A pseudo-penalized quasi-likelihood approach to the spatial misalignment problem with non-normal data.

PubMed

Lopiano, Kenneth K; Young, Linda J; Gotway, Carol A

2014-09-01

Spatially referenced datasets arising from multiple sources are routinely combined to assess relationships among various outcomes and covariates. The geographical units associated with the data, such as the geographical coordinates or areal-level administrative units, are often spatially misaligned, that is, observed at different locations or aggregated over different geographical units. As a result, the covariate is often predicted at the locations where the response is observed. The method used to align disparate datasets must be accounted for when subsequently modeling the aligned data. Here we consider the case where kriging is used to align datasets in point-to-point and point-to-areal misalignment problems when the response variable is non-normally distributed. If the relationship is modeled using generalized linear models, the additional uncertainty induced from using the kriging mean as a covariate introduces a Berkