problem with zero (0) values assigned for the z-components of both target and source points. The efficiency of the new algorithm is presented with the numerical examples and comparisons with the results of the previous studies which use the same data set. Simulation experiments for the evaluation and comparison of the proposed and the conventional weighted LS (WLS) method is also presented.

Population pharmacokinetics and maximum a posteriori probability Bayesian estimator of abacavir: application of individualized therapy in HIV-infected infants and toddlers

PubMed Central

Zhao, Wei; Cella, Massimo; Della Pasqua, Oscar; Burger, David; Jacqz-Aigrain, Evelyne

2012-01-01

AIMS To develop a population pharmacokinetic model for abacavir in HIV-infected infants and toddlers, which will be used to describe both once and twice daily pharmacokinetic profiles, identify covariates that explain variability and propose optimal time points to optimize the area under the concentration–time curve (AUC) targeted dosage and individualize therapy. METHODS The pharmacokinetics of abacavir was described with plasma concentrations from 23 patients using nonlinear mixed-effects modelling (NONMEM) software. A two-compartment model with first-order absorption and elimination was developed. The final model was validated using bootstrap, visual predictive check and normalized prediction distribution errors. The Bayesian estimator was validated using the cross-validation and simulation–estimation method. RESULTS The typical population pharmacokinetic parameters and relative standard errors (RSE) were apparent systemic clearance (CL) 13.4 l h−1 (RSE 6.3%), apparent central volume of distribution 4.94 l (RSE 28.7%), apparent peripheral volume of distribution 8.12 l (RSE14.2%), apparent intercompartment clearance 1.25 l h−1 (RSE 16.9%) and absorption rate constant 0.758 h−1 (RSE 5.8%). The covariate analysis identified weight as the individual factor influencing the apparent oral clearance: CL = 13.4 × (weight/12)1.14. The maximum a posteriori probability Bayesian estimator, based on three concentrations measured at 0, 1 or 2, and 3 h after drug intake allowed predicting individual AUC0–t. CONCLUSIONS The population pharmacokinetic model developed for abacavir in HIV-infected infants and toddlers accurately described both once and twice daily pharmacokinetic profiles. The maximum a posteriori probability Bayesian estimator of AUC0–t was developed from the final model and can be used routinely to optimize individual dosing. PMID:21988586

Estimation of attitude sensor timetag biases

NASA Technical Reports Server (NTRS)

Sedlak, J.

1995-01-01

This paper presents an extended Kalman filter for estimating attitude sensor timing errors. Spacecraft attitude is determined by finding the mean rotation from a set of reference vectors in inertial space to the corresponding observed vectors in the body frame. Any timing errors in the observations can lead to attitude errors if either the spacecraft is rotating or the reference vectors themselves vary with time. The state vector here consists of the attitude quaternion, timetag biases, and, optionally, gyro drift rate biases. The filter models the timetags as random walk processes: their expectation values propagate as constants and white noise contributes to their covariance. Thus, this filter is applicable to cases where the true timing errors are constant or slowly varying. The observability of the state vector is studied first through an examination of the algebraic observability condition and then through several examples with simulated star tracker timing errors. The examples use both simulated and actual flight data from the Extreme Ultraviolet Explorer (EUVE). The flight data come from times when EUVE had a constant rotation rate, while the simulated data feature large angle attitude maneuvers. The tests include cases with timetag errors on one or two sensors, both constant and time-varying, and with and without gyro bias errors. Due to EUVE's sensor geometry, the observability of the state vector is severely limited when the spacecraft rotation rate is constant. In the absence of attitude maneuvers, the state elements are highly correlated, and the state estimate is unreliable. The estimates are particularly sensitive to filter mistuning in this case. The EUVE geometry, though, is a degenerate case having coplanar sensors and rotation vector. Observability is much improved and the filter performs well when the rate is either varying or noncoplanar with the sensors, as during a slew. Even with bad geometry and constant rates, if gyro biases are independently known, the timetag error for a single sensor can be accurately estimated as long as its boresight is not too close to the spacecraft rotation axis.

Verification of Agricultural Methane Emission Inventories

NASA Astrophysics Data System (ADS)

Desjardins, R. L.; Pattey, E.; Worth, D. E.; VanderZaag, A.; Mauder, M.; Srinivasan, R.; Worthy, D.; Sweeney, C.; Metzger, S.

2017-12-01

It is estimated that agriculture contributes more than 40% of anthropogenic methane (CH4) emissions in North America. However, these estimates, which are either based on the Intergovernmental Panel on Climate Change (IPCC) methodology or inverse modeling techniques, are poorly validated due to the challenges of separating interspersed CH4 sources within agroecosystems. A flux aircraft, instrumented with a fast-response Picarro CH4 analyzer for the eddy covariance (EC) technique and a sampling system for the relaxed eddy accumulation technique (REA), was flown at an altitude of about 150 m along several 20-km transects over an agricultural region in Eastern Canada. For all flight days, the top-down CH4 flux density measurements were compared to the footprint adjusted bottom-up estimates based on an IPCC Tier II methodology. Information on the animal population, land use type and atmospheric and surface variables were available for each transect. Top-down and bottom-up estimates of CH4 emissions were found to be poorly correlated, and wetlands were the most frequent confounding source of CH4; however, there were other sources such as waste treatment plants and biodigesters. Spatially resolved wavelet covariance estimates of CH4 emissions helped identify the contribution of wetlands to the overall CH4 flux, and the dependence of these emissions on temperature. When wetland contribution in the flux footprint was minimized, top-down and bottom-up estimates agreed to within measurement error. This research demonstrates that although existing aircraft-based technology can be used to verify regional ( 100 km2) agricultural CH4 emissions, it remains challenging due to diverse sources of CH4 present in many regions. The use of wavelet covariance to generate spatially-resolved flux estimates was found to be the best way to separate interspersed sources of CH4.

Robustness of meta-analyses in finding gene × environment interactions

PubMed Central

Shi, Gang; Nehorai, Arye

2017-01-01

Meta-analyses that synthesize statistical evidence across studies have become important analytical tools for genetic studies. Inspired by the success of genome-wide association studies of the genetic main effect, researchers are searching for gene × environment interactions. Confounders are routinely included in the genome-wide gene × environment interaction analysis as covariates; however, this does not control for any confounding effects on the results if covariate × environment interactions are present. We carried out simulation studies to evaluate the robustness to the covariate × environment confounder for meta-regression and joint meta-analysis, which are two commonly used meta-analysis methods for testing the gene × environment interaction or the genetic main effect and interaction jointly. Here we show that meta-regression is robust to the covariate × environment confounder while joint meta-analysis is subject to the confounding effect with inflated type I error rates. Given vast sample sizes employed in genome-wide gene × environment interaction studies, non-significant covariate × environment interactions at the study level could substantially elevate the type I error rate at the consortium level. When covariate × environment confounders are present, type I errors can be controlled in joint meta-analysis by including the covariate × environment terms in the analysis at the study level. Alternatively, meta-regression can be applied, which is robust to potential covariate × environment confounders. PMID:28362796

Global Simultaneous Estimation of Present-Day Surface Mass Trend and GIA Using Multi-Sensor Geodetic Data Combination

NASA Astrophysics Data System (ADS)

Wu, X.; Heflin, M. B.; Schotman, H.; Vermeersen, B. L.; Dong, D.; Gross, R. S.; Ivins, E. R.; Moore, A. W.; Owen, S. E.

2009-12-01

Separating geodetic signatures of present-day surface mass trend and Glacial Isostatic Adjustment (GIA) requires multi-data types of different physical characteristics. We take a kinematic approach to the global simultaneous estimation problem. Three sets of global spherical harmonic coefficients from degree 1 to 60 of the present-day surface mass trend, vertical and horizontal GIA induced surface velocity fields, as well as rotation vectors of 15 major tectonic plates are solved for. The estimation is carried out using GRACE geoid trend, 3-dimensional velocities measured at 664 SLR/VLBI/GPS sites, the data-assimilated JPL ECCO ocean model. The ICE-5G/IJ05 (VM2) predictions are used as a priori GIA mean model. An a priori covariance matrix is constructed in the spherical harmonic domain for the GIA model by propagating the covariance matrices of random and geographically correlated ice thickness errors and upper/lower mantle viscosity errors so that the resulting magnitude and geographic pattern of the geoid uncertainties roughly reflect the difference between two recent GIA models. Unprecedented high-precision results are achieved. For example, geocenter velocities due to present-day surface mass trend and due to GIA are both determined to uncertainties of better than 0.1 mm/yr without using direct geodetic geocenter information. Information content of the data sets, future improvements, and benefits from new data will also be explored in the global inverse framework.

INS/GNSS Tightly-Coupled Integration Using Quaternion-Based AUPF for USV.

PubMed

Xia, Guoqing; Wang, Guoqing

2016-08-02

This paper addresses the problem of integration of Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) for the purpose of developing a low-cost, robust and highly accurate navigation system for unmanned surface vehicles (USVs). A tightly-coupled integration approach is one of the most promising architectures to fuse the GNSS data with INS measurements. However, the resulting system and measurement models turn out to be nonlinear, and the sensor stochastic measurement errors are non-Gaussian and distributed in a practical system. Particle filter (PF), one of the most theoretical attractive non-linear/non-Gaussian estimation methods, is becoming more and more attractive in navigation applications. However, the large computation burden limits its practical usage. For the purpose of reducing the computational burden without degrading the system estimation accuracy, a quaternion-based adaptive unscented particle filter (AUPF), which combines the adaptive unscented Kalman filter (AUKF) with PF, has been proposed in this paper. The unscented Kalman filter (UKF) is used in the algorithm to improve the proposal distribution and generate a posterior estimates, which specify the PF importance density function for generating particles more intelligently. In addition, the computational complexity of the filter is reduced with the avoidance of the re-sampling step. Furthermore, a residual-based covariance matching technique is used to adapt the measurement error covariance. A trajectory simulator based on a dynamic model of USV is used to test the proposed algorithm. Results show that quaternion-based AUPF can significantly improve the overall navigation accuracy and reliability.

Use of global positioning system measurements to determine geocentric coordinates and variations in Earth orientation

NASA Technical Reports Server (NTRS)

Malla, R. P.; Wu, S.-C.; Lichten, S. M.

1993-01-01

Geocentric tracking station coordinates and short-period Earth-orientation variations can be measured with Global Positioning System (GPS) measurements. Unless calibrated, geocentric coordinate errors and changes in Earth orientation can lead to significant deep-space tracking errors. Ground-based GPS estimates of daily and subdaily changes in Earth orientation presently show centimeter-level precision. Comparison between GPS-estimated Earth-rotation variations, which are the differences between Universal Time 1 and Universal Coordinated Time (UT1-UTC), and those calculated from ocean tide models suggests that observed subdaily variations in Earth rotation are dominated by oceanic tidal effects. Preliminary GPS estimates for the geocenter location (from a 3-week experiment) agree with independent satellite laser-ranging estimates to better than 10 cm. Covariance analysis predicts that temporal resolution of GPS estimates for Earth orientation and geocenter improves significantly when data collected from low Earth-orbiting satellites as well as from ground sites are combined. The low Earth GPS tracking data enhance the accuracy and resolution for measuring high-frequency global geodynamical signals over time scales of less than 1 day.

Merging Multi-model CMIP5/PMIP3 Past-1000 Ensemble Simulations with Tree Ring Proxy Data by Optimal Interpolation Approach

NASA Astrophysics Data System (ADS)

Chen, Xin; Luo, Yong; Xing, Pei; Nie, Suping; Tian, Qinhua

2015-04-01

Two sets of gridded annual mean surface air temperature in past millennia over the Northern Hemisphere was constructed employing optimal interpolation (OI) method so as to merge the tree ring proxy records with the simulations from CMIP5 (the fifth phase of the Climate Model Intercomparison Project). Both the uncertainties in proxy reconstruction and model simulations can be taken into account applying OI algorithm. For better preservation of physical coordinated features and spatial-temporal completeness of climate variability in 7 copies of model results, we perform the Empirical Orthogonal Functions (EOF) analysis to truncate the ensemble mean field as the first guess (background field) for OI. 681 temperature sensitive tree-ring chronologies are collected and screened from International Tree Ring Data Bank (ITRDB) and Past Global Changes (PAGES-2k) project. Firstly, two methods (variance matching and linear regression) are employed to calibrate the tree ring chronologies with instrumental data (CRUTEM4v) individually. In addition, we also remove the bias of both the background field and proxy records relative to instrumental dataset. Secondly, time-varying background error covariance matrix (B) and static "observation" error covariance matrix (R) are calculated for OI frame. In our scheme, matrix B was calculated locally, and "observation" error covariance are partially considered in R matrix (the covariance value between the pairs of tree ring sites that are very close to each other would be counted), which is different from the traditional assumption that R matrix should be diagonal. Comparing our results, it turns out that regional averaged series are not sensitive to the selection for calibration methods. The Quantile-Quantile plots indicate regional climatologies based on both methods are tend to be more agreeable with regional reconstruction of PAGES-2k in 20th century warming period than in little ice age (LIA). Lager volcanic cooling response over Asia and Europe in context of recent millennium are detected in our datasets than that revealed in regional reconstruction from PAGES-2k network. Verification experiments have showed that the merging approach really reconcile the proxy data and model ensemble simulations in an optimal way (with smaller errors than both of them). Further research is needed to improve the error estimation on them.

Comparative test on several forms of background error covariance in 3DVar

NASA Astrophysics Data System (ADS)

Shao, Aimei

2013-04-01

The background error covariance matrix (Hereinafter referred to as B matrix) plays an important role in the three-dimensional variational (3DVar) data assimilation method. However, it is difficult to get B matrix accurately because true atmospheric state is unknown. Therefore, some methods were developed to estimate B matrix (e.g. NMC method, innovation analysis method, recursive filters, and ensemble method such as EnKF). Prior to further development and application of these methods, the function of several B matrixes estimated by these methods in 3Dvar is worth studying and evaluating. For this reason, NCEP reanalysis data and forecast data are used to test the effectiveness of the several B matrixes with VAF (Huang, 1999) method. Here the NCEP analysis is treated as the truth and in this case the forecast error is known. The data from 2006 to 2007 is used as the samples to estimate B matrix and the data in 2008 is used to verify the assimilation effects. The 48h and 24h forecast valid at the same time is used to estimate B matrix with NMC method. B matrix can be represented by a correlation part (a non-diagonal matrix) and a variance part (a diagonal matrix of variances). Gaussian filter function as an approximate approach is used to represent the variation of correlation coefficients with distance in numerous 3DVar systems. On the basis of the assumption, the following several forms of B matrixes are designed and test with VAF in the comparative experiments: (1) error variance and the characteristic lengths are fixed and setted to their mean value averaged over the analysis domain; (2) similar to (1), but the mean characteristic lengths reduce to 50 percent for the height and 60 percent for the temperature of the original; (3) similar to (2), but error variance calculated directly by the historical data is space-dependent; (4) error variance and characteristic lengths are all calculated directly by the historical data; (5) B matrix is estimated directly by the historical data; (6) similar to (5), but a localization process is performed; (7) B matrix is estimated by NMC method but error variance is reduced by 1.7 times in order that the value is close to that calculated from the true forecast error samples; (8) similar to (7), but the localization similar to (6) is performed. Experimental results with the different B matrixes show that for the Gaussian-type B matrix the characteristic lengths calculated from the true error samples don't bring a good analysis results. However, the reduced characteristic lengths (about half of the original one) can lead to a good analysis. If the B matrix estimated directly from the historical data is used in 3DVar, the assimilation effect can not reach to the best. The better assimilation results are generated with the application of reduced characteristic length and localization. Even so, it hasn't obvious advantage compared with Gaussian-type B matrix with the optimal characteristic length. It implies that the Gaussian-type B matrix, widely used for operational 3DVar system, can get a good analysis with the appropriate characteristic lengths. The crucial problem is how to determine the appropriate characteristic lengths. (This work is supported by the National Natural Science Foundation of China (41275102, 40875063), and the Fundamental Research Funds for the Central Universities (lzujbky-2010-9) )

Reducing errors in aircraft atmospheric inversion estimates of point-source emissions: the Aliso Canyon natural gas leak as a natural tracer experiment

NASA Astrophysics Data System (ADS)

Gourdji, S. M.; Yadav, V.; Karion, A.; Mueller, K. L.; Conley, S.; Ryerson, T.; Nehrkorn, T.; Kort, E. A.

2018-04-01

Urban greenhouse gas (GHG) flux estimation with atmospheric measurements and modeling, i.e. the ‘top-down’ approach, can potentially support GHG emission reduction policies by assessing trends in surface fluxes and detecting anomalies from bottom-up inventories. Aircraft-collected GHG observations also have the potential to help quantify point-source emissions that may not be adequately sampled by fixed surface tower-based atmospheric observing systems. Here, we estimate CH4 emissions from a known point source, the Aliso Canyon natural gas leak in Los Angeles, CA from October 2015–February 2016, using atmospheric inverse models with airborne CH4 observations from twelve flights ≈4 km downwind of the leak and surface sensitivities from a mesoscale atmospheric transport model. This leak event has been well-quantified previously using various methods by the California Air Resources Board, thereby providing high confidence in the mass-balance leak rate estimates of (Conley et al 2016), used here for comparison to inversion results. Inversions with an optimal setup are shown to provide estimates of the leak magnitude, on average, within a third of the mass balance values, with remaining errors in estimated leak rates predominantly explained by modeled wind speed errors of up to 10 m s‑1, quantified by comparing airborne meteorological observations with modeled values along the flight track. An inversion setup using scaled observational wind speed errors in the model-data mismatch covariance matrix is shown to significantly reduce the influence of transport model errors on spatial patterns and estimated leak rates from the inversions. In sum, this study takes advantage of a natural tracer release experiment (i.e. the Aliso Canyon natural gas leak) to identify effective approaches for reducing the influence of transport model error on atmospheric inversions of point-source emissions, while suggesting future potential for integrating surface tower and aircraft atmospheric GHG observations in top-down urban emission monitoring systems.

Robust adaptive multichannel SAR processing based on covariance matrix reconstruction

NASA Astrophysics Data System (ADS)

Tan, Zhen-ya; He, Feng

2018-04-01

With the combination of digital beamforming (DBF) processing, multichannel synthetic aperture radar(SAR) systems in azimuth promise well in high-resolution and wide-swath imaging, whereas conventional processing methods don't take the nonuniformity of scattering coefficient into consideration. This paper brings up a robust adaptive Multichannel SAR processing method which utilizes the Capon spatial spectrum estimator to obtain the spatial spectrum distribution over all ambiguous directions first, and then the interference-plus-noise covariance Matrix is reconstructed based on definition to acquire the Multichannel SAR processing filter. The performance of processing under nonuniform scattering coefficient is promoted by this novel method and it is robust again array errors. The experiments with real measured data demonstrate the effectiveness and robustness of the proposed method.

Improved L-BFGS diagonal preconditioners for a large-scale 4D-Var inversion system: application to CO2 flux constraints and analysis error calculation

NASA Astrophysics Data System (ADS)

Bousserez, Nicolas; Henze, Daven; Bowman, Kevin; Liu, Junjie; Jones, Dylan; Keller, Martin; Deng, Feng

2013-04-01

This work presents improved analysis error estimates for 4D-Var systems. From operational NWP models to top-down constraints on trace gas emissions, many of today's data assimilation and inversion systems in atmospheric science rely on variational approaches. This success is due to both the mathematical clarity of these formulations and the availability of computationally efficient minimization algorithms. However, unlike Kalman Filter-based algorithms, these methods do not provide an estimate of the analysis or forecast error covariance matrices, these error statistics being propagated only implicitly by the system. From both a practical (cycling assimilation) and scientific perspective, assessing uncertainties in the solution of the variational problem is critical. For large-scale linear systems, deterministic or randomization approaches can be considered based on the equivalence between the inverse Hessian of the cost function and the covariance matrix of analysis error. For perfectly quadratic systems, like incremental 4D-Var, Lanczos/Conjugate-Gradient algorithms have proven to be most efficient in generating low-rank approximations of the Hessian matrix during the minimization. For weakly non-linear systems though, the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), a quasi-Newton descent algorithm, is usually considered the best method for the minimization. Suitable for large-scale optimization, this method allows one to generate an approximation to the inverse Hessian using the latest m vector/gradient pairs generated during the minimization, m depending upon the available core memory. At each iteration, an initial low-rank approximation to the inverse Hessian has to be provided, which is called preconditioning. The ability of the preconditioner to retain useful information from previous iterations largely determines the efficiency of the algorithm. Here we assess the performance of different preconditioners to estimate the inverse Hessian of a large-scale 4D-Var system. The impact of using the diagonal preconditioners proposed by Gilbert and Le Maréchal (1989) instead of the usual Oren-Spedicato scalar will be first presented. We will also introduce new hybrid methods that combine randomization estimates of the analysis error variance with L-BFGS diagonal updates to improve the inverse Hessian approximation. Results from these new algorithms will be evaluated against standard large ensemble Monte-Carlo simulations. The methods explored here are applied to the problem of inferring global atmospheric CO2 fluxes using remote sensing observations, and are intended to be integrated with the future NASA Carbon Monitoring System.

Observability of satellite launcher navigation with INS, GPS, attitude sensors and reference trajectory

NASA Astrophysics Data System (ADS)

Beaudoin, Yanick; Desbiens, André; Gagnon, Eric; Landry, René

2018-01-01

The navigation system of a satellite launcher is of paramount importance. In order to correct the trajectory of the launcher, the position, velocity and attitude must be known with the best possible precision. In this paper, the observability of four navigation solutions is investigated. The first one is the INS/GPS couple. Then, attitude reference sensors, such as magnetometers, are added to the INS/GPS solution. The authors have already demonstrated that the reference trajectory could be used to improve the navigation performance. This approach is added to the two previously mentioned navigation systems. For each navigation solution, the observability is analyzed with different sensor error models. First, sensor biases are neglected. Then, sensor biases are modelled as random walks and as first order Markov processes. The observability is tested with the rank and condition number of the observability matrix, the time evolution of the covariance matrix and sensitivity to measurement outlier tests. The covariance matrix is exploited to evaluate the correlation between states in order to detect structural unobservability problems. Finally, when an unobservable subspace is detected, the result is verified with theoretical analysis of the navigation equations. The results show that evaluating only the observability of a model does not guarantee the ability of the aiding sensors to correct the INS estimates within the mission time. The analysis of the covariance matrix time evolution could be a powerful tool to detect this situation, however in some cases, the problem is only revealed with a sensitivity to measurement outlier test. None of the tested solutions provide GPS position bias observability. For the considered mission, the modelling of the sensor biases as random walks or Markov processes gives equivalent results. Relying on the reference trajectory can improve the precision of the roll estimates. But, in the context of a satellite launcher, the roll estimation error and gyroscope bias are only observable if attitude reference sensors are present.

The Influence of Normalization Weight in Population Pharmacokinetic Covariate Models.

PubMed

Goulooze, Sebastiaan C; Völler, Swantje; Välitalo, Pyry A J; Calvier, Elisa A M; Aarons, Leon; Krekels, Elke H J; Knibbe, Catherijne A J

2018-03-23

In covariate (sub)models of population pharmacokinetic models, most covariates are normalized to the median value; however, for body weight, normalization to 70 kg or 1 kg is often applied. In this article, we illustrate the impact of normalization weight on the precision of population clearance (CL pop ) parameter estimates. The influence of normalization weight (70, 1 kg or median weight) on the precision of the CL pop estimate, expressed as relative standard error (RSE), was illustrated using data from a pharmacokinetic study in neonates with a median weight of 2.7 kg. In addition, a simulation study was performed to show the impact of normalization to 70 kg in pharmacokinetic studies with paediatric or obese patients. The RSE of the CL pop parameter estimate in the neonatal dataset was lowest with normalization to median weight (8.1%), compared with normalization to 1 kg (10.5%) or 70 kg (48.8%). Typical clearance (CL) predictions were independent of the normalization weight used. Simulations showed that the increase in RSE of the CL pop estimate with 70 kg normalization was highest in studies with a narrow weight range and a geometric mean weight away from 70 kg. When, instead of normalizing with median weight, a weight outside the observed range is used, the RSE of the CL pop estimate will be inflated, and should therefore not be used for model selection. Instead, established mathematical principles can be used to calculate the RSE of the typical CL (CL TV ) at a relevant weight to evaluate the precision of CL predictions.

Simultaneous orbit determination

NASA Technical Reports Server (NTRS)

Wright, J. R.

1988-01-01

Simultaneous orbit determination is demonstrated using live range and Doppler data for the NASA/Goddard tracking configuration defined by the White Sands Ground Terminal (WSGT), the Tracking and Data Relay Satellite (TDRS), and the Earth Radiation Budget Satellite (ERBS). A physically connected sequential filter-smoother was developed for this demonstration. Rigorous necessary conditions are used to show that the state error covariance functions are realistic; and this enables the assessment of orbit estimation accuracies for both TDRS and ERBS.

A Kalman filter for a two-dimensional shallow-water model

NASA Technical Reports Server (NTRS)

Parrish, D. F.; Cohn, S. E.

1985-01-01

A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.

Measurement error is often neglected in medical literature: a systematic review.

PubMed

Brakenhoff, Timo B; Mitroiu, Marian; Keogh, Ruth H; Moons, Karel G M; Groenwold, Rolf H H; van Smeden, Maarten

2018-06-01

In medical research, covariates (e.g., exposure and confounder variables) are often measured with error. While it is well accepted that this introduces bias and imprecision in exposure-outcome relations, it is unclear to what extent such issues are currently considered in research practice. The objective was to study common practices regarding covariate measurement error via a systematic review of general medicine and epidemiology literature. Original research published in 2016 in 12 high impact journals was full-text searched for phrases relating to measurement error. Reporting of measurement error and methods to investigate or correct for it were quantified and characterized. Two hundred and forty-seven (44%) of the 565 original research publications reported on the presence of measurement error. 83% of these 247 did so with respect to the exposure and/or confounder variables. Only 18 publications (7% of 247) used methods to investigate or correct for measurement error. Consequently, it is difficult for readers to judge the robustness of presented results to the existence of measurement error in the majority of publications in high impact journals. Our systematic review highlights the need for increased awareness about the possible impact of covariate measurement error. Additionally, guidance on the use of measurement error correction methods is necessary. Copyright © 2018 Elsevier Inc. All rights reserved.

Robust linear discriminant analysis with distance based estimators

NASA Astrophysics Data System (ADS)

Lim, Yai-Fung; Yahaya, Sharipah Soaad Syed; Ali, Hazlina

2017-11-01

Linear discriminant analysis (LDA) is one of the supervised classification techniques concerning relationship between a categorical variable and a set of continuous variables. The main objective of LDA is to create a function to distinguish between populations and allocating future observations to previously defined populations. Under the assumptions of normality and homoscedasticity, the LDA yields optimal linear discriminant rule (LDR) between two or more groups. However, the optimality of LDA highly relies on the sample mean and pooled sample covariance matrix which are known to be sensitive to outliers. To alleviate these conflicts, a new robust LDA using distance based estimators known as minimum variance vector (MVV) has been proposed in this study. The MVV estimators were used to substitute the classical sample mean and classical sample covariance to form a robust linear discriminant rule (RLDR). Simulation and real data study were conducted to examine on the performance of the proposed RLDR measured in terms of misclassification error rates. The computational result showed that the proposed RLDR is better than the classical LDR and was comparable with the existing robust LDR.

On the estimate of the transpiration in Mediterranean heterogeneous ecosystems with the coupled use of eddy covariance and sap flow techniques.

NASA Astrophysics Data System (ADS)

Corona, Roberto; Curreli, Matteo; Montaldo, Nicola; Oren, Ram

2013-04-01

Mediterranean ecosystems are commonly heterogeneous savanna-like ecosystems, with contrasting plant functional types (PFT) competing for the water use. Mediterranean regions suffer water scarcity due to the dry climate conditions. In semi-arid regions evapotranspiration (ET) is the leading loss term of the root-zone water budget with a yearly magnitude that may be roughly equal to the precipitation. Despite the attention these ecosystems are receiving, a general lack of knowledge persists about the estimate of ET and the relationship between ET and the plant survival strategies for the different PFTs under water stress. During the dry summers these water-limited heterogeneous ecosystems are mainly characterized by a simple dual PFT-landscapes with strong-resistant woody vegetation and bare soil since grass died. In these conditions due to the low signal of the land surface fluxes captured by the sonic anemometer and gas analyzer the widely used eddy covariance may fail and its ET estimate is not robust enough. In these conditions the use of the sap flow technique may have a key role, because theoretically it provides a direct estimate of the woody vegetation transpiration. Through the coupled use of the sap flow sensor observations, a 2D foot print model of the eddy covariance tower and high resolution satellite images for the estimate of the foot print land cover map, the eddy covariance measurements can be correctly interpreted, and ET components (bare soil evaporation and woody vegetation transpiration) can be separated. The case study is at the Orroli site in Sardinia (Italy). The site landscape is a mixture of Mediterranean patchy vegetation types: trees, including wild olives and cork oaks, different shrubs and herbaceous species. An extensive field campaign started in 2004. Land-surface fluxes and CO2 fluxes are estimated by an eddy covariance technique based micrometeorological tower. Soil moisture profiles were also continuously estimated using water content reflectometers and gravimetric method, and periodically leaf area index (LAI) PFTs are estimated. From 2012 sap flow sensors based on the thermal Dissipation Method are installed on numerous trees around the tower. Preliminary results show first the need of careful use sap flow sensors outputs which are affected by errors in the estimates of their main parameters, mainly allometric relationships between, for instance, sapwood area, diameter, canopy cover area, which affect the upscale of the local tree measurements to the site plot larger scale. Finally we demonstrate that the sap flow sensors are essential for the estimate of ET in such dry conditions, typical of Mediterranean ecosystems.

Bayesian statistics and Monte Carlo methods

NASA Astrophysics Data System (ADS)

Koch, K. R.

2018-03-01

The Bayesian approach allows an intuitive way to derive the methods of statistics. Probability is defined as a measure of the plausibility of statements or propositions. Three rules are sufficient to obtain the laws of probability. If the statements refer to the numerical values of variables, the so-called random variables, univariate and multivariate distributions follow. They lead to the point estimation by which unknown quantities, i.e. unknown parameters, are computed from measurements. The unknown parameters are random variables, they are fixed quantities in traditional statistics which is not founded on Bayes' theorem. Bayesian statistics therefore recommends itself for Monte Carlo methods, which generate random variates from given distributions. Monte Carlo methods, of course, can also be applied in traditional statistics. The unknown parameters, are introduced as functions of the measurements, and the Monte Carlo methods give the covariance matrix and the expectation of these functions. A confidence region is derived where the unknown parameters are situated with a given probability. Following a method of traditional statistics, hypotheses are tested by determining whether a value for an unknown parameter lies inside or outside the confidence region. The error propagation of a random vector by the Monte Carlo methods is presented as an application. If the random vector results from a nonlinearly transformed vector, its covariance matrix and its expectation follow from the Monte Carlo estimate. This saves a considerable amount of derivatives to be computed, and errors of the linearization are avoided. The Monte Carlo method is therefore efficient. If the functions of the measurements are given by a sum of two or more random vectors with different multivariate distributions, the resulting distribution is generally not known. TheMonte Carlo methods are then needed to obtain the covariance matrix and the expectation of the sum.

Covariation of Peptide Abundances Accurately Reflects Protein Concentration Differences*

PubMed Central

Pirmoradian, Mohammad

2017-01-01

Most implementations of mass spectrometry-based proteomics involve enzymatic digestion of proteins, expanding the analysis to multiple proteolytic peptides for each protein. Currently, there is no consensus of how to summarize peptides' abundances to protein concentrations, and such efforts are complicated by the fact that error control normally is applied to the identification process, and do not directly control errors linking peptide abundance measures to protein concentration. Peptides resulting from suboptimal digestion or being partially modified are not representative of the protein concentration. Without a mechanism to remove such unrepresentative peptides, their abundance adversely impacts the estimation of their protein's concentration. Here, we present a relative quantification approach, Diffacto, that applies factor analysis to extract the covariation of peptides' abundances. The method enables a weighted geometrical average summarization and automatic elimination of incoherent peptides. We demonstrate, based on a set of controlled label-free experiments using standard mixtures of proteins, that the covariation structure extracted by the factor analysis accurately reflects protein concentrations. In the 1% peptide-spectrum match-level FDR data set, as many as 11% of the peptides have abundance differences incoherent with the other peptides attributed to the same protein. If not controlled, such contradicting peptide abundance have a severe impact on protein quantifications. When adding the quantities of each protein's three most abundant peptides, we note as many as 14% of the proteins being estimated as having a negative correlation with their actual concentration differences between samples. Diffacto reduced the amount of such obviously incorrectly quantified proteins to 1.6%. Furthermore, by analyzing clinical data sets from two breast cancer studies, our method revealed the persistent proteomic signatures linked to three subtypes of breast cancer. We conclude that Diffacto can facilitate the interpretation and enhance the utility of most types of proteomics data. PMID:28302922

Modeling uncertainty of evapotranspiration measurements from multiple eddy covariance towers over a crop canopy

USDA-ARS?s Scientific Manuscript database

All measurements have random error associated with them. With fluxes in an eddy covariance system, measurement error can been modelled in several ways, often involving a statistical description of turbulence at its core. Using a field experiment with four towers, we generated four replicates of meas...

System identification for modeling for control of flexible structures

NASA Technical Reports Server (NTRS)

Mettler, Edward; Milman, Mark

1986-01-01

The major components of a design and operational flight strategy for flexible structure control systems are presented. In this strategy an initial distributed parameter control design is developed and implemented from available ground test data and on-orbit identification using sophisticated modeling and synthesis techniques. The reliability of this high performance controller is directly linked to the accuracy of the parameters on which the design is based. Because uncertainties inevitably grow without system monitoring, maintaining the control system requires an active on-line system identification function to supply parameter updates and covariance information. Control laws can then be modified to improve performance when the error envelopes are decreased. In terms of system safety and stability the covariance information is of equal importance as the parameter values themselves. If the on-line system ID function detects an increase in parameter error covariances, then corresponding adjustments must be made in the control laws to increase robustness. If the error covariances exceed some threshold, an autonomous calibration sequence could be initiated to restore the error enveloped to an acceptable level.

A Bayesian model for estimating multi-state disease progression.

PubMed

Shen, Shiwen; Han, Simon X; Petousis, Panayiotis; Weiss, Robert E; Meng, Frank; Bui, Alex A T; Hsu, William

2017-02-01

A growing number of individuals who are considered at high risk of cancer are now routinely undergoing population screening. However, noted harms such as radiation exposure, overdiagnosis, and overtreatment underscore the need for better temporal models that predict who should be screened and at what frequency. The mean sojourn time (MST), an average duration period when a tumor can be detected by imaging but with no observable clinical symptoms, is a critical variable for formulating screening policy. Estimation of MST has been long studied using continuous Markov model (CMM) with Maximum likelihood estimation (MLE). However, a lot of traditional methods assume no observation error of the imaging data, which is unlikely and can bias the estimation of the MST. In addition, the MLE may not be stably estimated when data is sparse. Addressing these shortcomings, we present a probabilistic modeling approach for periodic cancer screening data. We first model the cancer state transition using a three state CMM model, while simultaneously considering observation error. We then jointly estimate the MST and observation error within a Bayesian framework. We also consider the inclusion of covariates to estimate individualized rates of disease progression. Our approach is demonstrated on participants who underwent chest x-ray screening in the National Lung Screening Trial (NLST) and validated using posterior predictive p-values and Pearson's chi-square test. Our model demonstrates more accurate and sensible estimates of MST in comparison to MLE. Copyright © 2016 Elsevier Ltd. All rights reserved.

Eddy-covariance data with low signal-to-noise ratio: time-lag determination, uncertainties and limit of detection

NASA Astrophysics Data System (ADS)

Langford, B.; Acton, W.; Ammann, C.; Valach, A.; Nemitz, E.

2015-10-01

All eddy-covariance flux measurements are associated with random uncertainties which are a combination of sampling error due to natural variability in turbulence and sensor noise. The former is the principal error for systems where the signal-to-noise ratio of the analyser is high, as is usually the case when measuring fluxes of heat, CO2 or H2O. Where signal is limited, which is often the case for measurements of other trace gases and aerosols, instrument uncertainties dominate. Here, we are applying a consistent approach based on auto- and cross-covariance functions to quantify the total random flux error and the random error due to instrument noise separately. As with previous approaches, the random error quantification assumes that the time lag between wind and concentration measurement is known. However, if combined with commonly used automated methods that identify the individual time lag by looking for the maximum in the cross-covariance function of the two entities, analyser noise additionally leads to a systematic bias in the fluxes. Combining data sets from several analysers and using simulations, we show that the method of time-lag determination becomes increasingly important as the magnitude of the instrument error approaches that of the sampling error. The flux bias can be particularly significant for disjunct data, whereas using a prescribed time lag eliminates these effects (provided the time lag does not fluctuate unduly over time). We also demonstrate that when sampling at higher elevations, where low frequency turbulence dominates and covariance peaks are broader, both the probability and magnitude of bias are magnified. We show that the statistical significance of noisy flux data can be increased (limit of detection can be decreased) by appropriate averaging of individual fluxes, but only if systematic biases are avoided by using a prescribed time lag. Finally, we make recommendations for the analysis and reporting of data with low signal-to-noise and their associated errors.

Eddy-covariance data with low signal-to-noise ratio: time-lag determination, uncertainties and limit of detection

NASA Astrophysics Data System (ADS)

Langford, B.; Acton, W.; Ammann, C.; Valach, A.; Nemitz, E.

2015-03-01

All eddy-covariance flux measurements are associated with random uncertainties which are a combination of sampling error due to natural variability in turbulence and sensor noise. The former is the principal error for systems where the signal-to-noise ratio of the analyser is high, as is usually the case when measuring fluxes of heat, CO2 or H2O. Where signal is limited, which is often the case for measurements of other trace gases and aerosols, instrument uncertainties dominate. We are here applying a consistent approach based on auto- and cross-covariance functions to quantifying the total random flux error and the random error due to instrument noise separately. As with previous approaches, the random error quantification assumes that the time-lag between wind and concentration measurement is known. However, if combined with commonly used automated methods that identify the individual time-lag by looking for the maximum in the cross-covariance function of the two entities, analyser noise additionally leads to a systematic bias in the fluxes. Combining datasets from several analysers and using simulations we show that the method of time-lag determination becomes increasingly important as the magnitude of the instrument error approaches that of the sampling error. The flux bias can be particularly significant for disjunct data, whereas using a prescribed time-lag eliminates these effects (provided the time-lag does not fluctuate unduly over time). We also demonstrate that when sampling at higher elevations, where low frequency turbulence dominates and covariance peaks are broader, both the probability and magnitude of bias are magnified. We show that the statistical significance of noisy flux data can be increased (limit of detection can be decreased) by appropriate averaging of individual fluxes, but only if systematic biases are avoided by using a prescribed time-lag. Finally, we make recommendations for the analysis and reporting of data with low signal-to-noise and their associated errors.

Performance of internal covariance estimators for cosmic shear correlation functions

DOE PAGES

Friedrich, O.; Seitz, S.; Eifler, T. F.; ...

2015-12-31

Data re-sampling methods such as the delete-one jackknife are a common tool for estimating the covariance of large scale structure probes. In this paper we investigate the concepts of internal covariance estimation in the context of cosmic shear two-point statistics. We demonstrate how to use log-normal simulations of the convergence field and the corresponding shear field to carry out realistic tests of internal covariance estimators and find that most estimators such as jackknife or sub-sample covariance can reach a satisfactory compromise between bias and variance of the estimated covariance. In a forecast for the complete, 5-year DES survey we show that internally estimated covariance matrices can provide a large fraction of the true uncertainties on cosmological parameters in a 2D cosmic shear analysis. The volume inside contours of constant likelihood in themore » $$\\Omega_m$$-$$\\sigma_8$$ plane as measured with internally estimated covariance matrices is on average $$\\gtrsim 85\\%$$ of the volume derived from the true covariance matrix. The uncertainty on the parameter combination $$\\Sigma_8 \\sim \\sigma_8 \\Omega_m^{0.5}$$ derived from internally estimated covariances is $$\\sim 90\\%$$ of the true uncertainty.« less

Turbulent CO2 Flux Measurements by Lidar: Length Scales, Results and Comparison with In-Situ Sensors

NASA Technical Reports Server (NTRS)

Gilbert, Fabien; Koch, Grady J.; Beyon, Jeffrey Y.; Hilton, Timothy W.; Davis, Kenneth J.; Andrews, Arlyn; Ismail, Syed; Singh, Upendra N.

2009-01-01

The vertical CO2 flux in the atmospheric boundary layer (ABL) is investigated with a Doppler differential absorption lidar (DIAL). The instrument was operated next to the WLEF instrumented tall tower in Park Falls, Wisconsin during three days and nights in June 2007. Profiles of turbulent CO2 mixing ratio and vertical velocity fluctuations are measured by in-situ sensors and Doppler DIAL. Time and space scales of turbulence are precisely defined in the ABL. The eddy-covariance method is applied to calculate turbulent CO2 flux both by lidar and in-situ sensors. We show preliminary mean lidar CO2 flux measurements in the ABL with a time and space resolution of 6 h and 1500 m respectively. The flux instrumental errors decrease linearly with the standard deviation of the CO2 data, as expected. Although turbulent fluctuations of CO2 are negligible with respect to the mean (0.1 %), we show that the eddy-covariance method can provide 2-h, 150-m range resolved CO2 flux estimates as long as the CO2 mixing ratio instrumental error is no greater than 10 ppm and the vertical velocity error is lower than the natural fluctuations over a time resolution of 10 s.

Exploratory graphical models of functional and structural connectivity patterns for Alzheimer's Disease diagnosis.

PubMed

Ortiz, Andrés; Munilla, Jorge; Álvarez-Illán, Ignacio; Górriz, Juan M; Ramírez, Javier

2015-01-01

Alzheimer's Disease (AD) is the most common neurodegenerative disease in elderly people. Its development has been shown to be closely related to changes in the brain connectivity network and in the brain activation patterns along with structural changes caused by the neurodegenerative process. Methods to infer dependence between brain regions are usually derived from the analysis of covariance between activation levels in the different areas. However, these covariance-based methods are not able to estimate conditional independence between variables to factor out the influence of other regions. Conversely, models based on the inverse covariance, or precision matrix, such as Sparse Gaussian Graphical Models allow revealing conditional independence between regions by estimating the covariance between two variables given the rest as constant. This paper uses Sparse Inverse Covariance Estimation (SICE) methods to learn undirected graphs in order to derive functional and structural connectivity patterns from Fludeoxyglucose (18F-FDG) Position Emission Tomography (PET) data and segmented Magnetic Resonance images (MRI), drawn from the ADNI database, for Control, MCI (Mild Cognitive Impairment Subjects), and AD subjects. Sparse computation fits perfectly here as brain regions usually only interact with a few other areas. The models clearly show different metabolic covariation patters between subject groups, revealing the loss of strong connections in AD and MCI subjects when compared to Controls. Similarly, the variance between GM (Gray Matter) densities of different regions reveals different structural covariation patterns between the different groups. Thus, the different connectivity patterns for controls and AD are used in this paper to select regions of interest in PET and GM images with discriminative power for early AD diagnosis. Finally, functional an structural models are combined to leverage the classification accuracy. The results obtained in this work show the usefulness of the Sparse Gaussian Graphical models to reveal functional and structural connectivity patterns. This information provided by the sparse inverse covariance matrices is not only used in an exploratory way but we also propose a method to use it in a discriminative way. Regression coefficients are used to compute reconstruction errors for the different classes that are then introduced in a SVM for classification. Classification experiments performed using 68 Controls, 70 AD, and 111 MCI images and assessed by cross-validation show the effectiveness of the proposed method.

Hyper-X Mach 10 Trajectory Reconstruction

NASA Technical Reports Server (NTRS)

Karlgaard, Christopher D.; Martin, John G.; Tartabini, Paul V.; Thornblom, Mark N.

2005-01-01

This paper discusses the formulation and development of a trajectory reconstruction tool for the NASA X-43A/Hyper-X high speed research vehicle, and its implementation for the reconstruction and analysis of flight test data. Extended Kalman filtering techniques are employed to reconstruct the trajectory of the vehicle, based upon numerical integration of inertial measurement data along with redundant measurements of the vehicle state. The equations of motion are formulated in order to include the effects of several systematic error sources, whose values may also be estimated by the filtering routines. Additionally, smoothing algorithms have been implemented in which the final value of the state (or an augmented state that includes other systematic error parameters to be estimated) and covariance are propagated back to the initial time to generate the best-estimated trajectory, based upon all available data. The methods are applied to the problem of reconstructing the trajectory of the Hyper-X vehicle from data obtained during the Mach 10 test flight, which occurred on November 16th 2004.

A method to estimate statistical errors of properties derived from charge-density modelling

PubMed Central

Lecomte, Claude

2018-01-01

Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This ‘SSD methodology’ procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling. PMID:29724964

Further Improvements to Linear Mixed Models for Genome-Wide Association Studies

PubMed Central

Widmer, Christian; Lippert, Christoph; Weissbrod, Omer; Fusi, Nicolo; Kadie, Carl; Davidson, Robert; Listgarten, Jennifer; Heckerman, David

2014-01-01

We examine improvements to the linear mixed model (LMM) that better correct for population structure and family relatedness in genome-wide association studies (GWAS). LMMs rely on the estimation of a genetic similarity matrix (GSM), which encodes the pairwise similarity between every two individuals in a cohort. These similarities are estimated from single nucleotide polymorphisms (SNPs) or other genetic variants. Traditionally, all available SNPs are used to estimate the GSM. In empirical studies across a wide range of synthetic and real data, we find that modifications to this approach improve GWAS performance as measured by type I error control and power. Specifically, when only population structure is present, a GSM constructed from SNPs that well predict the phenotype in combination with principal components as covariates controls type I error and yields more power than the traditional LMM. In any setting, with or without population structure or family relatedness, a GSM consisting of a mixture of two component GSMs, one constructed from all SNPs and another constructed from SNPs that well predict the phenotype again controls type I error and yields more power than the traditional LMM. Software implementing these improvements and the experimental comparisons are available at http://microsoft.com/science. PMID:25387525

Further Improvements to Linear Mixed Models for Genome-Wide Association Studies

NASA Astrophysics Data System (ADS)

Widmer, Christian; Lippert, Christoph; Weissbrod, Omer; Fusi, Nicolo; Kadie, Carl; Davidson, Robert; Listgarten, Jennifer; Heckerman, David

2014-11-01

We examine improvements to the linear mixed model (LMM) that better correct for population structure and family relatedness in genome-wide association studies (GWAS). LMMs rely on the estimation of a genetic similarity matrix (GSM), which encodes the pairwise similarity between every two individuals in a cohort. These similarities are estimated from single nucleotide polymorphisms (SNPs) or other genetic variants. Traditionally, all available SNPs are used to estimate the GSM. In empirical studies across a wide range of synthetic and real data, we find that modifications to this approach improve GWAS performance as measured by type I error control and power. Specifically, when only population structure is present, a GSM constructed from SNPs that well predict the phenotype in combination with principal components as covariates controls type I error and yields more power than the traditional LMM. In any setting, with or without population structure or family relatedness, a GSM consisting of a mixture of two component GSMs, one constructed from all SNPs and another constructed from SNPs that well predict the phenotype again controls type I error and yields more power than the traditional LMM. Software implementing these improvements and the experimental comparisons are available at http://microsoft.com/science.

Further improvements to linear mixed models for genome-wide association studies.

PubMed

Widmer, Christian; Lippert, Christoph; Weissbrod, Omer; Fusi, Nicolo; Kadie, Carl; Davidson, Robert; Listgarten, Jennifer; Heckerman, David

2014-11-12

We examine improvements to the linear mixed model (LMM) that better correct for population structure and family relatedness in genome-wide association studies (GWAS). LMMs rely on the estimation of a genetic similarity matrix (GSM), which encodes the pairwise similarity between every two individuals in a cohort. These similarities are estimated from single nucleotide polymorphisms (SNPs) or other genetic variants. Traditionally, all available SNPs are used to estimate the GSM. In empirical studies across a wide range of synthetic and real data, we find that modifications to this approach improve GWAS performance as measured by type I error control and power. Specifically, when only population structure is present, a GSM constructed from SNPs that well predict the phenotype in combination with principal components as covariates controls type I error and yields more power than the traditional LMM. In any setting, with or without population structure or family relatedness, a GSM consisting of a mixture of two component GSMs, one constructed from all SNPs and another constructed from SNPs that well predict the phenotype again controls type I error and yields more power than the traditional LMM. Software implementing these improvements and the experimental comparisons are available at http://microsoft.com/science.

Detection of the pairwise kinematic Sunyaev-Zel'dovich effect with BOSS DR11 and the Atacama Cosmology Telescope

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernardis, F. De; Vavagiakis, E.M.; Niemack, M.D.

We present a new measurement of the kinematic Sunyaev-Zel'dovich effect using data from the Atacama Cosmology Telescope (ACT) and the Baryon Oscillation Spectroscopic Survey (BOSS). Using 600 square degrees of overlapping sky area, we evaluate the mean pairwise baryon momentum associated with the positions of 50,000 bright galaxies in the BOSS DR11 Large Scale Structure catalog. A non-zero signal arises from the large-scale motions of halos containing the sample galaxies. The data fits an analytical signal model well, with the optical depth to microwave photon scattering as a free parameter determining the overall signal amplitude. We estimate the covariance matrixmore » of the mean pairwise momentum as a function of galaxy separation, using microwave sky simulations, jackknife evaluation, and bootstrap estimates. The most conservative simulation-based errors give signal-to-noise estimates between 3.6 and 4.1 for varying galaxy luminosity cuts. We discuss how the other error determinations can lead to higher signal-to-noise values, and consider the impact of several possible systematic errors. Estimates of the optical depth from the average thermal Sunyaev-Zel'dovich signal at the sample galaxy positions are broadly consistent with those obtained from the mean pairwise momentum signal.« less

Detection of the Pairwise Kinematic Sunyaev-Zel'dovich Effect with BOSS DR11 and the Atacama Cosmology Telescope

NASA Technical Reports Server (NTRS)

De Bernardis, F.; Aiola, S.; Vavagiakis, E. M.; Battaglia, N.; Niemack, M. D.; Beall, J.; Becker, D. T.; Bond, J. R.; Calabrese, E.; Cho, H.;

Detection of the pairwise kinematic Sunyaev-Zel'dovich effect with BOSS DR11 and the Atacama Cosmology Telescope

NASA Astrophysics Data System (ADS)

De Bernardis, F.; Aiola, S.; Vavagiakis, E. M.; Battaglia, N.; Niemack, M. D.; Beall, J.; Becker, D. T.; Bond, J. R.; Calabrese, E.; Cho, H.; Coughlin, K.; Datta, R.; Devlin, M.; Dunkley, J.; Dunner, R.; Ferraro, S.; Fox, A.; Gallardo, P. A.; Halpern, M.; Hand, N.; Hasselfield, M.; Henderson, S. W.; Hill, J. C.; Hilton, G. C.; Hilton, M.; Hincks, A. D.; Hlozek, R.; Hubmayr, J.; Huffenberger, K.; Hughes, J. P.; Irwin, K. D.; Koopman, B. J.; Kosowsky, A.; Li, D.; Louis, T.; Lungu, M.; Madhavacheril, M. S.; Maurin, L.; McMahon, J.; Moodley, K.; Naess, S.; Nati, F.; Newburgh, L.; Nibarger, J. P.; Page, L. A.; Partridge, B.; Schaan, E.; Schmitt, B. L.; Sehgal, N.; Sievers, J.; Simon, S. M.; Spergel, D. N.; Staggs, S. T.; Stevens, J. R.; Thornton, R. J.; van Engelen, A.; Van Lanen, J.; Wollack, E. J.

2017-03-01

We present a new measurement of the kinematic Sunyaev-Zel'dovich effect using data from the Atacama Cosmology Telescope (ACT) and the Baryon Oscillation Spectroscopic Survey (BOSS). Using 600 square degrees of overlapping sky area, we evaluate the mean pairwise baryon momentum associated with the positions of 50,000 bright galaxies in the BOSS DR11 Large Scale Structure catalog. A non-zero signal arises from the large-scale motions of halos containing the sample galaxies. The data fits an analytical signal model well, with the optical depth to microwave photon scattering as a free parameter determining the overall signal amplitude. We estimate the covariance matrix of the mean pairwise momentum as a function of galaxy separation, using microwave sky simulations, jackknife evaluation, and bootstrap estimates. The most conservative simulation-based errors give signal-to-noise estimates between 3.6 and 4.1 for varying galaxy luminosity cuts. We discuss how the other error determinations can lead to higher signal-to-noise values, and consider the impact of several possible systematic errors. Estimates of the optical depth from the average thermal Sunyaev-Zel'dovich signal at the sample galaxy positions are broadly consistent with those obtained from the mean pairwise momentum signal.

Fitting a function to time-dependent ensemble averaged data.

PubMed

Fogelmark, Karl; Lomholt, Michael A; Irbäck, Anders; Ambjörnsson, Tobias

2018-05-03

Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared displacements) with a function and extract parameters (such as diffusion constants). A commonly overlooked challenge in such function fitting procedures is that fluctuations around mean values, by construction, exhibit temporal correlations. We show that the only available general purpose function fitting methods, correlated chi-square method and the weighted least squares method (which neglects correlation), fail at either robust parameter estimation or accurate error estimation. We remedy this by deriving a new closed-form error estimation formula for weighted least square fitting. The new formula uses the full covariance matrix, i.e., rigorously includes temporal correlations, but is free of the robustness issues, inherent to the correlated chi-square method. We demonstrate its accuracy in four examples of importance in many fields: Brownian motion, damped harmonic oscillation, fractional Brownian motion and continuous time random walks. We also successfully apply our method, weighted least squares including correlation in error estimation (WLS-ICE), to particle tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and we provide a publically available WLS-ICE software.

Nonlinear problems in data-assimilation : Can synchronization help?

NASA Astrophysics Data System (ADS)

Tribbia, J. J.; Duane, G. S.

2009-12-01

Over the past several years, operational weather centers have initiated ensemble prediction and assimilation techniques to estimate the error covariance of forecasts in the short and the medium range. The ensemble techniques used are based on linear methods. The theory This technique s been shown to be a useful indicator of skill in the linear range where forecast errors are small relative to climatological variance. While this advance has been impressive, there are still ad hoc aspects of its use in practice, like the need for covariance inflation which are troubling. Furthermore, to be of utility in the nonlinear range an ensemble assimilation and prediction method must be capable of giving probabilistic information for the situation where a probability density forecast becomes multi-modal. A prototypical, simplest example of such a situation is the planetary-wave regime transition where the pdf is bimodal. Our recent research show how the inconsistencies and extensions of linear methodology can be consistently treated using the paradigm of synchronization which views the problems of assimilation and forecasting as that of optimizing the forecast model state with respect to the future evolution of the atmosphere.

Adaptive optimisation-offline cyber attack on remote state estimator

NASA Astrophysics Data System (ADS)

Huang, Xin; Dong, Jiuxiang

2017-10-01

Security issues of cyber-physical systems have received increasing attentions in recent years. In this paper, deception attacks on the remote state estimator equipped with the chi-squared failure detector are considered, and it is assumed that the attacker can monitor and modify all the sensor data. A novel adaptive optimisation-offline cyber attack strategy is proposed, where using the current and previous sensor data, the attack can yield the largest estimation error covariance while ensuring to be undetected by the chi-squared monitor. From the attacker's perspective, the attack is better than the existing linear deception attacks to degrade the system performance. Finally, some numerical examples are provided to demonstrate theoretical results.

Testing and Estimating Shape-Constrained Nonparametric Density and Regression in the Presence of Measurement Error.

PubMed

Carroll, Raymond J; Delaigle, Aurore; Hall, Peter

2011-03-01

In many applications we can expect that, or are interested to know if, a density function or a regression curve satisfies some specific shape constraints. For example, when the explanatory variable, X, represents the value taken by a treatment or dosage, the conditional mean of the response, Y , is often anticipated to be a monotone function of X. Indeed, if this regression mean is not monotone (in the appropriate direction) then the medical or commercial value of the treatment is likely to be significantly curtailed, at least for values of X that lie beyond the point at which monotonicity fails. In the case of a density, common shape constraints include log-concavity and unimodality. If we can correctly guess the shape of a curve, then nonparametric estimators can be improved by taking this information into account. Addressing such problems requires a method for testing the hypothesis that the curve of interest satisfies a shape constraint, and, if the conclusion of the test is positive, a technique for estimating the curve subject to the constraint. Nonparametric methodology for solving these problems already exists, but only in cases where the covariates are observed precisely. However in many problems, data can only be observed with measurement errors, and the methods employed in the error-free case typically do not carry over to this error context. In this paper we develop a novel approach to hypothesis testing and function estimation under shape constraints, which is valid in the context of measurement errors. Our method is based on tilting an estimator of the density or the regression mean until it satisfies the shape constraint, and we take as our test statistic the distance through which it is tilted. Bootstrap methods are used to calibrate the test. The constrained curve estimators that we develop are also based on tilting, and in that context our work has points of contact with methodology in the error-free case.

Risks of Large Portfolios

PubMed Central

Fan, Jianqing; Liao, Yuan; Shi, Xiaofeng

2014-01-01

The risk of a large portfolio is often estimated by substituting a good estimator of the volatility matrix. However, the accuracy of such a risk estimator is largely unknown. We study factor-based risk estimators under a large amount of assets, and introduce a high-confidence level upper bound (H-CLUB) to assess the estimation. The H-CLUB is constructed using the confidence interval of risk estimators with either known or unknown factors. We derive the limiting distribution of the estimated risks in high dimensionality. We find that when the dimension is large, the factor-based risk estimators have the same asymptotic variance no matter whether the factors are known or not, which is slightly smaller than that of the sample covariance-based estimator. Numerically, H-CLUB outperforms the traditional crude bounds, and provides an insightful risk assessment. In addition, our simulated results quantify the relative error in the risk estimation, which is usually negligible using 3-month daily data. PMID:26195851

On the regularity of the covariance matrix of a discretized scalar field on the sphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bilbao-Ahedo, J.D.; Barreiro, R.B.; Herranz, D.

2017-02-01

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizationsmore » that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.« less

Inadequacy of internal covariance estimation for super-sample covariance

NASA Astrophysics Data System (ADS)

Lacasa, Fabien; Kunz, Martin

2017-08-01

We give an analytical interpretation of how subsample-based internal covariance estimators lead to biased estimates of the covariance, due to underestimating the super-sample covariance (SSC). This includes the jackknife and bootstrap methods as estimators for the full survey area, and subsampling as an estimator of the covariance of subsamples. The limitations of the jackknife covariance have been previously presented in the literature because it is effectively a rescaling of the covariance of the subsample area. However we point out that subsampling is also biased, but for a different reason: the subsamples are not independent, and the corresponding lack of power results in SSC underprediction. We develop the formalism in the case of cluster counts that allows the bias of each covariance estimator to be exactly predicted. We find significant effects for a small-scale area or when a low number of subsamples is used, with auto-redshift biases ranging from 0.4% to 15% for subsampling and from 5% to 75% for jackknife covariance estimates. The cross-redshift covariance is even more affected; biases range from 8% to 25% for subsampling and from 50% to 90% for jackknife. Owing to the redshift evolution of the probe, the covariances cannot be debiased by a simple rescaling factor, and an exact debiasing has the same requirements as the full SSC prediction. These results thus disfavour the use of internal covariance estimators on data itself or a single simulation, leaving analytical prediction and simulations suites as possible SSC predictors.

Event-Based Sensing and Control for Remote Robot Guidance: An Experimental Case

PubMed Central

Santos, Carlos; Martínez-Rey, Miguel; Santiso, Enrique

2017-01-01

This paper describes the theoretical and practical foundations for remote control of a mobile robot for nonlinear trajectory tracking using an external localisation sensor. It constitutes a classical networked control system, whereby event-based techniques for both control and state estimation contribute to efficient use of communications and reduce sensor activity. Measurement requests are dictated by an event-based state estimator by setting an upper bound to the estimation error covariance matrix. The rest of the time, state prediction is carried out with the Unscented transformation. This prediction method makes it possible to select the appropriate instants at which to perform actuations on the robot so that guidance performance does not degrade below a certain threshold. Ultimately, we obtained a combined event-based control and estimation solution that drastically reduces communication accesses. The magnitude of this reduction is set according to the tracking error margin of a P3-DX robot following a nonlinear trajectory, remotely controlled with a mini PC and whose pose is detected by a camera sensor. PMID:28878144

Exploration and extension of an improved Riemann track fitting algorithm

NASA Astrophysics Data System (ADS)

Strandlie, A.; Frühwirth, R.

2017-09-01

Recently, a new Riemann track fit which operates on translated and scaled measurements has been proposed. This study shows that the new Riemann fit is virtually as precise as popular approaches such as the Kalman filter or an iterative non-linear track fitting procedure, and significantly more precise than other, non-iterative circular track fitting approaches over a large range of measurement uncertainties. The fit is then extended in two directions: first, the measurements are allowed to lie on plane sensors of arbitrary orientation; second, the full error propagation from the measurements to the estimated circle parameters is computed. The covariance matrix of the estimated track parameters can therefore be computed without recourse to asymptotic properties, and is consequently valid for any number of observation. It does, however, assume normally distributed measurement errors. The calculations are validated on a simulated track sample and show excellent agreement with the theoretical expectations.

Development of adaptive observation strategy using retrospective optimal interpolation

NASA Astrophysics Data System (ADS)

Noh, N.; Kim, S.; Song, H.; Lim, G.

2011-12-01

Retrospective optimal interpolation (ROI) is a method that is used to minimize cost functions with multiple minima without using adjoint models. Song and Lim (2011) perform the experiments to reduce the computational costs for implementing ROI by transforming the control variables into eigenvectors of background error covariance. We adapt the ROI algorithm to compute sensitivity estimates of severe weather events over the Korean peninsula. The eigenvectors of the ROI algorithm is modified every time the observations are assimilated. This implies that the modified eigenvectors shows the error distribution of control variables which are updated by assimilating observations. So, We can estimate the effects of the specific observations. In order to verify the adaptive observation strategy, High-impact weather over the Korean peninsula is simulated and interpreted using WRF modeling system and sensitive regions for each high-impact weather is calculated. The effects of assimilation for each observation type is discussed.

Submillimeter, millimeter, and microwave spectral line catalogue

NASA Technical Reports Server (NTRS)

Poynter, R. L.; Pickett, H. M.

1984-01-01

This report describes a computer accessible catalogue of submillimeter, millimeter, and microwave spectral lines in the frequency range between 0 and 10000 GHz (i.e., wavelengths longer than 30 micrometers). The catalogue can be used as a planning guide or as an aid in the identification and analysis of observed spectral lines. The information listed for each spectral line includes the frequency and its estimated error, the intensity, lower state energy, and quantum number assignment. The catalogue has been constructed using theoretical least squares fits of published spectral lines to accepted molecular models. The associated predictions and their estimated errors are based upon the resultant fitted parameters and their covariances. Future versions of this catalogue will add more atoms and molecules and update the present listings (151 species) as new data appear. The catalogue is available from the authors as a magnetic tape recorded in card images and as a set of microfiche records.

Submillimeter, millimeter, and microwave spectral line catalogue

NASA Technical Reports Server (NTRS)

Poynter, R. L.; Pickett, H. M.

1981-01-01

A computer accessible catalogue of submillimeter, millimeter and microwave spectral lines in the frequency range between 0 and 3000 GHZ (i.e., wavelengths longer than 100 mu m) is presented which can be used a planning guide or as an aid in the identification and analysis of observed spectral lines. The information listed for each spectral line includes the frequency and its estimated error, the intensity, lower state energy, and quantum number assignment. The catalogue was constructed by using theoretical least squares fits of published spectral lines to accepted molecular models. The associated predictions and their estimated errors are based upon the resultant fitted parameters and their covariances. Future versions of this catalogue will add more atoms and molecules and update the present listings (133 species) as new data appear. The catalogue is available as a magnetic tape recorded in card images and as a set of microfiche records.

Site Distribution and Aliasing Effects in the Inversion for Load Coefficients and Geocenter Motion from GPS Data

NASA Technical Reports Server (NTRS)

Wu, Xiaoping; Argus, Donald F.; Heflin, Michael B.; Ivins, Erik R.; Webb, Frank H.

2002-01-01

Precise GPS measurements of elastic relative site displacements due to surface mass loading offer important constraints on global surface mass transport. We investigate effects of site distribution and aliasing by higher-degree (n greater than or equal 2) loading terms on inversion of GPS data for n = 1 load coefficients and geocenter motion. Covariance and simulation analyses are conducted to assess the sensitivity of the inversion to aliasing and mismodeling errors and possible uncertainties in the n = 1 load coefficient determination. We found that the use of center-of-figure approximation in the inverse formulation could cause 10- 15% errors in the inverted load coefficients. n = 1 load estimates may be contaminated significantly by unknown higher-degree terms, depending on the load scenario and the GPS site distribution. The uncertainty in n = 1 zonal load estimate is at the level of 80 - 95% for two load scenarios.

Consequences of incomplete surface energy balance closure for CO2 fluxes from open-path CO2/H2O infrared gas analyzers

Treesearch

Heping Liu; James T. Randerson; Jamie Lindfors; William J. Massman; Thomas Foken

2006-01-01

We present an approach for assessing the impact of systematic biases in measured energy fluxes on CO2 flux estimates obtained from open-path eddy-covariance systems. In our analysis, we present equations to analyse the propagation of errors through the Webb, Pearman, and Leuning (WPL) algorithm [Quart. J. Roy. Meteorol. Soc. 106, 85­100, 1980] that is widely used to...

Fast Generation of Ensembles of Cosmological N-Body Simulations via Mode-Resampling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schneider, M D; Cole, S; Frenk, C S

2011-02-14

We present an algorithm for quickly generating multiple realizations of N-body simulations to be used, for example, for cosmological parameter estimation from surveys of large-scale structure. Our algorithm uses a new method to resample the large-scale (Gaussian-distributed) Fourier modes in a periodic N-body simulation box in a manner that properly accounts for the nonlinear mode-coupling between large and small scales. We find that our method for adding new large-scale mode realizations recovers the nonlinear power spectrum to sub-percent accuracy on scales larger than about half the Nyquist frequency of the simulation box. Using 20 N-body simulations, we obtain a powermore » spectrum covariance matrix estimate that matches the estimator from Takahashi et al. (from 5000 simulations) with < 20% errors in all matrix elements. Comparing the rates of convergence, we determine that our algorithm requires {approx}8 times fewer simulations to achieve a given error tolerance in estimates of the power spectrum covariance matrix. The degree of success of our algorithm indicates that we understand the main physical processes that give rise to the correlations in the matter power spectrum. Namely, the large-scale Fourier modes modulate both the degree of structure growth through the variation in the effective local matter density and also the spatial frequency of small-scale perturbations through large-scale displacements. We expect our algorithm to be useful for noise modeling when constraining cosmological parameters from weak lensing (cosmic shear) and galaxy surveys, rescaling summary statistics of N-body simulations for new cosmological parameter values, and any applications where the influence of Fourier modes larger than the simulation size must be accounted for.« less

Stable Estimation of a Covariance Matrix Guided by Nuclear Norm Penalties

PubMed Central

Chi, Eric C.; Lange, Kenneth

2014-01-01

Estimation of a covariance matrix or its inverse plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. The current paper introduces a novel prior to ensure a well-conditioned maximum a posteriori (MAP) covariance estimate. The prior shrinks the sample covariance estimator towards a stable target and leads to a MAP estimator that is consistent and asymptotically efficient. Thus, the MAP estimator gracefully transitions towards the sample covariance matrix as the number of samples grows relative to the number of covariates. The utility of the MAP estimator is demonstrated in two standard applications – discriminant analysis and EM clustering – in this sampling regime. PMID:25143662

Improving mass-univariate analysis of neuroimaging data by modelling important unknown covariates: Application to Epigenome-Wide Association Studies.

PubMed

Guillaume, Bryan; Wang, Changqing; Poh, Joann; Shen, Mo Jun; Ong, Mei Lyn; Tan, Pei Fang; Karnani, Neerja; Meaney, Michael; Qiu, Anqi

2018-06-01

Statistical inference on neuroimaging data is often conducted using a mass-univariate model, equivalent to fitting a linear model at every voxel with a known set of covariates. Due to the large number of linear models, it is challenging to check if the selection of covariates is appropriate and to modify this selection adequately. The use of standard diagnostics, such as residual plotting, is clearly not practical for neuroimaging data. However, the selection of covariates is crucial for linear regression to ensure valid statistical inference. In particular, the mean model of regression needs to be reasonably well specified. Unfortunately, this issue is often overlooked in the field of neuroimaging. This study aims to adopt the existing Confounder Adjusted Testing and Estimation (CATE) approach and to extend it for use with neuroimaging data. We propose a modification of CATE that can yield valid statistical inferences using Principal Component Analysis (PCA) estimators instead of Maximum Likelihood (ML) estimators. We then propose a non-parametric hypothesis testing procedure that can improve upon parametric testing. Monte Carlo simulations show that the modification of CATE allows for more accurate modelling of neuroimaging data and can in turn yield a better control of False Positive Rate (FPR) and Family-Wise Error Rate (FWER). We demonstrate its application to an Epigenome-Wide Association Study (EWAS) on neonatal brain imaging and umbilical cord DNA methylation data obtained as part of a longitudinal cohort study. Software for this CATE study is freely available at http://www.bioeng.nus.edu.sg/cfa/Imaging_Genetics2.html. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

Three Cs in measurement models: causal indicators, composite indicators, and covariates.

PubMed

Bollen, Kenneth A; Bauldry, Shawn

2011-09-01

In the last 2 decades attention to causal (and formative) indicators has grown. Accompanying this growth has been the belief that one can classify indicators into 2 categories: effect (reflective) indicators and causal (formative) indicators. We argue that the dichotomous view is too simple. Instead, there are effect indicators and 3 types of variables on which a latent variable depends: causal indicators, composite (formative) indicators, and covariates (the "Three Cs"). Causal indicators have conceptual unity, and their effects on latent variables are structural. Covariates are not concept measures, but are variables to control to avoid bias in estimating the relations between measures and latent variables. Composite (formative) indicators form exact linear combinations of variables that need not share a concept. Their coefficients are weights rather than structural effects, and composites are a matter of convenience. The failure to distinguish the Three Cs has led to confusion and questions, such as, Are causal and formative indicators different names for the same indicator type? Should an equation with causal or formative indicators have an error term? Are the coefficients of causal indicators less stable than effect indicators? Distinguishing between causal and composite indicators and covariates goes a long way toward eliminating this confusion. We emphasize the key role that subject matter expertise plays in making these distinctions. We provide new guidelines for working with these variable types, including identification of models, scaling latent variables, parameter estimation, and validity assessment. A running empirical example on self-perceived health illustrates our major points.

Full-Duplex Bidirectional Secure Communications Under Perfect and Distributionally Ambiguous Eavesdropper's CSI

NASA Astrophysics Data System (ADS)

Li, Qiang; Zhang, Ying; Lin, Jingran; Wu, Sissi Xiaoxiao

2017-09-01

Consider a full-duplex (FD) bidirectional secure communication system, where two communication nodes, named Alice and Bob, simultaneously transmit and receive confidential information from each other, and an eavesdropper, named Eve, overhears the transmissions. Our goal is to maximize the sum secrecy rate (SSR) of the bidirectional transmissions by optimizing the transmit covariance matrices at Alice and Bob. To tackle this SSR maximization (SSRM) problem, we develop an alternating difference-of-concave (ADC) programming approach to alternately optimize the transmit covariance matrices at Alice and Bob. We show that the ADC iteration has a semi-closed-form beamforming solution, and is guaranteed to converge to a stationary solution of the SSRM problem. Besides the SSRM design, this paper also deals with a robust SSRM transmit design under a moment-based random channel state information (CSI) model, where only some roughly estimated first and second-order statistics of Eve's CSI are available, but the exact distribution or other high-order statistics is not known. This moment-based error model is new and different from the widely used bounded-sphere error model and the Gaussian random error model. Under the consider CSI error model, the robust SSRM is formulated as an outage probability-constrained SSRM problem. By leveraging the Lagrangian duality theory and DC programming, a tractable safe solution to the robust SSRM problem is derived. The effectiveness and the robustness of the proposed designs are demonstrated through simulations.

Polarimetric image reconstruction algorithms

NASA Astrophysics Data System (ADS)

Valenzuela, John R.

In the field of imaging polarimetry Stokes parameters are sought and must be inferred from noisy and blurred intensity measurements. Using a penalized-likelihood estimation framework we investigate reconstruction quality when estimating intensity images and then transforming to Stokes parameters (traditional estimator), and when estimating Stokes parameters directly (Stokes estimator). We define our cost function for reconstruction by a weighted least squares data fit term and a regularization penalty. It is shown that under quadratic regularization, the traditional and Stokes estimators can be made equal by appropriate choice of regularization parameters. It is empirically shown that, when using edge preserving regularization, estimating the Stokes parameters directly leads to lower RMS error in reconstruction. Also, the addition of a cross channel regularization term further lowers the RMS error for both methods especially in the case of low SNR. The technique of phase diversity has been used in traditional incoherent imaging systems to jointly estimate an object and optical system aberrations. We extend the technique of phase diversity to polarimetric imaging systems. Specifically, we describe penalized-likelihood methods for jointly estimating Stokes images and optical system aberrations from measurements that contain phase diversity. Jointly estimating Stokes images and optical system aberrations involves a large parameter space. A closed-form expression for the estimate of the Stokes images in terms of the aberration parameters is derived and used in a formulation that reduces the dimensionality of the search space to the number of aberration parameters only. We compare the performance of the joint estimator under both quadratic and edge-preserving regularization. The joint estimator with edge-preserving regularization yields higher fidelity polarization estimates than with quadratic regularization. Under quadratic regularization, using the reduced-parameter search strategy, accurate aberration estimates can be obtained without recourse to regularization "tuning". Phase-diverse wavefront sensing is emerging as a viable candidate wavefront sensor for adaptive-optics systems. In a quadratically penalized weighted least squares estimation framework a closed form expression for the object being imaged in terms of the aberrations in the system is available. This expression offers a dramatic reduction of the dimensionality of the estimation problem and thus is of great interest for practical applications. We have derived an expression for an approximate joint covariance matrix for object and aberrations in the phase diversity context. Our expression for the approximate joint covariance is compared with the "known-object" Cramer-Rao lower bound that is typically used for system parameter optimization. Estimates of the optimal amount of defocus in a phase-diverse wavefront sensor derived from the joint-covariance matrix, the known-object Cramer-Rao bound, and Monte Carlo simulations are compared for an extended scene and a point object. It is found that our variance approximation, that incorporates the uncertainty of the object, leads to an improvement in predicting the optimal amount of defocus to use in a phase-diverse wavefront sensor.

Uncertainty Propagation for Terrestrial Mobile Laser Scanner

NASA Astrophysics Data System (ADS)

Mezian, c.; Vallet, Bruno; Soheilian, Bahman; Paparoditis, Nicolas

2016-06-01

Laser scanners are used more and more in mobile mapping systems. They provide 3D point clouds that are used for object reconstruction and registration of the system. For both of those applications, uncertainty analysis of 3D points is of great interest but rarely investigated in the literature. In this paper we present a complete pipeline that takes into account all the sources of uncertainties and allows to compute a covariance matrix per 3D point. The sources of uncertainties are laser scanner, calibration of the scanner in relation to the vehicle and direct georeferencing system. We suppose that all the uncertainties follow the Gaussian law. The variances of the laser scanner measurements (two angles and one distance) are usually evaluated by the constructors. This is also the case for integrated direct georeferencing devices. Residuals of the calibration process were used to estimate the covariance matrix of the 6D transformation between scanner laser and the vehicle system. Knowing the variances of all sources of uncertainties, we applied uncertainty propagation technique to compute the variance-covariance matrix of every obtained 3D point. Such an uncertainty analysis enables to estimate the impact of different laser scanners and georeferencing devices on the quality of obtained 3D points. The obtained uncertainty values were illustrated using error ellipsoids on different datasets.

Trans-dimensional inversion of microtremor array dispersion data with hierarchical autoregressive error models

NASA Astrophysics Data System (ADS)

Dettmer, Jan; Molnar, Sheri; Steininger, Gavin; Dosso, Stan E.; Cassidy, John F.

2012-02-01

This paper applies a general trans-dimensional Bayesian inference methodology and hierarchical autoregressive data-error models to the inversion of microtremor array dispersion data for shear wave velocity (vs) structure. This approach accounts for the limited knowledge of the optimal earth model parametrization (e.g. the number of layers in the vs profile) and of the data-error statistics in the resulting vs parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A trans-dimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the indexing parameter) are considered in the results. The earth model is parametrized in terms of a partition model with interfaces given over a depth-range of interest. In this work, the number of interfaces (layers) in the partition model represents the trans-dimensional model indexing. In addition, serial data-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate data-error statistics, and have no requirement for computing the inverse or determinant of a data-error covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the state space that spans multiple subspaces of different dimensionalities. The order of the autoregressive process required to fit the data is determined here by posterior residual-sample examination and statistical tests. Inference for earth model parameters is carried out on the trans-dimensional posterior probability distribution by considering ensembles of parameter vectors. In particular, vs uncertainty estimates are obtained by marginalizing the trans-dimensional posterior distribution in terms of vs-profile marginal distributions. The methodology is applied to microtremor array dispersion data collected at two sites with significantly different geology in British Columbia, Canada. At both sites, results show excellent agreement with estimates from invasive measurements.

Prediction of true test scores from observed item scores and ancillary data.

PubMed

Haberman, Shelby J; Yao, Lili; Sinharay, Sandip

2015-05-01

In many educational tests which involve constructed responses, a traditional test score is obtained by adding together item scores obtained through holistic scoring by trained human raters. For example, this practice was used until 2008 in the case of GRE(®) General Analytical Writing and until 2009 in the case of TOEFL(®) iBT Writing. With use of natural language processing, it is possible to obtain additional information concerning item responses from computer programs such as e-rater(®). In addition, available information relevant to examinee performance may include scores on related tests. We suggest application of standard results from classical test theory to the available data to obtain best linear predictors of true traditional test scores. In performing such analysis, we require estimation of variances and covariances of measurement errors, a task which can be quite difficult in the case of tests with limited numbers of items and with multiple measurements per item. As a consequence, a new estimation method is suggested based on samples of examinees who have taken an assessment more than once. Such samples are typically not random samples of the general population of examinees, so that we apply statistical adjustment methods to obtain the needed estimated variances and covariances of measurement errors. To examine practical implications of the suggested methods of analysis, applications are made to GRE General Analytical Writing and TOEFL iBT Writing. Results obtained indicate that substantial improvements are possible both in terms of reliability of scoring and in terms of assessment reliability. © 2015 The British Psychological Society.

Analysis of Covariance: Is It the Appropriate Model to Study Change?

ERIC Educational Resources Information Center

Marston, Paul T., Borich, Gary D.

The four main approaches to measuring treatment effects in schools; raw gain, residual gain, covariance, and true scores; were compared. A simulation study showed true score analysis produced a large number of Type-I errors. When corrected for this error, this method showed the least power of the four. This outcome was clearly the result of the…

A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix.

PubMed

Hu, Zongliang; Dong, Kai; Dai, Wenlin; Tong, Tiejun

2017-09-21

The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.

Covariance specification and estimation to improve top-down Green House Gas emission estimates

NASA Astrophysics Data System (ADS)

Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Whetstone, J. R.

2015-12-01

The National Institute of Standards and Technology (NIST) operates the North-East Corridor (NEC) project and the Indianapolis Flux Experiment (INFLUX) in order to develop measurement methods to quantify sources of Greenhouse Gas (GHG) emissions as well as their uncertainties in urban domains using a top down inversion method. Top down inversion updates prior knowledge using observations in a Bayesian way. One primary consideration in a Bayesian inversion framework is the covariance structure of (1) the emission prior residuals and (2) the observation residuals (i.e. the difference between observations and model predicted observations). These covariance matrices are respectively referred to as the prior covariance matrix and the model-data mismatch covariance matrix. It is known that the choice of these covariances can have large effect on estimates. The main objective of this work is to determine the impact of different covariance models on inversion estimates and their associated uncertainties in urban domains. We use a pseudo-data Bayesian inversion framework using footprints (i.e. sensitivities of tower measurements of GHGs to surface emissions) and emission priors (based on Hestia project to quantify fossil-fuel emissions) to estimate posterior emissions using different covariance schemes. The posterior emission estimates and uncertainties are compared to the hypothetical truth. We find that, if we correctly specify spatial variability and spatio-temporal variability in prior and model-data mismatch covariances respectively, then we can compute more accurate posterior estimates. We discuss few covariance models to introduce space-time interacting mismatches along with estimation of the involved parameters. We then compare several candidate prior spatial covariance models from the Matern covariance class and estimate their parameters with specified mismatches. We find that best-fitted prior covariances are not always best in recovering the truth. To achieve accuracy, we perform a sensitivity study to further tune covariance parameters. Finally, we introduce a shrinkage based sample covariance estimation technique for both prior and mismatch covariances. This technique allows us to achieve similar accuracy nonparametrically in a more efficient and automated way.

Monthly ENSO Forecast Skill and Lagged Ensemble Size

PubMed Central

DelSole, T.; Tippett, M.K.; Pegion, K.

2018-01-01

Abstract The mean square error (MSE) of a lagged ensemble of monthly forecasts of the Niño 3.4 index from the Climate Forecast System (CFSv2) is examined with respect to ensemble size and configuration. Although the real‐time forecast is initialized 4 times per day, it is possible to infer the MSE for arbitrary initialization frequency and for burst ensembles by fitting error covariances to a parametric model and then extrapolating to arbitrary ensemble size and initialization frequency. Applying this method to real‐time forecasts, we find that the MSE consistently reaches a minimum for a lagged ensemble size between one and eight days, when four initializations per day are included. This ensemble size is consistent with the 8–10 day lagged ensemble configuration used operationally. Interestingly, the skill of both ensemble configurations is close to the estimated skill of the infinite ensemble. The skill of the weighted, lagged, and burst ensembles are found to be comparable. Certain unphysical features of the estimated error growth were tracked down to problems with the climatology and data discontinuities. PMID:29937973

Monthly ENSO Forecast Skill and Lagged Ensemble Size

NASA Astrophysics Data System (ADS)

Trenary, L.; DelSole, T.; Tippett, M. K.; Pegion, K.

2018-04-01

The mean square error (MSE) of a lagged ensemble of monthly forecasts of the Niño 3.4 index from the Climate Forecast System (CFSv2) is examined with respect to ensemble size and configuration. Although the real-time forecast is initialized 4 times per day, it is possible to infer the MSE for arbitrary initialization frequency and for burst ensembles by fitting error covariances to a parametric model and then extrapolating to arbitrary ensemble size and initialization frequency. Applying this method to real-time forecasts, we find that the MSE consistently reaches a minimum for a lagged ensemble size between one and eight days, when four initializations per day are included. This ensemble size is consistent with the 8-10 day lagged ensemble configuration used operationally. Interestingly, the skill of both ensemble configurations is close to the estimated skill of the infinite ensemble. The skill of the weighted, lagged, and burst ensembles are found to be comparable. Certain unphysical features of the estimated error growth were tracked down to problems with the climatology and data discontinuities.

Estimation and Application of Ecological Memory Functions in Time and Space

NASA Astrophysics Data System (ADS)

Itter, M.; Finley, A. O.; Dawson, A.

2017-12-01

A common goal in quantitative ecology is the estimation or prediction of ecological processes as a function of explanatory variables (or covariates). Frequently, the ecological process of interest and associated covariates vary in time, space, or both. Theory indicates many ecological processes exhibit memory to local, past conditions. Despite such theoretical understanding, few methods exist to integrate observations from the recent past or within a local neighborhood as drivers of these processes. We build upon recent methodological advances in ecology and spatial statistics to develop a Bayesian hierarchical framework to estimate so-called ecological memory functions; that is, weight-generating functions that specify the relative importance of local, past covariate observations to ecological processes. Memory functions are estimated using a set of basis functions in time and/or space, allowing for flexible ecological memory based on a reduced set of parameters. Ecological memory functions are entirely data driven under the Bayesian hierarchical framework—no a priori assumptions are made regarding functional forms. Memory function uncertainty follows directly from posterior distributions for model parameters allowing for tractable propagation of error to predictions of ecological processes. We apply the model framework to simulated spatio-temporal datasets generated using memory functions of varying complexity. The framework is also applied to estimate the ecological memory of annual boreal forest growth to local, past water availability. Consistent with ecological understanding of boreal forest growth dynamics, memory to past water availability peaks in the year previous to growth and slowly decays to zero in five to eight years. The Bayesian hierarchical framework has applicability to a broad range of ecosystems and processes allowing for increased understanding of ecosystem responses to local and past conditions and improved prediction of ecological processes.

Fried food intake estimated by the multiple source method is associated with gestational weight gain.

PubMed

Sartorelli, Daniela S; Barbieri, Patrícia; Perdoná, Gleici C S

2014-08-01

This present study aimed to test the association between fried food intake estimated by a semiquantitative food frequency questionnaire (FFQ), multiple 24-hour dietary recalls (24hRs), and the application of the multiple source method (MSM) in relation to gestational weight gain at the second and third trimesters and weight gain ratio (observed weight gain/expected weight gain). We hypothesized that distinct relationships with weight gain would be found given the measurement errors of self-reported dietary approaches. A prospective study was conducted with 88 adult pregnant women. Fried food intake during pregnancy was assessed using a validated 85-item FFQ, two to six 24hRs per woman, and the MSM with and without frequency of food intake as covariate. Linear regression models were used to evaluate the relationship between fried food estimated by the methods and weight gain. For every 100-g increment of fried food intake, the β (95% confidence interval) for weight gain was β 1.87 (0.34, 3.40) and β 2.00 0.55, 3.45) for estimates using MSM with and without the frequency of intake as covariate, respectively, after multiple adjustments. We found that fried food intake estimated by the FFQ and 24hRs β 0.40 (-0.68, 1.48) and β 0.49 (-0.53, 1.52), respectively, was unrelated to weight gain. In relation to weight gain ratio, a positive association was found for estimates using the MSM with [β 0.29 (0.03, 0.54)] and without the frequency of intake as covariate [β 0.31 (0.07, 0.55)]; and no associations were found for estimates by the FFQ or 24hRs. The data showed that fried food intake estimated the MSM, but not by the FFQ and 24hRs, is associated with excessive weight gain during pregnancy. Copyright © 2014 Elsevier Inc. All rights reserved.

Remediating Non-Positive Definite State Covariances for Collision Probability Estimation

NASA Technical Reports Server (NTRS)

Hall, Doyle T.; Hejduk, Matthew D.; Johnson, Lauren C.

2017-01-01

The NASA Conjunction Assessment Risk Analysis team estimates the probability of collision (Pc) for a set of Earth-orbiting satellites. The Pc estimation software processes satellite position+velocity states and their associated covariance matri-ces. On occasion, the software encounters non-positive definite (NPD) state co-variances, which can adversely affect or prevent the Pc estimation process. Inter-polation inaccuracies appear to account for the majority of such covariances, alt-hough other mechanisms contribute also. This paper investigates the origin of NPD state covariance matrices, three different methods for remediating these co-variances when and if necessary, and the associated effects on the Pc estimation process.

The Potential Observation Network Design with Mesoscale Ensemble Sensitivities in Complex Terrain

DTIC Science & Technology

2012-03-01

in synoptic storms , extratropical transition and developing hurricanes. Because they rely on lagged covariances from a finite-sized ensemble, they...diagnose predictors of forecast error in synoptic storms , extratropical transition and developing hurricanes. Because they rely on lagged covariances...sensitivities can be used successfully to diagnose predictors of forecast error in synoptic storms (Torn and Hakim 2008), extratropical transition (Torn and

Smooth conditional distribution function and quantiles under random censorship.

PubMed

Leconte, Eve; Poiraud-Casanova, Sandrine; Thomas-Agnan, Christine

2002-09-01

We consider a nonparametric random design regression model in which the response variable is possibly right censored. The aim of this paper is to estimate the conditional distribution function and the conditional alpha-quantile of the response variable. We restrict attention to the case where the response variable as well as the explanatory variable are unidimensional and continuous. We propose and discuss two classes of estimators which are smooth with respect to the response variable as well as to the covariate. Some simulations demonstrate that the new methods have better mean square error performances than the generalized Kaplan-Meier estimator introduced by Beran (1981) and considered in the literature by Dabrowska (1989, 1992) and Gonzalez-Manteiga and Cadarso-Suarez (1994).

A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance.

PubMed

Zheng, Binqi; Fu, Pengcheng; Li, Baoqing; Yuan, Xiaobing

2018-03-07

The Unscented Kalman filter (UKF) may suffer from performance degradation and even divergence while mismatch between the noise distribution assumed as a priori by users and the actual ones in a real nonlinear system. To resolve this problem, this paper proposes a robust adaptive UKF (RAUKF) to improve the accuracy and robustness of state estimation with uncertain noise covariance. More specifically, at each timestep, a standard UKF will be implemented first to obtain the state estimations using the new acquired measurement data. Then an online fault-detection mechanism is adopted to judge if it is necessary to update current noise covariance. If necessary, innovation-based method and residual-based method are used to calculate the estimations of current noise covariance of process and measurement, respectively. By utilizing a weighting factor, the filter will combine the last noise covariance matrices with the estimations as the new noise covariance matrices. Finally, the state estimations will be corrected according to the new noise covariance matrices and previous state estimations. Compared with the standard UKF and other adaptive UKF algorithms, RAUKF converges faster to the actual noise covariance and thus achieves a better performance in terms of robustness, accuracy, and computation for nonlinear estimation with uncertain noise covariance, which is demonstrated by the simulation results.

A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance

PubMed Central

Zheng, Binqi; Yuan, Xiaobing

2018-01-01

The Unscented Kalman filter (UKF) may suffer from performance degradation and even divergence while mismatch between the noise distribution assumed as a priori by users and the actual ones in a real nonlinear system. To resolve this problem, this paper proposes a robust adaptive UKF (RAUKF) to improve the accuracy and robustness of state estimation with uncertain noise covariance. More specifically, at each timestep, a standard UKF will be implemented first to obtain the state estimations using the new acquired measurement data. Then an online fault-detection mechanism is adopted to judge if it is necessary to update current noise covariance. If necessary, innovation-based method and residual-based method are used to calculate the estimations of current noise covariance of process and measurement, respectively. By utilizing a weighting factor, the filter will combine the last noise covariance matrices with the estimations as the new noise covariance matrices. Finally, the state estimations will be corrected according to the new noise covariance matrices and previous state estimations. Compared with the standard UKF and other adaptive UKF algorithms, RAUKF converges faster to the actual noise covariance and thus achieves a better performance in terms of robustness, accuracy, and computation for nonlinear estimation with uncertain noise covariance, which is demonstrated by the simulation results. PMID:29518960

Developing a Data Driven Process-Based Model for Remote Sensing of Ecosystem Production

NASA Astrophysics Data System (ADS)

Elmasri, B.; Rahman, A. F.

2010-12-01

Estimating ecosystem carbon fluxes at various spatial and temporal scales is essential for quantifying the global carbon cycle. Numerous models have been developed for this purpose using several environmental variables as well as vegetation indices derived from remotely sensed data. Here we present a data driven modeling approach for gross primary production (GPP) that is based on a process based model BIOME-BGC. The proposed model was run using available remote sensing data and it does not depend on look-up tables. Furthermore, this approach combines the merits of both empirical and process models, and empirical models were used to estimate certain input variables such as light use efficiency (LUE). This was achieved by using remotely sensed data to the mathematical equations that represent biophysical photosynthesis processes in the BIOME-BGC model. Moreover, a new spectral index for estimating maximum photosynthetic activity, maximum photosynthetic rate index (MPRI), is also developed and presented here. This new index is based on the ratio between the near infrared and the green bands (ρ858.5/ρ555). The model was tested and validated against MODIS GPP product and flux measurements from two eddy covariance flux towers located at Morgan Monroe State Forest (MMSF) in Indiana and Harvard Forest in Massachusetts. Satellite data acquired by the Advanced Microwave Scanning Radiometer (AMSR-E) and MODIS were used. The data driven model showed a strong correlation between the predicted and measured GPP at the two eddy covariance flux towers sites. This methodology produced better predictions of GPP than did the MODIS GPP product. Moreover, the proportion of error in the predicted GPP for MMSF and Harvard forest was dominated by unsystematic errors suggesting that the results are unbiased. The analysis indicated that maintenance respiration is one of the main factors that dominate the overall model outcome errors and improvement in maintenance respiration estimation will result in improved GPP predictions. Although there might be a room for improvements in our model outcomes through improved parameterization, our results suggest that such a methodology for running BIOME-BGC model based entirely on routinely available data can produce good predictions of GPP.

Final report on "Carbon Data Assimilation with a Coupled Ensemble Kalman Filter"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalnay, Eugenia; Kang, Ji-Sun; Fung, Inez

2014-07-23

We proposed (and accomplished) the development of an Ensemble Kalman Filter (EnKF) approach for the estimation of surface carbon fluxes as if they were parameters, augmenting the model with them. Our system is quite different from previous approaches, such as carbon flux inversions, 4D-Var, and EnKF with approximate background error covariance (Peters et al., 2008). We showed (using observing system simulation experiments, OSSEs) that these differences lead to a more accurate estimation of the evolving surface carbon fluxes at model grid-scale resolution. The main properties of the LETKF-C are: a) The carbon cycle LETKF is coupled with the simultaneous assimilationmore » of the standard atmospheric variables, so that the ensemble wind transport of the CO2 provides an estimation of the carbon transport uncertainty. b) The use of an assimilation window (6hr) much shorter than the months-long windows used in other methods. This avoids the inevitable “blurring” of the signal that takes place in long windows due to turbulent mixing since the CO2 does not have time to mix before the next window. In this development we introduced new, advanced techniques that have since been adopted by the EnKF community (Kang, 2009, Kang et al., 2011, Kang et al. 2012). These advances include “variable localization” that reduces sampling errors in the estimation of the forecast error covariance, more advanced adaptive multiplicative and additive inflations, and vertical localization based on the time scale of the processes. The main result has been obtained using the LETKF-C with all these advances, and assimilating simulated atmospheric CO2 observations from different observing systems (surface flask observations of CO2 but no surface carbon fluxes observations, total column CO2 from GoSAT/OCO-2, and upper troposphere AIRS retrievals). After a spin-up of about one month, the LETKF-C succeeded in reconstructing the true evolving surface fluxes of carbon at a model grid resolution. When applied to the CAM3.5 model, the LETKF gave very promising results as well, although only one month is available.« less

Final Technical Report [Carbon Data Assimilation with a Coupled Ensemble Kalman Filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalnay, Eugenia

2013-08-30

We proposed (and accomplished) the development of an Ensemble Kalman Filter (EnKF) approach for the estimation of surface carbon fluxes as if they were parameters, augmenting the model with them. Our system is quite different from previous approaches, such as carbon flux inversions, 4D-­Var, and EnKF with approximate background error covariance (Peters et al., 2008). We showed (using observing system simulation experiments, OSSEs) that these differences lead to a more accurate estimation of the evolving surface carbon fluxes at model grid-scale resolution. The main properties of the LETKF-­C are: a) The carbon cycle LETKF is coupled with the simultaneous assimilationmore » of the standard atmospheric variables, so that the ensemble wind transport of the CO2 provides an estimation of the carbon transport uncertainty. b) The use of an assimilation window (6hr) much shorter than the months-long windows used in other methods. This avoids the inevitable “blurring” of the signal that takes place in long windows due to turbulent mixing since the CO2 does not have time to mix before the next window. In this development we introduced new, advanced techniques that have since been adopted by the EnKF community (Kang, 2009, Kang et al., 2011, Kang et al. 2012). These advances include “variable localization” that reduces sampling errors in the estimation of the forecast error covariance, more advanced adaptive multiplicative and additive inflations, and vertical localization based on the time scale of the processes. The main result has been obtained using the LETKF-­C with all these advances, and assimilating simulated atmospheric CO2 observations from different observing systems (surface flask observations of CO2 but no surface carbon fluxes observations, total column CO2 from GoSAT/OCO-­2, and upper troposphere AIRS retrievals). After a spin-­up of about one month, the LETKF-­C succeeded in reconstructing the true evolving surface fluxes of carbon at a model grid resolution. When applied to the CAM3.5 model, the LETKF gave very promising results as well, although only one month is available.« less

Estimating the reliability of repeatedly measured endpoints based on linear mixed-effects models. A tutorial.

PubMed

Van der Elst, Wim; Molenberghs, Geert; Hilgers, Ralf-Dieter; Verbeke, Geert; Heussen, Nicole

2016-11-01

There are various settings in which researchers are interested in the assessment of the correlation between repeated measurements that are taken within the same subject (i.e., reliability). For example, the same rating scale may be used to assess the symptom severity of the same patients by multiple physicians, or the same outcome may be measured repeatedly over time in the same patients. Reliability can be estimated in various ways, for example, using the classical Pearson correlation or the intra-class correlation in clustered data. However, contemporary data often have a complex structure that goes well beyond the restrictive assumptions that are needed with the more conventional methods to estimate reliability. In the current paper, we propose a general and flexible modeling approach that allows for the derivation of reliability estimates, standard errors, and confidence intervals - appropriately taking hierarchies and covariates in the data into account. Our methodology is developed for continuous outcomes together with covariates of an arbitrary type. The methodology is illustrated in a case study, and a Web Appendix is provided which details the computations using the R package CorrMixed and the SAS software. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Reconciling resource utilization and resource selection functions

USGS Publications Warehouse

Hooten, Mevin B.; Hanks, Ephraim M.; Johnson, Devin S.; Alldredge, Mat W.

2013-01-01

Summary: 1. Analyses based on utilization distributions (UDs) have been ubiquitous in animal space use studies, largely because they are computationally straightforward and relatively easy to employ. Conventional applications of resource utilization functions (RUFs) suggest that estimates of UDs can be used as response variables in a regression involving spatial covariates of interest. 2. It has been claimed that contemporary implementations of RUFs can yield inference about resource selection, although to our knowledge, an explicit connection has not been described. 3. We explore the relationships between RUFs and resource selection functions from a hueristic and simulation perspective. We investigate several sources of potential bias in the estimation of resource selection coefficients using RUFs (e.g. the spatial covariance modelling that is often used in RUF analyses). 4. Our findings illustrate that RUFs can, in fact, serve as approximations to RSFs and are capable of providing inference about resource selection, but only with some modification and under specific circumstances. 5. Using real telemetry data as an example, we provide guidance on which methods for estimating resource selection may be more appropriate and in which situations. In general, if telemetry data are assumed to arise as a point process, then RSF methods may be preferable to RUFs; however, modified RUFs may provide less biased parameter estimates when the data are subject to location error.

Quasi-Likelihood Techniques in a Logistic Regression Equation for Identifying Simulium damnosum s.l. Larval Habitats Intra-cluster Covariates in Togo.

PubMed

Jacob, Benjamin G; Novak, Robert J; Toe, Laurent; Sanfo, Moussa S; Afriyie, Abena N; Ibrahim, Mohammed A; Griffith, Daniel A; Unnasch, Thomas R

2012-01-01

The standard methods for regression analyses of clustered riverine larval habitat data of Simulium damnosum s.l. a major black-fly vector of Onchoceriasis, postulate models relating observational ecological-sampled parameter estimators to prolific habitats without accounting for residual intra-cluster error correlation effects. Generally, this correlation comes from two sources: (1) the design of the random effects and their assumed covariance from the multiple levels within the regression model; and, (2) the correlation structure of the residuals. Unfortunately, inconspicuous errors in residual intra-cluster correlation estimates can overstate precision in forecasted S.damnosum s.l. riverine larval habitat explanatory attributes regardless how they are treated (e.g., independent, autoregressive, Toeplitz, etc). In this research, the geographical locations for multiple riverine-based S. damnosum s.l. larval ecosystem habitats sampled from 2 pre-established epidemiological sites in Togo were identified and recorded from July 2009 to June 2010. Initially the data was aggregated into proc genmod. An agglomerative hierarchical residual cluster-based analysis was then performed. The sampled clustered study site data was then analyzed for statistical correlations using Monthly Biting Rates (MBR). Euclidean distance measurements and terrain-related geomorphological statistics were then generated in ArcGIS. A digital overlay was then performed also in ArcGIS using the georeferenced ground coordinates of high and low density clusters stratified by Annual Biting Rates (ABR). This data was overlain onto multitemporal sub-meter pixel resolution satellite data (i.e., QuickBird 0.61m wavbands ). Orthogonal spatial filter eigenvectors were then generated in SAS/GIS. Univariate and non-linear regression-based models (i.e., Logistic, Poisson and Negative Binomial) were also employed to determine probability distributions and to identify statistically significant parameter estimators from the sampled data. Thereafter, Durbin-Watson test statistics were used to test the null hypothesis that the regression residuals were not autocorrelated against the alternative that the residuals followed an autoregressive process in AUTOREG. Bayesian uncertainty matrices were also constructed employing normal priors for each of the sampled estimators in PROC MCMC. The residuals revealed both spatially structured and unstructured error effects in the high and low ABR-stratified clusters. The analyses also revealed that the estimators, levels of turbidity and presence of rocks were statistically significant for the high-ABR-stratified clusters, while the estimators distance between habitats and floating vegetation were important for the low-ABR-stratified cluster. Varying and constant coefficient regression models, ABR- stratified GIS-generated clusters, sub-meter resolution satellite imagery, a robust residual intra-cluster diagnostic test, MBR-based histograms, eigendecomposition spatial filter algorithms and Bayesian matrices can enable accurate autoregressive estimation of latent uncertainity affects and other residual error probabilities (i.e., heteroskedasticity) for testing correlations between georeferenced S. damnosum s.l. riverine larval habitat estimators. The asymptotic distribution of the resulting residual adjusted intra-cluster predictor error autocovariate coefficients can thereafter be established while estimates of the asymptotic variance can lead to the construction of approximate confidence intervals for accurately targeting productive S. damnosum s.l habitats based on spatiotemporal field-sampled count data.

The impact of multiple endpoint dependency on Q and I(2) in meta-analysis.

PubMed

Thompson, Christopher Glen; Becker, Betsy Jane

2014-09-01

A common assumption in meta-analysis is that effect sizes are independent. When correlated effect sizes are analyzed using traditional univariate techniques, this assumption is violated. This research assesses the impact of dependence arising from treatment-control studies with multiple endpoints on homogeneity measures Q and I(2) in scenarios using the unbiased standardized-mean-difference effect size. Univariate and multivariate meta-analysis methods are examined. Conditions included different overall outcome effects, study sample sizes, numbers of studies, between-outcomes correlations, dependency structures, and ways of computing the correlation. The univariate approach used typical fixed-effects analyses whereas the multivariate approach used generalized least-squares (GLS) estimates of a fixed-effects model, weighted by the inverse variance-covariance matrix. Increased dependence among effect sizes led to increased Type I error rates from univariate models. When effect sizes were strongly dependent, error rates were drastically higher than nominal levels regardless of study sample size and number of studies. In contrast, using GLS estimation to account for multiple-endpoint dependency maintained error rates within nominal levels. Conversely, mean I(2) values were not greatly affected by increased amounts of dependency. Last, we point out that the between-outcomes correlation should be estimated as a pooled within-groups correlation rather than using a full-sample estimator that does not consider treatment/control group membership. Copyright © 2014 John Wiley & Sons, Ltd.

Airborne radar technology for windshear detection

NASA Technical Reports Server (NTRS)

Hibey, Joseph L.; Khalaf, Camille S.

1988-01-01

The objectives and accomplishments of the two-and-a-half year effort to describe how returns from on-board Doppler radar are to be used to detect the presence of a wind shear are reported. The problem is modeled as one of first passage in terms of state variables, the state estimates are generated by a bank of extended Kalman filters working in parallel, and the decision strategy involves the use of a voting algorithm for a series of likelihood ratio tests. The performance issue for filtering is addressed in terms of error-covariance reduction and filter divergence, and the performance issue for detection is addressed in terms of using a probability measure transformation to derive theoretical expressions for the error probabilities of a false alarm and a miss.

Sampling errors in the estimation of empirical orthogonal functions. [for climatology studies

NASA Technical Reports Server (NTRS)

North, G. R.; Bell, T. L.; Cahalan, R. F.; Moeng, F. J.

1982-01-01

Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is 'close' to a neighboring one. A rule of thumb indicating when an EOF is likely to be subject to large sampling fluctuations is presented. An explicit example, based on the statistics of the 500 mb geopotential height field, displays large intersample variability in the EOF's for sample sizes of a few hundred independent realizations, a size seldom exceeded by meteorological data sets.

Dynamic State Estimation for Multi-Machine Power System by Unscented Kalman Filter With Enhanced Numerical Stability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qi, Junjian; Sun, Kai; Wang, Jianhui

In this paper, in order to enhance the numerical stability of the unscented Kalman filter (UKF) used for power system dynamic state estimation, a new UKF with guaranteed positive semidifinite estimation error covariance (UKFGPS) is proposed and compared with five existing approaches, including UKFschol, UKF-kappa, UKFmodified, UKF-Delta Q, and the squareroot UKF (SRUKF). These methods and the extended Kalman filter (EKF) are tested by performing dynamic state estimation on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system. For WSCC system, all methods obtain good estimates. However, for NPCC system, both EKF and the classic UKF fail. It is foundmore » that UKFschol, UKF-kappa, and UKF-Delta Q do not work well in some estimations while UKFGPS works well in most cases. UKFmodified and SRUKF can always work well, indicating their better scalability mainly due to the enhanced numerical stability.« less

Estimation of single plane unbalance parameters of a rotor-bearing system using Kalman filtering based force estimation technique

NASA Astrophysics Data System (ADS)

Shrivastava, Akash; Mohanty, A. R.

2018-03-01

This paper proposes a model-based method to estimate single plane unbalance parameters (amplitude and phase angle) in a rotor using Kalman filter and recursive least square based input force estimation technique. Kalman filter based input force estimation technique requires state-space model and response measurements. A modified system equivalent reduction expansion process (SEREP) technique is employed to obtain a reduced-order model of the rotor system so that limited response measurements can be used. The method is demonstrated using numerical simulations on a rotor-disk-bearing system. Results are presented for different measurement sets including displacement, velocity, and rotational response. Effects of measurement noise level, filter parameters (process noise covariance and forgetting factor), and modeling error are also presented and it is observed that the unbalance parameter estimation is robust with respect to measurement noise.

Longitudinal design considerations to optimize power to detect variances and covariances among rates of change: Simulation results based on actual longitudinal studies

PubMed Central

Rast, Philippe; Hofer, Scott M.

2014-01-01

We investigated the power to detect variances and covariances in rates of change in the context of existing longitudinal studies using linear bivariate growth curve models. Power was estimated by means of Monte Carlo simulations. Our findings show that typical longitudinal study designs have substantial power to detect both variances and covariances among rates of change in a variety of cognitive, physical functioning, and mental health outcomes. We performed simulations to investigate the interplay among number and spacing of occasions, total duration of the study, effect size, and error variance on power and required sample size. The relation between growth rate reliability (GRR) and effect size to the sample size required to detect power ≥ .80 was non-linear, with rapidly decreasing sample sizes needed as GRR increases. The results presented here stand in contrast to previous simulation results and recommendations (Hertzog, Lindenberger, Ghisletta, & von Oertzen, 2006; Hertzog, von Oertzen, Ghisletta, & Lindenberger, 2008; von Oertzen, Ghisletta, & Lindenberger, 2010), which are limited due to confounds between study length and number of waves, error variance with GCR, and parameter values which are largely out of bounds of actual study values. Power to detect change is generally low in the early phases (i.e. first years) of longitudinal studies but can substantially increase if the design is optimized. We recommend additional assessments, including embedded intensive measurement designs, to improve power in the early phases of long-term longitudinal studies. PMID:24219544

Estimating seasonal evapotranspiration from temporal satellite images

USGS Publications Warehouse

Singh, Ramesh K.; Liu, Shu-Guang; Tieszen, Larry L.; Suyker, Andrew E.; Verma, Shashi B.

2012-01-01

Estimating seasonal evapotranspiration (ET) has many applications in water resources planning and management, including hydrological and ecological modeling. Availability of satellite remote sensing images is limited due to repeat cycle of satellite or cloud cover. This study was conducted to determine the suitability of different methods namely cubic spline, fixed, and linear for estimating seasonal ET from temporal remotely sensed images. Mapping Evapotranspiration at high Resolution with Internalized Calibration (METRIC) model in conjunction with the wet METRIC (wMETRIC), a modified version of the METRIC model, was used to estimate ET on the days of satellite overpass using eight Landsat images during the 2001 crop growing season in Midwest USA. The model-estimated daily ET was in good agreement (R2 = 0.91) with the eddy covariance tower-measured daily ET. The standard error of daily ET was 0.6 mm (20%) at three validation sites in Nebraska, USA. There was no statistically significant difference (P > 0.05) among the cubic spline, fixed, and linear methods for computing seasonal (July–December) ET from temporal ET estimates. Overall, the cubic spline resulted in the lowest standard error of 6 mm (1.67%) for seasonal ET. However, further testing of this method for multiple years is necessary to determine its suitability.

A weighted least squares approach to retrieve aerosol layer height over bright surfaces applied to GOME-2 measurements of the oxygen A band for forest fire cases over Europe

NASA Astrophysics Data System (ADS)

Nanda, Swadhin; Pepijn Veefkind, J.; de Graaf, Martin; Sneep, Maarten; Stammes, Piet; de Haan, Johan F.; Sanders, Abram F. J.; Apituley, Arnoud; Tuinder, Olaf; Levelt, Pieternel F.

2018-06-01

This paper presents a weighted least squares approach to retrieve aerosol layer height from top-of-atmosphere reflectance measurements in the oxygen A band (758-770 nm) over bright surfaces. A property of the measurement error covariance matrix is discussed, due to which photons travelling from the surface are given a higher preference over photons that scatter back from the aerosol layer. This is a potential source of biases in the estimation of aerosol properties over land, which can be mitigated by revisiting the design of the measurement error covariance matrix. The alternative proposed in this paper, which we call the dynamic scaling method, introduces a scene-dependent and wavelength-dependent modification in the measurement signal-to-noise ratio in order to influence this matrix. This method is generally applicable to other retrieval algorithms using weighted least squares. To test this method, synthetic experiments are done in addition to application to GOME-2A and GOME-2B measurements of the oxygen A band over the August 2010 Russian wildfires and the October 2017 Portugal wildfire plume over western Europe.

Population pharmacokinetics and maximum a posteriori probability Bayesian estimator of abacavir: application of individualized therapy in HIV-infected infants and toddlers.

PubMed

Zhao, Wei; Cella, Massimo; Della Pasqua, Oscar; Burger, David; Jacqz-Aigrain, Evelyne

2012-04-01

Abacavir is used to treat HIV infection in both adults and children. The recommended paediatric dose is 8 mg kg(-1) twice daily up to a maximum of 300 mg twice daily. Weight was identified as the central covariate influencing pharmacokinetics of abacavir in children. A population pharmacokinetic model was developed to describe both once and twice daily pharmacokinetic profiles of abacavir in infants and toddlers. Standard dosage regimen is associated with large interindividual variability in abacavir concentrations. A maximum a posteriori probability Bayesian estimator of AUC(0-) (t) based on three time points (0, 1 or 2, and 3 h) is proposed to support area under the concentration-time curve (AUC) targeted individualized therapy in infants and toddlers. To develop a population pharmacokinetic model for abacavir in HIV-infected infants and toddlers, which will be used to describe both once and twice daily pharmacokinetic profiles, identify covariates that explain variability and propose optimal time points to optimize the area under the concentration-time curve (AUC) targeted dosage and individualize therapy. The pharmacokinetics of abacavir was described with plasma concentrations from 23 patients using nonlinear mixed-effects modelling (NONMEM) software. A two-compartment model with first-order absorption and elimination was developed. The final model was validated using bootstrap, visual predictive check and normalized prediction distribution errors. The Bayesian estimator was validated using the cross-validation and simulation-estimation method. The typical population pharmacokinetic parameters and relative standard errors (RSE) were apparent systemic clearance (CL) 13.4 () h−1 (RSE 6.3%), apparent central volume of distribution 4.94 () (RSE 28.7%), apparent peripheral volume of distribution 8.12 () (RSE14.2%), apparent intercompartment clearance 1.25 () h−1 (RSE 16.9%) and absorption rate constant 0.758 h−1 (RSE 5.8%). The covariate analysis identified weight as the individual factor influencing the apparent oral clearance: CL = 13.4 × (weight/12)1.14. The maximum a posteriori probability Bayesian estimator, based on three concentrations measured at 0, 1 or 2, and 3 h after drug intake allowed predicting individual AUC0–t. The population pharmacokinetic model developed for abacavir in HIV-infected infants and toddlers accurately described both once and twice daily pharmacokinetic profiles. The maximum a posteriori probability Bayesian estimator of AUC(0-) (t) was developed from the final model and can be used routinely to optimize individual dosing. © 2011 The Authors. British Journal of Clinical Pharmacology © 2011 The British Pharmacological Society.

Three Cs in Measurement Models: Causal Indicators, Composite Indicators, and Covariates

PubMed Central

Bollen, Kenneth A.; Bauldry, Shawn

2013-01-01

In the last two decades attention to causal (and formative) indicators has grown. Accompanying this growth has been the belief that we can classify indicators into two categories, effect (reflective) indicators and causal (formative) indicators. This paper argues that the dichotomous view is too simple. Instead, there are effect indicators and three types of variables on which a latent variable depends: causal indicators, composite (formative) indicators, and covariates (the “three Cs”). Causal indicators have conceptual unity and their effects on latent variables are structural. Covariates are not concept measures, but are variables to control to avoid bias in estimating the relations between measures and latent variable(s). Composite (formative) indicators form exact linear combinations of variables that need not share a concept. Their coefficients are weights rather than structural effects and composites are a matter of convenience. The failure to distinguish the “three Cs” has led to confusion and questions such as: are causal and formative indicators different names for the same indicator type? Should an equation with causal or formative indicators have an error term? Are the coefficients of causal indicators less stable than effect indicators? Distinguishing between causal and composite indicators and covariates goes a long way toward eliminating this confusion. We emphasize the key role that subject matter expertise plays in making these distinctions. We provide new guidelines for working with these variable types, including identification of models, scaling latent variables, parameter estimation, and validity assessment. A running empirical example on self-perceived health illustrates our major points. PMID:21767021

Eddy Covariance Method: Overview of General Guidelines and Conventional Workflow

NASA Astrophysics Data System (ADS)

Burba, G. G.; Anderson, D. J.; Amen, J. L.

2007-12-01

Atmospheric flux measurements are widely used to estimate water, heat, carbon dioxide and trace gas exchange between the ecosystem and the atmosphere. The Eddy Covariance method is one of the most direct, defensible ways to measure and calculate turbulent fluxes within the atmospheric boundary layer. However, the method is mathematically complex, and requires significant care to set up and process data. These reasons may be why the method is currently used predominantly by micrometeorologists. Modern instruments and software can potentially expand the use of this method beyond micrometeorology and prove valuable for plant physiology, hydrology, biology, ecology, entomology, and other non-micrometeorological areas of research. The main challenge of the method for a non-expert is the complexity of system design, implementation, and processing of the large volume of data. In the past several years, efforts of the flux networks (e.g., FluxNet, Ameriflux, CarboEurope, Fluxnet-Canada, Asiaflux, etc.) have led to noticeable progress in unification of the terminology and general standardization of processing steps. The methodology itself, however, is difficult to unify, because various experimental sites and different purposes of studies dictate different treatments, and site-, measurement- and purpose-specific approaches. Here we present an overview of theory and typical workflow of the Eddy Covariance method in a format specifically designed to (i) familiarize a non-expert with general principles, requirements, applications, and processing steps of the conventional Eddy Covariance technique, (ii) to assist in further understanding the method through more advanced references such as textbooks, network guidelines and journal papers, (iii) to help technicians, students and new researchers in the field deployment of the Eddy Covariance method, and (iv) to assist in its use beyond micrometeorology. The overview is based, to a large degree, on the frequently asked questions received from new users of the Eddy Covariance method and relevant instrumentation, and employs non-technical language to be of practical use to those new to this field. Information is provided on theory of the method (including state of methodology, basic derivations, practical formulations, major assumptions and sources of errors, error treatment, and use in non- traditional terrains), practical workflow (e.g., experimental design, implementation, data processing, and quality control), alternative methods and applications, and the most frequently overlooked details of the measurements. References and access to an extended 141-page Eddy Covariance Guideline in three electronic formats are also provided.

Covariance NMR Processing and Analysis for Protein Assignment.

PubMed

Harden, Bradley J; Frueh, Dominique P

2018-01-01

During NMR resonance assignment it is often necessary to relate nuclei to one another indirectly, through their common correlations to other nuclei. Covariance NMR has emerged as a powerful technique to correlate such nuclei without relying on error-prone peak peaking. However, false-positive artifacts in covariance spectra have impeded a general application to proteins. We recently introduced pre- and postprocessing steps to reduce the prevalence of artifacts in covariance spectra, allowing for the calculation of a variety of 4D covariance maps obtained from diverse combinations of pairs of 3D spectra, and we have employed them to assign backbone and sidechain resonances in two large and challenging proteins. In this chapter, we present a detailed protocol describing how to (1) properly prepare existing 3D spectra for covariance, (2) understand and apply our processing script, and (3) navigate and interpret the resulting 4D spectra. We also provide solutions to a number of errors that may occur when using our script, and we offer practical advice when assigning difficult signals. We believe such 4D spectra, and covariance NMR in general, can play an integral role in the assignment of NMR signals.

Offline handwritten word recognition using MQDF-HMMs

NASA Astrophysics Data System (ADS)

Ramachandrula, Sitaram; Hambarde, Mangesh; Patial, Ajay; Sahoo, Dushyant; Kochar, Shaivi

2015-01-01

We propose an improved HMM formulation for offline handwriting recognition (HWR). The main contribution of this work is using modified quadratic discriminant function (MQDF) [1] within HMM framework. In an MQDF-HMM the state observation likelihood is calculated by a weighted combination of MQDF likelihoods of individual Gaussians of GMM (Gaussian Mixture Model). The quadratic discriminant function (QDF) of a multivariate Gaussian can be rewritten by avoiding the inverse of covariance matrix by using the Eigen values and Eigen vectors of it. The MQDF is derived from QDF by substituting few of badly estimated lower-most Eigen values by an appropriate constant. The estimation errors of non-dominant Eigen vectors and Eigen values of covariance matrix for which the training data is insufficient can be controlled by this approach. MQDF has been successfully shown to improve the character recognition performance [1]. The usage of MQDF in HMM improves the computation, storage and modeling power of HMM when there is limited training data. We have got encouraging results on offline handwritten character (NIST database) and word recognition in English using MQDF HMMs.

Assessment of Infrared Sounder Radiometric Noise from Analysis of Spectral Residuals

NASA Astrophysics Data System (ADS)

Dufour, E.; Klonecki, A.; Standfuss, C.; Tournier, B.; Serio, C.; Masiello, G.; Tjemkes, S.; Stuhlmann, R.

2016-08-01

For the preparation and performance monitoring of the future generation of hyperspectral InfraRed sounders dedicated to the precise vertical profiling of the atmospheric state, such as the Meteosat Third Generation hyperspectral InfraRed Sounder, a reliable assessment of the instrument radiometric error covariance matrix is needed.Ideally, an inflight estimation of the radiometrric noise is recommended as certain sources of noise can be driven by the spectral signature of the observed Earth/ atmosphere radiance. Also, unknown correlated noise sources, generally related to incomplete knowledge of the instrument state, can be present, so a caracterisation of the noise spectral correlation is also neeed.A methodology, relying on the analysis of post-retreival spectral residuals, is designed and implemented to derive in-flight the covariance matrix on the basis of Earth scenes measurements. This methodology is successfully demonstrated using IASI observations as MTG-IRS proxy data and made it possible to highlight anticipated correlation structures explained by apodization and micro-vibration effects (ghost). This analysis is corroborated by a parallel estimation based on an IASI black body measurement dataset and the results of an independent micro-vibration model.

Planck 2015 results. VI. LFI mapmaking

NASA Astrophysics Data System (ADS)

Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Chamballu, A.; Chary, R.-R.; Christensen, P. R.; Colombi, S.; Colombo, L. P. L.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Dickinson, C.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F. K.; Hanson, D.; Harrison, D. L.; Henrot-Versillé, S.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Hurier, G.; Jaffe, A. H.; Jaffe, T. R.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kiiveri, K.; Kisner, T. S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C. R.; Leahy, J. P.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; Lindholm, V.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Martin, P. G.; Martínez-González, E.; Masi, S.; Matarrese, S.; Mazzotta, P.; McGehee, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Novikov, D.; Novikov, I.; Paci, F.; Pagano, L.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, T. J.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Pierpaoli, E.; Pietrobon, D.; Pointecouteau, E.; Polenta, G.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renzi, A.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Spencer, L. D.; Stolyarov, V.; Stompor, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vassallo, T.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; Watson, R.; Wehus, I. K.; Yvon, D.; Zacchei, A.; Zonca, A.

2016-09-01

This paper describes the mapmaking procedure applied to Planck Low Frequency Instrument (LFI) data. The mapmaking step takes as input the calibrated timelines and pointing information. The main products are sky maps of I, Q, and U Stokes components. For the first time, we present polarization maps at LFI frequencies. The mapmaking algorithm is based on a destriping technique, which is enhanced with a noise prior. The Galactic region is masked to reduce errors arising from bandpass mismatch and high signal gradients. We apply horn-uniform radiometer weights to reduce the effects of beam-shape mismatch. The algorithm is the same as used for the 2013 release, apart from small changes in parameter settings. We validate the procedure through simulations. Special emphasis is put on the control of systematics, which is particularly important for accurate polarization analysis. We also produce low-resolution versions of the maps and corresponding noise covariance matrices. These serve as input in later analysis steps and parameter estimation. The noise covariance matrices are validated through noise Monte Carlo simulations. The residual noise in the map products is characterized through analysis of half-ring maps, noise covariance matrices, and simulations.

Magnetometer-only attitude and angular velocity filtering estimation for attitude changing spacecraft

NASA Astrophysics Data System (ADS)

Ma, Hongliang; Xu, Shijie

2014-09-01

This paper presents an improved real-time sequential filter (IRTSF) for magnetometer-only attitude and angular velocity estimation of spacecraft during its attitude changing (including fast and large angular attitude maneuver, rapidly spinning or uncontrolled tumble). In this new magnetometer-only attitude determination technique, both attitude dynamics equation and first time derivative of measured magnetic field vector are directly leaded into filtering equations based on the traditional single vector attitude determination method of gyroless and real-time sequential filter (RTSF) of magnetometer-only attitude estimation. The process noise model of IRTSF includes attitude kinematics and dynamics equations, and its measurement model consists of magnetic field vector and its first time derivative. The observability of IRTSF for small or large angular velocity changing spacecraft is evaluated by an improved Lie-Differentiation, and the degrees of observability of IRTSF for different initial estimation errors are analyzed by the condition number and a solved covariance matrix. Numerical simulation results indicate that: (1) the attitude and angular velocity of spacecraft can be estimated with sufficient accuracy using IRTSF from magnetometer-only data; (2) compared with that of RTSF, the estimation accuracies and observability degrees of attitude and angular velocity using IRTSF from magnetometer-only data are both improved; and (3) universality: the IRTSF of magnetometer-only attitude and angular velocity estimation is observable for any different initial state estimation error vector.

Generalized Fisher matrices

NASA Astrophysics Data System (ADS)

Heavens, A. F.; Seikel, M.; Nord, B. D.; Aich, M.; Bouffanais, Y.; Bassett, B. A.; Hobson, M. P.

2014-12-01

The Fisher Information Matrix formalism (Fisher 1935) is extended to cases where the data are divided into two parts (X, Y), where the expectation value of Y depends on X according to some theoretical model, and X and Y both have errors with arbitrary covariance. In the simplest case, (X, Y) represent data pairs of abscissa and ordinate, in which case the analysis deals with the case of data pairs with errors in both coordinates, but X can be any measured quantities on which Y depends. The analysis applies for arbitrary covariance, provided all errors are Gaussian, and provided the errors in X are small, both in comparison with the scale over which the expected signal Y changes, and with the width of the prior distribution. This generalizes the Fisher Matrix approach, which normally only considers errors in the `ordinate' Y. In this work, we include errors in X by marginalizing over latent variables, effectively employing a Bayesian hierarchical model, and deriving the Fisher Matrix for this more general case. The methods here also extend to likelihood surfaces which are not Gaussian in the parameter space, and so techniques such as DALI (Derivative Approximation for Likelihoods) can be generalized straightforwardly to include arbitrary Gaussian data error covariances. For simple mock data and theoretical models, we compare to Markov Chain Monte Carlo experiments, illustrating the method with cosmological supernova data. We also include the new method in the FISHER4CAST software.

A geopotential model from satellite tracking, altimeter, and surface gravity data: GEM-T3

NASA Technical Reports Server (NTRS)

Lerch, F. J.; Nerem, R. S.; Putney, B. H.; Felsentreger, T. L.; Sanchez, B. V.; Marshall, J. A.; Klosko, S. M.; Patel, G. B.; Williamson, R. G.; Chinn, D. S.

1994-01-01

An improved model of Earth's gravitational field, Goddard Earth Model T-3 (GEM-T3), has been developed from a combination of satellite tracking, satellite altimeter, and surface gravimetric data. GEM-T3 provides a significant improvement in the modeling of the gravity field at half wavelengths of 400 km and longer. This model, complete to degree and order 50, yields more accurate satellite orbits and an improved geoid representation than previous Goddard Earth Models. GEM-T3 uses altimeter data from GEOS 3 (1975-1976), Seasat (1978) and Geosat (1986-1987). Tracking information used in the solution includes more than 1300 arcs of data encompassing 31 different satellites. The recovery of the long-wavelength components of the solution relies mostly on highly precise satellite laser ranging (SLR) data, but also includes Tracking Network (TRANET) Doppler, optical, and satellite-to-satellite tracking acquired between the ATS 6 and GEOS 3 satellites. The main advances over GEM-T2 (beyond the inclusion of altimeter and surface gravity information which is essential for the resolution of the shorter wavelength geoid) are some improved tracking data analysis approaches and additional SLR data. Although the use of altimeter data has greatly enhanced the modeling of the ocean geoid between 65 deg N and 60 deg S latitudes in GEM-T3, the lack of accurate detailed surface gravimetry leaves poor geoid resolution over many continental regions of great tectonic interest (e.g., Himalayas, Andes). Estimates of polar motion, tracking station coordinates, and long-wavelength ocean tidal terms were also made (accounting for 6330 parameters). GEM-T3 has undergone error calibration using a technique based on subset solutions to produce reliable error estimates. The calibration is based on the condition that the expected mean square deviation of a subset gravity solution from the full set values is predicted by the solutions' error covariances. Data weights are iteratively adjusted until this condition for the error calibration is satisfied. In addition, gravity field tests were performed on strong satellite data sets withheld from the solution (thereby ensuring their independence). In these tests, the performance of the subset models on the withheld observations is compared to error projections based on their calibrated error covariances. These results demonstrate that orbit accuracy projections are reliable for new satellites which were not included in GEM-T3.

Evaluation of three lidar scanning strategies for turbulence measurements

NASA Astrophysics Data System (ADS)

Newman, J. F.; Klein, P. M.; Wharton, S.; Sathe, A.; Bonin, T. A.; Chilson, P. B.; Muschinski, A.

2015-11-01

Several errors occur when a traditional Doppler-beam swinging (DBS) or velocity-azimuth display (VAD) strategy is used to measure turbulence with a lidar. To mitigate some of these errors, a scanning strategy was recently developed which employs six beam positions to independently estimate the u, v, and w velocity variances and covariances. In order to assess the ability of these different scanning techniques to measure turbulence, a Halo scanning lidar, WindCube v2 pulsed lidar and ZephIR continuous wave lidar were deployed at field sites in Oklahoma and Colorado with collocated sonic anemometers. Results indicate that the six-beam strategy mitigates some of the errors caused by VAD and DBS scans, but the strategy is strongly affected by errors in the variance measured at the different beam positions. The ZephIR and WindCube lidars overestimated horizontal variance values by over 60 % under unstable conditions as a result of variance contamination, where additional variance components contaminate the true value of the variance. A correction method was developed for the WindCube lidar that uses variance calculated from the vertical beam position to reduce variance contamination in the u and v variance components. The correction method reduced WindCube variance estimates by over 20 % at both the Oklahoma and Colorado sites under unstable conditions, when variance contamination is largest. This correction method can be easily applied to other lidars that contain a vertical beam position and is a promising method for accurately estimating turbulence with commercially available lidars.

Evaluation of three lidar scanning strategies for turbulence measurements

NASA Astrophysics Data System (ADS)

Newman, Jennifer F.; Klein, Petra M.; Wharton, Sonia; Sathe, Ameya; Bonin, Timothy A.; Chilson, Phillip B.; Muschinski, Andreas

2016-05-01

Several errors occur when a traditional Doppler beam swinging (DBS) or velocity-azimuth display (VAD) strategy is used to measure turbulence with a lidar. To mitigate some of these errors, a scanning strategy was recently developed which employs six beam positions to independently estimate the u, v, and w velocity variances and covariances. In order to assess the ability of these different scanning techniques to measure turbulence, a Halo scanning lidar, WindCube v2 pulsed lidar, and ZephIR continuous wave lidar were deployed at field sites in Oklahoma and Colorado with collocated sonic anemometers.Results indicate that the six-beam strategy mitigates some of the errors caused by VAD and DBS scans, but the strategy is strongly affected by errors in the variance measured at the different beam positions. The ZephIR and WindCube lidars overestimated horizontal variance values by over 60 % under unstable conditions as a result of variance contamination, where additional variance components contaminate the true value of the variance. A correction method was developed for the WindCube lidar that uses variance calculated from the vertical beam position to reduce variance contamination in the u and v variance components. The correction method reduced WindCube variance estimates by over 20 % at both the Oklahoma and Colorado sites under unstable conditions, when variance contamination is largest. This correction method can be easily applied to other lidars that contain a vertical beam position and is a promising method for accurately estimating turbulence with commercially available lidars.

Using Kriging with a heterogeneous measurement error to improve the accuracy of extreme precipitation return level estimation

NASA Astrophysics Data System (ADS)

Yin, Shui-qing; Wang, Zhonglei; Zhu, Zhengyuan; Zou, Xu-kai; Wang, Wen-ting

2018-07-01

Extreme precipitation can cause flooding and may result in great economic losses and deaths. The return level is a commonly used measure of extreme precipitation events and is required for hydrological engineer designs, including those of sewerage systems, dams, reservoirs and bridges. In this paper, we propose a two-step method to estimate the return level and its uncertainty for a study region. In the first step, we use the generalized extreme value distribution, the L-moment method and the stationary bootstrap to estimate the return level and its uncertainty at the site with observations. In the second step, a spatial model incorporating the heterogeneous measurement errors and covariates is trained to estimate return levels at sites with no observations and to improve the estimates at sites with limited information. The proposed method is applied to the daily rainfall data from 273 weather stations in the Haihe river basin of North China. We compare the proposed method with two alternatives: the first one is based on the ordinary Kriging method without measurement error, and the second one smooths the estimated location and scale parameters of the generalized extreme value distribution by the universal Kriging method. Results show that the proposed method outperforms its counterparts. We also propose a novel approach to assess the two-step method by comparing it with the at-site estimation method with a series of reduced length of observations. Estimates of the 2-, 5-, 10-, 20-, 50- and 100-year return level maps and the corresponding uncertainties are provided for the Haihe river basin, and a comparison with those released by the Hydrology Bureau of Ministry of Water Resources of China is made.

Integration of Harvest and Time-to-Event Data Used to Estimate Demographic Parameters for White-tailed Deer

NASA Astrophysics Data System (ADS)

Norton, Andrew S.

An integral component of managing game species is an understanding of population dynamics and relative abundance. Harvest data are frequently used to estimate abundance of white-tailed deer. Unless harvest age-structure is representative of the population age-structure and harvest vulnerability remains constant from year to year, these data alone are of limited value. Additional model structure and auxiliary information has accommodated this shortcoming. Specifically, integrated age-at-harvest (AAH) state-space population models can formally combine multiple sources of data, and regularization via hierarchical model structure can increase flexibility of model parameters. I collected known fates data, which I evaluated and used to inform trends in survival parameters for an integrated AAH model. I used temperature and snow depth covariates to predict survival outside of the hunting season, and opening weekend temperature and percent of corn harvest covariates to predict hunting season survival. When auxiliary empirical data were unavailable for the AAH model, moderately informative priors provided sufficient information for convergence and parameter estimates. The AAH model was most sensitive to errors in initial abundance, but this error was calibrated after 3 years. Among vital rates, the AAH model was most sensitive to reporting rates (percentage of mortality during the hunting season related to harvest). The AAH model, using only harvest data, was able to track changing abundance trends due to changes in survival rates even when prior models did not inform these changes (i.e. prior models were constant when truth varied). I also compared AAH model results with estimates from the Wisconsin Department of Natural Resources (WIDNR). Trends in abundance estimates from both models were similar, although AAH model predictions were systematically higher than WIDNR estimates in the East study area. When I incorporated auxiliary information (i.e. integrated AAH model) about survival outside the hunting season from known fates data, predicted trends appeared more closely related to what was expected. Disagreements between the AAH model and WIDNR estimates in the East were likely related to biased predictions for reporting and survival rates from the AAH model.

Computation of European carbon balance components through synergistic use of CARBOEUROPE eddy covariance, MODIS remote sensing data and advanced ecosystem and statistical modeling

NASA Astrophysics Data System (ADS)

Reichstein, M.; Dinh, N.; Running, S.; Seufert, G.; Tenhunen, J.; Valentini, R.

2003-04-01

Here we present spatially distributed bottom-up estimates of European carbon balance components for the year 2001, that stem from a newly built modeling system that integrates CARBOEUROPE eddy covariance CO_2 exchange data, remotely sensed vegetation properties via the MODIS-Terra sensor, European-wide soils data, and a suite of carbon balance models of different complexity. These estimates are able to better constrain top-down atmospheric-inversion carbon balance estimates within the dual-constraint approach for estimating continental carbon balances. The models that are used to calculate gross primary production (GPP) include a detailed layered canopy model with Farquhar-type photosynthesis (PROXELNEE), sun-shade big-leaf formulations operating at a daily time-step and a simple radiation-use efficiency model. These models are parameterized from eddy covariance data through inverse estimation techniques. Also for the estimation of soil and ecosystem respiration (Rsoil, Reco) we profit from a large data set of eddy covariance and soil chamber measurements, that enables us to the parameterize and validate a recently developed semi-empirical model, that includes a variable temperature sensitivity of respiration. As the outcome of the modeling system we present the most likely daily to annual numbers of carbon balance components (GPP, Reco, Rsoil), but we also issue a thorough analysis of biases and uncertainties in carbon balance estimates that are introduced through errors in the meteorological and remote sensing input data and through uncertainties in the model parameterization. In particular, we analyze 1) the effect of cloud contamination of the MODIS data, 2) the sensitivity to the land-use classification (Corine versus MODIS), 3) the effect of different soil parameterizations as derived from new continental-scale soil maps, and 4) the necessity to include soil drought effects into models of GPP and respiration. While the models describe the eddy covariance data quite well with r^2 values always greater than 0.7, there are still uncertainties in the European carbon balance estimate that exceed 0.3 PgC/yr. In northern (boreal) regions the carbon balance estimate is very much contingent on a high-quality filling of cloud contaminated remote sensing data, while in the southern (Mediterranean) regions a correct description of the soil water holding capacity is crucial. A major source of uncertainty also still is the estimation of heterotrophic respiration at continental scales. Consequently more spatial surveys on soil carbon stocks, turnover and history are needed. The study demonstrates that both, the inclusion of considerable geo-biological variability into a carbon balance modeling system, a high-quality cloud screening and gap-filling of the MODIS remote sensing data, and a correct description of soil drought effects are mandatory for realistic bottom-up estimates of European carbon balance components.

Sequential Least-Squares Using Orthogonal Transformations. [spacecraft communication/spacecraft tracking-data smoothing

NASA Technical Reports Server (NTRS)

Bierman, G. J.

1975-01-01

Square root information estimation, starting from its beginnings in least-squares parameter estimation, is considered. Special attention is devoted to discussions of sensitivity and perturbation matrices, computed solutions and their formal statistics, consider-parameters and consider-covariances, and the effects of a priori statistics. The constant-parameter model is extended to include time-varying parameters and process noise, and the error analysis capabilities are generalized. Efficient and elegant smoothing results are obtained as easy consequences of the filter formulation. The value of the techniques is demonstrated by the navigation results that were obtained for the Mariner Venus-Mercury (Mariner 10) multiple-planetary space probe and for the Viking Mars space mission.

Do stochastic inhomogeneities affect dark-energy precision measurements?

PubMed

Ben-Dayan, I; Gasperini, M; Marozzi, G; Nugier, F; Veneziano, G

2013-01-11

The effect of a stochastic background of cosmological perturbations on the luminosity-redshift relation is computed to second order through a recently proposed covariant and gauge-invariant light-cone averaging procedure. The resulting expressions are free from both ultraviolet and infrared divergences, implying that such perturbations cannot mimic a sizable fraction of dark energy. Different averages are estimated and depend on the particular function of the luminosity distance being averaged. The energy flux being minimally affected by perturbations at large z is proposed as the best choice for precision estimates of dark-energy parameters. Nonetheless, its irreducible (stochastic) variance induces statistical errors on Ω(Λ)(z) typically lying in the few-percent range.

Comparing models of change to estimate the mediated effect in the pretest-posttest control group design

PubMed Central

Valente, Matthew J.; MacKinnon, David P.

2017-01-01

Models to assess mediation in the pretest-posttest control group design are understudied in the behavioral sciences even though it is the design of choice for evaluating experimental manipulations. The paper provides analytical comparisons of the four most commonly used models used to estimate the mediated effect in this design: Analysis of Covariance (ANCOVA), difference score, residualized change score, and cross-sectional model. Each of these models are fitted using a Latent Change Score specification and a simulation study assessed bias, Type I error, power, and confidence interval coverage of the four models. All but the ANCOVA model make stringent assumptions about the stability and cross-lagged relations of the mediator and outcome that may not be plausible in real-world applications. When these assumptions do not hold, Type I error and statistical power results suggest that only the ANCOVA model has good performance. The four models are applied to an empirical example. PMID:28845097

Comparing models of change to estimate the mediated effect in the pretest-posttest control group design.

PubMed

Valente, Matthew J; MacKinnon, David P

2017-01-01

Models to assess mediation in the pretest-posttest control group design are understudied in the behavioral sciences even though it is the design of choice for evaluating experimental manipulations. The paper provides analytical comparisons of the four most commonly used models used to estimate the mediated effect in this design: Analysis of Covariance (ANCOVA), difference score, residualized change score, and cross-sectional model. Each of these models are fitted using a Latent Change Score specification and a simulation study assessed bias, Type I error, power, and confidence interval coverage of the four models. All but the ANCOVA model make stringent assumptions about the stability and cross-lagged relations of the mediator and outcome that may not be plausible in real-world applications. When these assumptions do not hold, Type I error and statistical power results suggest that only the ANCOVA model has good performance. The four models are applied to an empirical example.

Error analysis in stereo vision for location measurement of 3D point

NASA Astrophysics Data System (ADS)

Li, Yunting; Zhang, Jun; Tian, Jinwen

2015-12-01

Location measurement of 3D point in stereo vision is subjected to different sources of uncertainty that propagate to the final result. For current methods of error analysis, most of them are based on ideal intersection model to calculate the uncertainty region of point location via intersecting two fields of view of pixel that may produce loose bounds. Besides, only a few of sources of error such as pixel error or camera position are taken into account in the process of analysis. In this paper we present a straightforward and available method to estimate the location error that is taken most of source of error into account. We summed up and simplified all the input errors to five parameters by rotation transformation. Then we use the fast algorithm of midpoint method to deduce the mathematical relationships between target point and the parameters. Thus, the expectations and covariance matrix of 3D point location would be obtained, which can constitute the uncertainty region of point location. Afterwards, we turned back to the error propagation of the primitive input errors in the stereo system and throughout the whole analysis process from primitive input errors to localization error. Our method has the same level of computational complexity as the state-of-the-art method. Finally, extensive experiments are performed to verify the performance of our methods.

On the role of covariance information for GRACE K-band observations in the Celestial Mechanics Approach

NASA Astrophysics Data System (ADS)

Bentel, Katrin; Meyer, Ulrich; Arnold, Daniel; Jean, Yoomin; Jäggi, Adrian

2017-04-01

The Astronomical Institute at the University of Bern (AIUB) derives static and time-variable gravity fields by means of the Celestial Mechanics Approach (CMA) from GRACE (level 1B) data. This approach makes use of the close link between orbit and gravity field determination. GPS-derived kinematic GRACE orbit positions, inter-satellite K-band observations, which are the core observations of GRACE, and accelerometer data are combined to rigorously estimate orbit and spherical harmonic gravity field coefficients in one adjustment step. Pseudo-stochastic orbit parameters are set up to absorb unmodeled noise. The K-band range measurements in along-track direction lead to a much higher correlation of the observations in this direction compared to the other directions and thus, to north-south stripes in the unconstrained gravity field solutions, so-called correlated errors. By using a full covariance matrix for the K-band observations the correlation can be taken into account. One possibility is to derive correlation information from post-processing K-band residuals. This is then used in a second iteration step to derive an improved gravity field solution. We study the effects of pre-defined covariance matrices and residual-derived covariance matrices on the final gravity field product with the CMA.

A comparison of 12 algorithms for matching on the propensity score.

PubMed

Austin, Peter C

2014-03-15

Propensity-score matching is increasingly being used to reduce the confounding that can occur in observational studies examining the effects of treatments or interventions on outcomes. We used Monte Carlo simulations to examine the following algorithms for forming matched pairs of treated and untreated subjects: optimal matching, greedy nearest neighbor matching without replacement, and greedy nearest neighbor matching without replacement within specified caliper widths. For each of the latter two algorithms, we examined four different sub-algorithms defined by the order in which treated subjects were selected for matching to an untreated subject: lowest to highest propensity score, highest to lowest propensity score, best match first, and random order. We also examined matching with replacement. We found that (i) nearest neighbor matching induced the same balance in baseline covariates as did optimal matching; (ii) when at least some of the covariates were continuous, caliper matching tended to induce balance on baseline covariates that was at least as good as the other algorithms; (iii) caliper matching tended to result in estimates of treatment effect with less bias compared with optimal and nearest neighbor matching; (iv) optimal and nearest neighbor matching resulted in estimates of treatment effect with negligibly less variability than did caliper matching; (v) caliper matching had amongst the best performance when assessed using mean squared error; (vi) the order in which treated subjects were selected for matching had at most a modest effect on estimation; and (vii) matching with replacement did not have superior performance compared with caliper matching without replacement. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

A comparison of 12 algorithms for matching on the propensity score

PubMed Central

Austin, Peter C

2014-01-01

Propensity-score matching is increasingly being used to reduce the confounding that can occur in observational studies examining the effects of treatments or interventions on outcomes. We used Monte Carlo simulations to examine the following algorithms for forming matched pairs of treated and untreated subjects: optimal matching, greedy nearest neighbor matching without replacement, and greedy nearest neighbor matching without replacement within specified caliper widths. For each of the latter two algorithms, we examined four different sub-algorithms defined by the order in which treated subjects were selected for matching to an untreated subject: lowest to highest propensity score, highest to lowest propensity score, best match first, and random order. We also examined matching with replacement. We found that (i) nearest neighbor matching induced the same balance in baseline covariates as did optimal matching; (ii) when at least some of the covariates were continuous, caliper matching tended to induce balance on baseline covariates that was at least as good as the other algorithms; (iii) caliper matching tended to result in estimates of treatment effect with less bias compared with optimal and nearest neighbor matching; (iv) optimal and nearest neighbor matching resulted in estimates of treatment effect with negligibly less variability than did caliper matching; (v) caliper matching had amongst the best performance when assessed using mean squared error; (vi) the order in which treated subjects were selected for matching had at most a modest effect on estimation; and (vii) matching with replacement did not have superior performance compared with caliper matching without replacement. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24123228

Effects of Correlated Errors on the Analysis of Space Geodetic Data

NASA Technical Reports Server (NTRS)

Romero-Wolf, Andres; Jacobs, C. S.

2011-01-01

As thermal errors are reduced instrumental and troposphere correlated errors will increasingly become more important. Work in progress shows that troposphere covariance error models improve data analysis results. We expect to see stronger effects with higher data rates. Temperature modeling of delay errors may further reduce temporal correlations in the data.

The development of performance-monitoring function in the posterior medial frontal cortex

PubMed Central

Fitzgerald, Kate Dimond; Perkins, Suzanne C.; Angstadt, Mike; Johnson, Timothy; Stern, Emily R.; Welsh, Robert C.; Taylor, Stephan F.

2009-01-01

Background Despite its critical role in performance-monitoring, the development of posterior medial prefrontal cortex (pMFC) in goal-directed behaviors remains poorly understood. Performance monitoring depends on distinct, but related functions that may differentially activate the pMFC, such as monitoring response conflict and detecting errors. Developmental differences in conflict- and error-related activations, coupled with age-related changes in behavioral performance, may confound attempts to map the maturation of pMFC functions. To characterize the development of pMFC-based performance monitoring functions, we segregated interference and error-processing, while statistically controlling for performance. Methods Twenty-one adults and 23 youth performed an event-related version of the Multi-Source Interference Task during functional magnetic resonance imaging (fMRI). Linear modeling of interference and error contrast estimates derived from the pMFC were regressed on age, while covarying for performance. Results Interference- and error-processing were associated with robust activation of the pMFC in both youth and adults. Among youth, interference- and error-related activation of the pMFC increased with age, independent of performance. Greater accuracy associated with greater pMFC activity during error commission in both groups. Discussion Increasing pMFC response to interference and errors occurs with age, likely contributing to the improvement of performance monitoring capacity during development. PMID:19913101

Multi-Satellite Orbit Determination Using Interferometric Observables with RF Localization Applications

NASA Astrophysics Data System (ADS)

Geeraert, Jeroen L.

Very long baseline interferometry (VLBI) specifically same-beam interferometry (SBI), and dual-satellite geolocation are two fields of research not previously connected. This is due to the different application of each field, SBI is used for relative interplanetary navigation of two satellites while dual-satellite geolocation is used to locate the source of a radio frequency (RF) signal. In this dissertation however, we leverage both fields to create a novel method for multi-satellite orbit determination (OD) using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. The measurements are double differenced between the satellites and the stations, in so doing, many of the common errors are canceled which can significantly improve measurement precision. Provided with this novel OD technique, the observability is first analyzed to determine the benefits and limitations of this method. In all but a few scenarios the measurements successfully reduce the covariance when examining the Cramer-Rao Lower Bound (CRLB). Reduced observability is encountered with geostationary satellites as their motion with respect to the stations is limited, especially when only one baseline is used. However, when using satellite pairs with greater relative motion with respect to the stations, even satellites that are close to, but not exactly in a geostationary orbit can be estimated accurately. We find that in a strong majority of cases the OD technique provides lower uncertainties and solutions far more accurate than using conventional OD observables such as range and range-rate while also not being affected by common errors and biases. We specifically examine GEO-GEO, GEO-MEO, and GEO-LEO dual-satellite estimation cases. The work is further extended by developing a relative navigation scenario where the chief satellite is assumed to have perfect knowledge, or some small amount of uncertainty considered but not estimated, while estimating the deputy satellite state with respect to the chief. Once again the results demonstrate that the TDOA and FDOA OD results are favorable with faster dynamics over classical measurements. This dissertation not only explores the OD side, but also gaps in geolocation research. First the mapping of ephemeris uncertainty to the geolocation covariance to provide a more realistic covariance was implemented. Furthermore, the geolocation solution was improved by appending a probabilistic altitude constraint to the posterior covariance, significantly reducing the projected geolocation uncertainty ellipse. The feasibility of using the geolocation setup to passively locate a LEO satellite was also considered. Finally the simulated results were verified using a long-arc of real data. The use of FDOA for small-body navigation and gravity recovery was also examined as an extended application.

Measurement error in epidemiologic studies of air pollution based on land-use regression models.

PubMed

Basagaña, Xavier; Aguilera, Inmaculada; Rivera, Marcela; Agis, David; Foraster, Maria; Marrugat, Jaume; Elosua, Roberto; Künzli, Nino

2013-10-15

Land-use regression (LUR) models are increasingly used to estimate air pollution exposure in epidemiologic studies. These models use air pollution measurements taken at a small set of locations and modeling based on geographical covariates for which data are available at all study participant locations. The process of LUR model development commonly includes a variable selection procedure. When LUR model predictions are used as explanatory variables in a model for a health outcome, measurement error can lead to bias of the regression coefficients and to inflation of their variance. In previous studies dealing with spatial predictions of air pollution, bias was shown to be small while most of the effect of measurement error was on the variance. In this study, we show that in realistic cases where LUR models are applied to health data, bias in health-effect estimates can be substantial. This bias depends on the number of air pollution measurement sites, the number of available predictors for model selection, and the amount of explainable variability in the true exposure. These results should be taken into account when interpreting health effects from studies that used LUR models.

Bayesian correction for covariate measurement error: A frequentist evaluation and comparison with regression calibration.

PubMed

Bartlett, Jonathan W; Keogh, Ruth H

2018-06-01

Bayesian approaches for handling covariate measurement error are well established and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper, we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration, arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to regression calibration and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next, we describe the closely related maximum likelihood and multiple imputation approaches and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of regression calibration and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey.

Problems with small area surveys: lensing covariance of supernova distance measurements.

PubMed

Cooray, Asantha; Huterer, Dragan; Holz, Daniel E

2006-01-20

While luminosity distances from type Ia supernovae (SNe) are a powerful probe of cosmology, the accuracy with which these distances can be measured is limited by cosmic magnification due to gravitational lensing by the intervening large-scale structure. Spatial clustering of foreground mass leads to correlated errors in SNe distances. By including the full covariance matrix of SNe, we show that future wide-field surveys will remain largely unaffected by lensing correlations. However, "pencil beam" surveys, and those with narrow (but possibly long) fields of view, can be strongly affected. For a survey with 30 arcmin mean separation between SNe, lensing covariance leads to a approximately 45% increase in the expected errors in dark energy parameters.

Estimation for the Linear Model With Uncertain Covariance Matrices

NASA Astrophysics Data System (ADS)

Zachariah, Dave; Shariati, Nafiseh; Bengtsson, Mats; Jansson, Magnus; Chatterjee, Saikat

2014-03-01

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior inverse-Wishart distributions. The nonconvex problem of jointly estimating the signal of interest and the covariance matrices is tackled by a computationally efficient fixed-point iteration as well as an approximate variational Bayes solution. The statistical performance of estimators is compared numerically to state-of-the-art estimators from the literature and shown to perform favorably.

The performance of different propensity score methods for estimating marginal hazard ratios.

PubMed

Austin, Peter C

2013-07-20

Propensity score methods are increasingly being used to reduce or minimize the effects of confounding when estimating the effects of treatments, exposures, or interventions when using observational or non-randomized data. Under the assumption of no unmeasured confounders, previous research has shown that propensity score methods allow for unbiased estimation of linear treatment effects (e.g., differences in means or proportions). However, in biomedical research, time-to-event outcomes occur frequently. There is a paucity of research into the performance of different propensity score methods for estimating the effect of treatment on time-to-event outcomes. Furthermore, propensity score methods allow for the estimation of marginal or population-average treatment effects. We conducted an extensive series of Monte Carlo simulations to examine the performance of propensity score matching (1:1 greedy nearest-neighbor matching within propensity score calipers), stratification on the propensity score, inverse probability of treatment weighting (IPTW) using the propensity score, and covariate adjustment using the propensity score to estimate marginal hazard ratios. We found that both propensity score matching and IPTW using the propensity score allow for the estimation of marginal hazard ratios with minimal bias. Of these two approaches, IPTW using the propensity score resulted in estimates with lower mean squared error when estimating the effect of treatment in the treated. Stratification on the propensity score and covariate adjustment using the propensity score result in biased estimation of both marginal and conditional hazard ratios. Applied researchers are encouraged to use propensity score matching and IPTW using the propensity score when estimating the relative effect of treatment on time-to-event outcomes. Copyright © 2012 John Wiley & Sons, Ltd.

Functional mapping of reaction norms to multiple environmental signals through nonparametric covariance estimation

PubMed Central

2011-01-01

Background The identification of genes or quantitative trait loci that are expressed in response to different environmental factors such as temperature and light, through functional mapping, critically relies on precise modeling of the covariance structure. Previous work used separable parametric covariance structures, such as a Kronecker product of autoregressive one [AR(1)] matrices, that do not account for interaction effects of different environmental factors. Results We implement a more robust nonparametric covariance estimator to model these interactions within the framework of functional mapping of reaction norms to two signals. Our results from Monte Carlo simulations show that this estimator can be useful in modeling interactions that exist between two environmental signals. The interactions are simulated using nonseparable covariance models with spatio-temporal structural forms that mimic interaction effects. Conclusions The nonparametric covariance estimator has an advantage over separable parametric covariance estimators in the detection of QTL location, thus extending the breadth of use of functional mapping in practical settings. PMID:21269481

Measuring continuous baseline covariate imbalances in clinical trial data

PubMed Central

Ciolino, Jody D.; Martin, Renee’ H.; Zhao, Wenle; Hill, Michael D.; Jauch, Edward C.; Palesch, Yuko Y.

2014-01-01

This paper presents and compares several methods of measuring continuous baseline covariate imbalance in clinical trial data. Simulations illustrate that though the t-test is an inappropriate method of assessing continuous baseline covariate imbalance, the test statistic itself is a robust measure in capturing imbalance in continuous covariate distributions. Guidelines to assess effects of imbalance on bias, type I error rate, and power for hypothesis test for treatment effect on continuous outcomes are presented, and the benefit of covariate-adjusted analysis (ANCOVA) is also illustrated. PMID:21865270

Interpreting SBUV Smoothing Errors: an Example Using the Quasi-biennial Oscillation

NASA Technical Reports Server (NTRS)

Kramarova, N. A.; Bhartia, Pawan K.; Frith, S. M.; McPeters, R. D.; Stolarski, R. S.

2013-01-01

The Solar Backscattered Ultraviolet (SBUV) observing system consists of a series of instruments that have been measuring both total ozone and the ozone profile since 1970. SBUV measures the profile in the upper stratosphere with a resolution that is adequate to resolve most of the important features of that region. In the lower stratosphere the limited vertical resolution of the SBUV system means that there are components of the profile variability that SBUV cannot measure. The smoothing error, as defined in the optimal estimation retrieval method, describes the components of the profile variability that the SBUV observing system cannot measure. In this paper we provide a simple visual interpretation of the SBUV smoothing error by comparing SBUV ozone anomalies in the lower tropical stratosphere associated with the quasi-biennial oscillation (QBO) to anomalies obtained from the Aura Microwave Limb Sounder (MLS). We describe a methodology for estimating the SBUV smoothing error for monthly zonal mean (mzm) profiles. We construct covariance matrices that describe the statistics of the inter-annual ozone variability using a 6 yr record of Aura MLS and ozonesonde data. We find that the smoothing error is of the order of 1percent between 10 and 1 hPa, increasing up to 15-20 percent in the troposphere and up to 5 percent in the mesosphere. The smoothing error for total ozone columns is small, mostly less than 0.5 percent. We demonstrate that by merging the partial ozone columns from several layers in the lower stratosphere/troposphere into one thick layer, we can minimize the smoothing error. We recommend using the following layer combinations to reduce the smoothing error to about 1 percent: surface to 25 hPa (16 hPa) outside (inside) of the narrow equatorial zone 20 S-20 N.

A new Method for the Estimation of Initial Condition Uncertainty Structures in Mesoscale Models

NASA Astrophysics Data System (ADS)

Keller, J. D.; Bach, L.; Hense, A.

2012-12-01

The estimation of fast growing error modes of a system is a key interest of ensemble data assimilation when assessing uncertainty in initial conditions. Over the last two decades three methods (and variations of these methods) have evolved for global numerical weather prediction models: ensemble Kalman filter, singular vectors and breeding of growing modes (or now ensemble transform). While the former incorporates a priori model error information and observation error estimates to determine ensemble initial conditions, the latter two techniques directly address the error structures associated with Lyapunov vectors. However, in global models these structures are mainly associated with transient global wave patterns. When assessing initial condition uncertainty in mesoscale limited area models, several problems regarding the aforementioned techniques arise: (a) additional sources of uncertainty on the smaller scales contribute to the error and (b) error structures from the global scale may quickly move through the model domain (depending on the size of the domain). To address the latter problem, perturbation structures from global models are often included in the mesoscale predictions as perturbed boundary conditions. However, the initial perturbations (when used) are often generated with a variant of an ensemble Kalman filter which does not necessarily focus on the large scale error patterns. In the framework of the European regional reanalysis project of the Hans-Ertel-Center for Weather Research we use a mesoscale model with an implemented nudging data assimilation scheme which does not support ensemble data assimilation at all. In preparation of an ensemble-based regional reanalysis and for the estimation of three-dimensional atmospheric covariance structures, we implemented a new method for the assessment of fast growing error modes for mesoscale limited area models. The so-called self-breeding is development based on the breeding of growing modes technique. Initial perturbations are integrated forward for a short time period and then rescaled and added to the initial state again. Iterating this rapid breeding cycle provides estimates for the initial uncertainty structure (or local Lyapunov vectors) given a specific norm. To avoid that all ensemble perturbations converge towards the leading local Lyapunov vector we apply an ensemble transform variant to orthogonalize the perturbations in the sub-space spanned by the ensemble. By choosing different kind of norms to measure perturbation growth, this technique allows for estimating uncertainty patterns targeted at specific sources of errors (e.g. convection, turbulence). With case study experiments we show applications of the self-breeding method for different sources of uncertainty and different horizontal scales.

Bayesian hierarchical model for large-scale covariance matrix estimation.

PubMed

Zhu, Dongxiao; Hero, Alfred O

2007-12-01

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.

Improved characterisation and modelling of measurement errors in electrical resistivity tomography (ERT) surveys

NASA Astrophysics Data System (ADS)

Tso, Chak-Hau Michael; Kuras, Oliver; Wilkinson, Paul B.; Uhlemann, Sebastian; Chambers, Jonathan E.; Meldrum, Philip I.; Graham, James; Sherlock, Emma F.; Binley, Andrew

2017-11-01

Measurement errors can play a pivotal role in geophysical inversion. Most inverse models require users to prescribe or assume a statistical model of data errors before inversion. Wrongly prescribed errors can lead to over- or under-fitting of data; however, the derivation of models of data errors is often neglected. With the heightening interest in uncertainty estimation within hydrogeophysics, better characterisation and treatment of measurement errors is needed to provide improved image appraisal. Here we focus on the role of measurement errors in electrical resistivity tomography (ERT). We have analysed two time-lapse ERT datasets: one contains 96 sets of direct and reciprocal data collected from a surface ERT line within a 24 h timeframe; the other is a two-year-long cross-borehole survey at a UK nuclear site with 246 sets of over 50,000 measurements. Our study includes the characterisation of the spatial and temporal behaviour of measurement errors using autocorrelation and correlation coefficient analysis. We find that, in addition to well-known proportionality effects, ERT measurements can also be sensitive to the combination of electrodes used, i.e. errors may not be uncorrelated as often assumed. Based on these findings, we develop a new error model that allows grouping based on electrode number in addition to fitting a linear model to transfer resistance. The new model explains the observed measurement errors better and shows superior inversion results and uncertainty estimates in synthetic examples. It is robust, because it groups errors together based on the electrodes used to make the measurements. The new model can be readily applied to the diagonal data weighting matrix widely used in common inversion methods, as well as to the data covariance matrix in a Bayesian inversion framework. We demonstrate its application using extensive ERT monitoring datasets from the two aforementioned sites.

A New Understanding for the Rain Rate retrieval of Attenuating Radars Measurement

NASA Astrophysics Data System (ADS)

Koner, P.; Battaglia, A.; Simmer, C.

2009-04-01

The retrieval of rain rate from the attenuated radar (e.g. Cloud Profiling Radar on board of CloudSAT in orbit since June 2006) is a challenging problem. ĹEcuyer and Stephens [1] underlined this difficulty (for rain rates larger than 1.5 mm/h) and suggested the need of additional information (like path-integrated attenuations (PIA) derived from surface reference techniques or precipitation water path estimated from co-located passive microwave radiometer) to constrain the retrieval. It is generally discussed based on the optimal estimation theory that there are no solutions without constraining the problem in a case of visible attenuation because there is no enough information content to solve the problem. However, when the problem is constrained by the additional measurement of PIA, there is a reasonable solution. This raises the spontaneous question: Is all information enclosed in this additional measurement? This also contradicts with the information theory because one measurement can introduce only one degree of freedom in the retrieval. Why is one degree of freedom so important in the above problem? This question cannot be explained using the estimation and information theories of OEM. On the other hand, Koner and Drummond [2] argued that the OEM is basically a regularization method, where a-priori covariance is used as a stabilizer and the regularization strength is determined by the choices of the a-priori and error covariance matrices. The regularization is required for the reduction of the condition number of Jacobian, which drives the noise injection from the measurement and inversion spaces to the state space in an ill-posed inversion. In this work, the above mentioned question will be discussed based on the regularization theory, error mitigation and eigenvalue mathematics. References 1. L'Ecuyer TS and Stephens G. An estimation based precipitation retrieval algorithm for attenuating radar. J. Appl. Met., 2002, 41, 272-85. 2. Koner PK, Drummond JR. A comparison of regularization techniques for atmospheric trace gases retrievals. JQSRT 2008; 109:514-26.

Underestimating the effects of spatial heterogeneity due to individual movement and spatial scale: infectious disease as an example

USGS Publications Warehouse

Cross, Paul C.; Caillaud, Damien; Heisey, Dennis M.

2013-01-01

Many ecological and epidemiological studies occur in systems with mobile individuals and heterogeneous landscapes. Using a simulation model, we show that the accuracy of inferring an underlying biological process from observational data depends on movement and spatial scale of the analysis. As an example, we focused on estimating the relationship between host density and pathogen transmission. Observational data can result in highly biased inference about the underlying process when individuals move among sampling areas. Even without sampling error, the effect of host density on disease transmission is underestimated by approximately 50 % when one in ten hosts move among sampling areas per lifetime. Aggregating data across larger regions causes minimal bias when host movement is low, and results in less biased inference when movement rates are high. However, increasing data aggregation reduces the observed spatial variation, which would lead to the misperception that a spatially targeted control effort may not be very effective. In addition, averaging over the local heterogeneity will result in underestimating the importance of spatial covariates. Minimizing the bias due to movement is not just about choosing the best spatial scale for analysis, but also about reducing the error associated with using the sampling location as a proxy for an individual’s spatial history. This error associated with the exposure covariate can be reduced by choosing sampling regions with less movement, including longitudinal information of individuals’ movements, or reducing the window of exposure by using repeated sampling or younger individuals.

Estimating the variance and integral scale of the transmissivity field using head residual increments

USGS Publications Warehouse

Zheng, Li; Silliman, Stephen E.

2000-01-01

A modification of previously published solutions regarding the spatial variation of hydraulic heads is discussed whereby the semivariogram of increments of head residuals (termed head residual increments HRIs) are related to the variance and integral scale of the transmissivity field. A first‐order solution is developed for the case of a transmissivity field which is isotropic and whose second‐order behavior can be characterized by an exponential covariance structure. The estimates of the variance σY2 and the integral scale λ of the log transmissivity field are then obtained via fitting a theoretical semivariogram for the HRI to its sample semivariogram. This approach is applied to head data sampled from a series of two‐dimensional, simulated aquifers with isotropic, exponential covariance structures and varying degrees of heterogeneity (σY2 = 0.25, 0.5, 1.0, 2.0, and 5.0). The results show that this method provided reliable estimates for both λ and σY2 in aquifers with the value of σY2 up to 2.0, but the errors in those estimates were higher for σY2 equal to 5.0. It is also demonstrated through numerical experiments and theoretical arguments that the head residual increments will provide a sample semivariogram with a lower variance than will the use of the head residuals without calculation of increments.

Robust linear discriminant models to solve financial crisis in banking sectors

NASA Astrophysics Data System (ADS)

Lim, Yai-Fung; Yahaya, Sharipah Soaad Syed; Idris, Faoziah; Ali, Hazlina; Omar, Zurni

2014-12-01

Linear discriminant analysis (LDA) is a widely-used technique in patterns classification via an equation which will minimize the probability of misclassifying cases into their respective categories. However, the performance of classical estimators in LDA highly depends on the assumptions of normality and homoscedasticity. Several robust estimators in LDA such as Minimum Covariance Determinant (MCD), S-estimators and Minimum Volume Ellipsoid (MVE) are addressed by many authors to alleviate the problem of non-robustness of the classical estimates. In this paper, we investigate on the financial crisis of the Malaysian banking institutions using robust LDA and classical LDA methods. Our objective is to distinguish the "distress" and "non-distress" banks in Malaysia by using the LDA models. Hit ratio is used to validate the accuracy predictive of LDA models. The performance of LDA is evaluated by estimating the misclassification rate via apparent error rate. The results and comparisons show that the robust estimators provide a better performance than the classical estimators for LDA.

Spatio-Temporal Field Estimation Using Kriged Kalman Filter (KKF) with Sparsity-Enforcing Sensor Placement.

PubMed

Roy, Venkat; Simonetto, Andrea; Leus, Geert

2018-06-01

We propose a sensor placement method for spatio-temporal field estimation based on a kriged Kalman filter (KKF) using a network of static or mobile sensors. The developed framework dynamically designs the optimal constellation to place the sensors. We combine the estimation error (for the stationary as well as non-stationary component of the field) minimization problem with a sparsity-enforcing penalty to design the optimal sensor constellation in an economic manner. The developed sensor placement method can be directly used for a general class of covariance matrices (ill-conditioned or well-conditioned) modelling the spatial variability of the stationary component of the field, which acts as a correlated observation noise, while estimating the non-stationary component of the field. Finally, a KKF estimator is used to estimate the field using the measurements from the selected sensing locations. Numerical results are provided to exhibit the feasibility of the proposed dynamic sensor placement followed by the KKF estimation method.

An anthropomorphic phantom for quantitative evaluation of breast MRI.

PubMed

Freed, Melanie; de Zwart, Jacco A; Loud, Jennifer T; El Khouli, Riham H; Myers, Kyle J; Greene, Mark H; Duyn, Jeff H; Badano, Aldo

2011-02-01

In this study, the authors aim to develop a physical, tissue-mimicking phantom for quantitative evaluation of breast MRI protocols. The objective of this phantom is to address the need for improved standardization in breast MRI and provide a platform for evaluating the influence of image protocol parameters on lesion detection and discrimination. Quantitative comparisons between patient and phantom image properties are presented. The phantom is constructed using a mixture of lard and egg whites, resulting in a random structure with separate adipose- and glandular-mimicking components. T1 and T2 relaxation times of the lard and egg components of the phantom were estimated at 1.5 T from inversion recovery and spin-echo scans, respectively, using maximum-likelihood methods. The image structure was examined quantitatively by calculating and comparing spatial covariance matrices of phantom and patient images. A static, enhancing lesion was introduced by creating a hollow mold with stereolithography and filling it with a gadolinium-doped water solution. Measured phantom relaxation values fall within 2 standard errors of human values from the literature and are reasonably stable over 9 months of testing. Comparison of the covariance matrices of phantom and patient data demonstrates that the phantom and patient data have similar image structure. Their covariance matrices are the same to within error bars in the anterior-posterior direction and to within about two error bars in the right-left direction. The signal from the phantom's adipose-mimicking material can be suppressed using active fat-suppression protocols. A static, enhancing lesion can also be included with the ability to change morphology and contrast agent concentration. The authors have constructed a phantom and demonstrated its ability to mimic human breast images in terms of key physical properties that are relevant to breast MRI. This phantom provides a platform for the optimization and standardization of breast MRI imaging protocols for lesion detection and characterization.

Racial disparities in the health benefits of educational attainment: a study of inflammatory trajectories among African American and white adults.

PubMed

Fuller-Rowell, Thomas E; Curtis, David S; Doan, Stacey N; Coe, Christopher L

2015-01-01

The current study examined the prospective effects of educational attainment on proinflammatory physiology among African American and white adults. Participants were 1192 African Americans and 1487 whites who participated in Year 5 (mean [standard deviation] age = 30 [3.5] years), and Year 20 (mean [standard deviation] age = 45 [3.5]) of an ongoing longitudinal study. Initial analyses focused on age-related changes in fibrinogen across racial groups, and parallel analyses for C-reactive protein and interleukin-6 assessed at Year 20. Models then estimated the effects of educational attainment on changes in inflammation for African Americans and whites before and after controlling for four blocks of covariates: a) early life adversity, b) health and health behaviors at baseline, c) employment and financial measures at baseline and follow-up, and d) psychosocial stresses in adulthood. African Americans had larger increases in fibrinogen over time than whites (B = 24.93, standard error = 3.24, p < .001), and 37% of this difference was explained after including all covariates. Effects of educational attainment were weaker for African Americans than for whites (B = 10.11, standard error = 3.29, p = .002), and only 8% of this difference was explained by covariates. Analyses for C-reactive protein and interleukin-6 yielded consistent results. The effects of educational attainment on inflammation levels were stronger for white than for African American participants. Why African Americans do not show the same health benefits with educational attainment is an important question for health disparities research.

Bias estimation for moving optical sensor measurements with targets of opportunity

NASA Astrophysics Data System (ADS)

Belfadel, Djedjiga; Osborne, Richard W.; Bar-Shalom, Yaakov

2014-06-01

Integration of space based sensors into a Ballistic Missile Defense System (BMDS) allows for detection and tracking of threats over a larger area than ground based sensors [1]. This paper examines the effect of sensor bias error on the tracking quality of a Space Tracking and Surveillance System (STSS) for the highly non-linear problem of tracking a ballistic missile. The STSS constellation consists of two or more satellites (on known trajectories) for tracking ballistic targets. Each satellite is equipped with an IR sensor that provides azimuth and elevation to the target. The tracking problem is made more difficult due to a constant or slowly varying bias error present in each sensor's line of sight measurements. It is important to correct for these bias errors so that the multiple sensor measurements and/or tracks can be referenced as accurately as possible to a common tracking coordinate system. The measurements provided by these sensors are assumed time-coincident (synchronous) and perfectly associated. The line of sight (LOS) measurements from the sensors can be fused into measurements which are the Cartesian target position, i.e., linear in the target state. We evaluate the Cramér-Rao Lower Bound (CRLB) on the covariance of the bias estimates, which serves as a quantification of the available information about the biases. Statistical tests on the results of simulations show that this method is statistically efficient, even for small sample sizes (as few as two sensors and six points on the (unknown) trajectory of a single target of opportunity). We also show that the RMS position error is significantly improved with bias estimation compared with the target position estimation using the original biased measurements.

Estimation and correction of visibility bias in aerial surveys of wintering ducks

USGS Publications Warehouse

Pearse, A.T.; Gerard, P.D.; Dinsmore, S.J.; Kaminski, R.M.; Reinecke, K.J.

2008-01-01

Incomplete detection of all individuals leading to negative bias in abundance estimates is a pervasive source of error in aerial surveys of wildlife, and correcting that bias is a critical step in improving surveys. We conducted experiments using duck decoys as surrogates for live ducks to estimate bias associated with surveys of wintering ducks in Mississippi, USA. We found detection of decoy groups was related to wetland cover type (open vs. forested), group size (1?100 decoys), and interaction of these variables. Observers who detected decoy groups reported counts that averaged 78% of the decoys actually present, and this counting bias was not influenced by either covariate cited above. We integrated this sightability model into estimation procedures for our sample surveys with weight adjustments derived from probabilities of group detection (estimated by logistic regression) and count bias. To estimate variances of abundance estimates, we used bootstrap resampling of transects included in aerial surveys and data from the bias-correction experiment. When we implemented bias correction procedures on data from a field survey conducted in January 2004, we found bias-corrected estimates of abundance increased 36?42%, and associated standard errors increased 38?55%, depending on species or group estimated. We deemed our method successful for integrating correction of visibility bias in an existing sample survey design for wintering ducks in Mississippi, and we believe this procedure could be implemented in a variety of sampling problems for other locations and species.

A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.

PubMed

Houseman, E Andres; Virji, M Abbas

2017-08-01

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates were significant in some frequentist models, but in the Bayesian model their credible intervals contained zero; such discrepancies were observed in multiple datasets. Variance components from the Bayesian model reflected substantial autocorrelation, consistent with the frequentist models, except for the auto-regressive moving average model. Plots of means from the Bayesian model showed good fit to the observed data. The proposed Bayesian model provides an approach for modeling non-stationary autocorrelation in a hierarchical modeling framework to estimate task means, standard deviations, quantiles, and parameter estimates for covariates that are less biased and have better performance characteristics than some of the contemporary methods. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

Bayesian source term determination with unknown covariance of measurements

NASA Astrophysics Data System (ADS)

Belal, Alkomiet; Tichý, Ondřej; Šmídl, Václav

2017-04-01

Determination of a source term of release of a hazardous material into the atmosphere is a very important task for emergency response. We are concerned with the problem of estimation of the source term in the conventional linear inverse problem, y = Mx, where the relationship between the vector of observations y is described using the source-receptor-sensitivity (SRS) matrix M and the unknown source term x. Since the system is typically ill-conditioned, the problem is recast as an optimization problem minR,B(y - Mx)TR-1(y - Mx) + xTB-1x. The first term minimizes the error of the measurements with covariance matrix R, and the second term is a regularization of the source term. There are different types of regularization arising for different choices of matrices R and B, for example, Tikhonov regularization assumes covariance matrix B as the identity matrix multiplied by scalar parameter. In this contribution, we adopt a Bayesian approach to make inference on the unknown source term x as well as unknown R and B. We assume prior on x to be a Gaussian with zero mean and unknown diagonal covariance matrix B. The covariance matrix of the likelihood R is also unknown. We consider two potential choices of the structure of the matrix R. First is the diagonal matrix and the second is a locally correlated structure using information on topology of the measuring network. Since the inference of the model is intractable, iterative variational Bayes algorithm is used for simultaneous estimation of all model parameters. The practical usefulness of our contribution is demonstrated on an application of the resulting algorithm to real data from the European Tracer Experiment (ETEX). This research is supported by EEA/Norwegian Financial Mechanism under project MSMT-28477/2014 Source-Term Determination of Radionuclide Releases by Inverse Atmospheric Dispersion Modelling (STRADI).

Sequential estimation and satellite data assimilation in meteorology and oceanography

NASA Technical Reports Server (NTRS)

Ghil, M.

1986-01-01

The central theme of this review article is the role that dynamics plays in estimating the state of the atmosphere and of the ocean from incomplete and noisy data. Objective analysis and inverse methods represent an attempt at relying mostly on the data and minimizing the role of dynamics in the estimation. Four-dimensional data assimilation tries to balance properly the roles of dynamical and observational information. Sequential estimation is presented as the proper framework for understanding this balance, and the Kalman filter as the ideal, optimal procedure for data assimilation. The optimal filter computes forecast error covariances of a given atmospheric or oceanic model exactly, and hence data assimilation should be closely connected with predictability studies. This connection is described, and consequences drawn for currently active areas of the atmospheric and oceanic sciences, namely, mesoscale meteorology, medium and long-range forecasting, and upper-ocean dynamics.

Wavelet-based functional linear mixed models: an application to measurement error-corrected distributed lag models.

PubMed

Malloy, Elizabeth J; Morris, Jeffrey S; Adar, Sara D; Suh, Helen; Gold, Diane R; Coull, Brent A

2010-07-01

Frequently, exposure data are measured over time on a grid of discrete values that collectively define a functional observation. In many applications, researchers are interested in using these measurements as covariates to predict a scalar response in a regression setting, with interest focusing on the most biologically relevant time window of exposure. One example is in panel studies of the health effects of particulate matter (PM), where particle levels are measured over time. In such studies, there are many more values of the functional data than observations in the data set so that regularization of the corresponding functional regression coefficient is necessary for estimation. Additional issues in this setting are the possibility of exposure measurement error and the need to incorporate additional potential confounders, such as meteorological or co-pollutant measures, that themselves may have effects that vary over time. To accommodate all these features, we develop wavelet-based linear mixed distributed lag models that incorporate repeated measures of functional data as covariates into a linear mixed model. A Bayesian approach to model fitting uses wavelet shrinkage to regularize functional coefficients. We show that, as long as the exposure error induces fine-scale variability in the functional exposure profile and the distributed lag function representing the exposure effect varies smoothly in time, the model corrects for the exposure measurement error without further adjustment. Both these conditions are likely to hold in the environmental applications we consider. We examine properties of the method using simulations and apply the method to data from a study examining the association between PM, measured as hourly averages for 1-7 days, and markers of acute systemic inflammation. We use the method to fully control for the effects of confounding by other time-varying predictors, such as temperature and co-pollutants.

Evaluation of logistic regression models and effect of covariates for case-control study in RNA-Seq analysis.

PubMed

Choi, Seung Hoan; Labadorf, Adam T; Myers, Richard H; Lunetta, Kathryn L; Dupuis, Josée; DeStefano, Anita L

2017-02-06

Next generation sequencing provides a count of RNA molecules in the form of short reads, yielding discrete, often highly non-normally distributed gene expression measurements. Although Negative Binomial (NB) regression has been generally accepted in the analysis of RNA sequencing (RNA-Seq) data, its appropriateness has not been exhaustively evaluated. We explore logistic regression as an alternative method for RNA-Seq studies designed to compare cases and controls, where disease status is modeled as a function of RNA-Seq reads using simulated and Huntington disease data. We evaluate the effect of adjusting for covariates that have an unknown relationship with gene expression. Finally, we incorporate the data adaptive method in order to compare false positive rates. When the sample size is small or the expression levels of a gene are highly dispersed, the NB regression shows inflated Type-I error rates but the Classical logistic and Bayes logistic (BL) regressions are conservative. Firth's logistic (FL) regression performs well or is slightly conservative. Large sample size and low dispersion generally make Type-I error rates of all methods close to nominal alpha levels of 0.05 and 0.01. However, Type-I error rates are controlled after applying the data adaptive method. The NB, BL, and FL regressions gain increased power with large sample size, large log2 fold-change, and low dispersion. The FL regression has comparable power to NB regression. We conclude that implementing the data adaptive method appropriately controls Type-I error rates in RNA-Seq analysis. Firth's logistic regression provides a concise statistical inference process and reduces spurious associations from inaccurately estimated dispersion parameters in the negative binomial framework.

Noise in two-color electronic distance meter measurements revisited

USGS Publications Warehouse

Langbein, J.

2004-01-01

Frequent, high-precision geodetic data have temporally correlated errors. Temporal correlations directly affect both the estimate of rate and its standard error; the rate of deformation is a key product from geodetic measurements made in tectonically active areas. Various models of temporally correlated errors are developed and these provide relations between the power spectral density and the data covariance matrix. These relations are applied to two-color electronic distance meter (EDM) measurements made frequently in California over the past 15-20 years. Previous analysis indicated that these data have significant random walk error. Analysis using the noise models developed here indicates that the random walk model is valid for about 30% of the data. A second 30% of the data can be better modeled with power law noise with a spectral index between 1 and 2, while another 30% of the data can be modeled with a combination of band-pass-filtered plus random walk noise. The remaining 10% of the data can be best modeled as a combination of band-pass-filtered plus power law noise. This band-pass-filtered noise is a product of an annual cycle that leaks into adjacent frequency bands. For time spans of more than 1 year these more complex noise models indicate that the precision in rate estimates is better than that inferred by just the simpler, random walk model of noise.

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings. PMID:28042189

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Robust estimation for partially linear models with large-dimensional covariates

PubMed Central

Zhu, LiPing; Li, RunZe; Cui, HengJian

2014-01-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(n), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures. PMID:24955087

Mixed model approaches for diallel analysis based on a bio-model.

PubMed

Zhu, J; Weir, B S

1996-12-01

A MINQUE(1) procedure, which is minimum norm quadratic unbiased estimation (MINQUE) method with 1 for all the prior values, is suggested for estimating variance and covariance components in a bio-model for diallel crosses. Unbiasedness and efficiency of estimation were compared for MINQUE(1), restricted maximum likelihood (REML) and MINQUE theta which has parameter values for the prior values. MINQUE(1) is almost as efficient as MINQUE theta for unbiased estimation of genetic variance and covariance components. The bio-model is efficient and robust for estimating variance and covariance components for maternal and paternal effects as well as for nuclear effects. A procedure of adjusted unbiased prediction (AUP) is proposed for predicting random genetic effects in the bio-model. The jack-knife procedure is suggested for estimation of sampling variances of estimated variance and covariance components and of predicted genetic effects. Worked examples are given for estimation of variance and covariance components and for prediction of genetic merits.

Robust estimation for partially linear models with large-dimensional covariates.

PubMed

Zhu, LiPing; Li, RunZe; Cui, HengJian

2013-10-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.

Phobos laser ranging: Numerical Geodesy experiments for Martian system science

NASA Astrophysics Data System (ADS)

Dirkx, D.; Vermeersen, L. L. A.; Noomen, R.; Visser, P. N. A. M.

2014-09-01

Laser ranging is emerging as a technology for use over (inter)planetary distances, having the advantage of high (mm-cm) precision and accuracy and low mass and power consumption. We have performed numerical simulations to assess the science return in terms of geodetic observables of a hypothetical Phobos lander performing active two-way laser ranging with Earth-based stations. We focus our analysis on the estimation of Phobos and Mars gravitational, tidal and rotational parameters. We explicitly include systematic error sources in addition to uncorrelated random observation errors. This is achieved through the use of consider covariance parameters, specifically the ground station position and observation biases. Uncertainties for the consider parameters are set at 5 mm and at 1 mm for the Gaussian uncorrelated observation noise (for an observation integration time of 60 s). We perform the analysis for a mission duration up to 5 years. It is shown that a Phobos Laser Ranging (PLR) can contribute to a better understanding of the Martian system, opening the possibility for improved determination of a variety of physical parameters of Mars and Phobos. The simulations show that the mission concept is especially suited for estimating Mars tidal deformation parameters, estimating degree 2 Love numbers with absolute uncertainties at the 10-2 to 10-4 level after 1 and 4 years, respectively and providing separate estimates for the Martian quality factors at Sun and Phobos-forced frequencies. The estimation of Phobos libration amplitudes and gravity field coefficients provides an estimate of Phobos' relative equatorial and polar moments of inertia with an absolute uncertainty of 10-4 and 10-7, respectively, after 1 year. The observation of Phobos tidal deformation will be able to differentiate between a rubble pile and monolithic interior within 2 years. For all parameters, systematic errors have a much stronger influence (per unit uncertainty) than the uncorrelated Gaussian observation noise. This indicates the need for the inclusion of systematic errors in simulation studies and special attention to the mitigation of these errors in mission and system design.

An ensemble Kalman filter with a high-resolution atmosphere-ocean coupled model for tropical cyclone forecasts

NASA Astrophysics Data System (ADS)

Kunii, M.; Ito, K.; Wada, A.

2015-12-01

An ensemble Kalman filter (EnKF) using a regional mesoscale atmosphere-ocean coupled model was developed to represent the uncertainties of sea surface temperature (SST) in ensemble data assimilation strategies. The system was evaluated through data assimilation cycle experiments over a one-month period from July to August 2014, during which a tropical cyclone as well as severe rainfall events occurred. The results showed that the data assimilation cycle with the coupled model could reproduce SST distributions realistically even without updating SST and salinity during the data assimilation cycle. Therefore, atmospheric variables and radiation applied as a forcing to ocean models can control oceanic variables to some extent in the current data assimilation configuration. However, investigations of the forecast error covariance estimated in EnKF revealed that the correlation between atmospheric and oceanic variables could possibly lead to less flow-dependent error covariance for atmospheric variables owing to the difference in the time scales between atmospheric and oceanic variables. A verification of the analyses showed positive impacts of applying the ocean model to EnKF on precipitation forecasts. The use of EnKF with the coupled model system captured intensity changes of a tropical cyclone better than it did with an uncoupled atmosphere model, even though the impact on the track forecast was negligibly small.

A model of the general ocean circulation determined from a joint solution for the Earth's gravity field

NASA Technical Reports Server (NTRS)

Nerem, R. S.; Tapley, B. D.; Shum, C. K.; Yuan, D. N.

1989-01-01

If the geoid and the satellite position are known accurately, satellite altimetry can be used to determine the geostrophic velocity of the surface ocean currents. The purpose of this investigation is to simultaneously estimate the sea surface topography, zeta, the model for the gravity field, and the satellite orbit. Satellite tracking data from fourteen satellites were used; along with Seasat and Geosat altimeter data as well as surface gravity data for the solution. The estimated model of zeta compares well at long wavelengths with the hydrographic model of zeta. Covariance studies show that the geoid is separable from zeta up to degree 9, at which point geoid error becomes comparable to the signal of zeta.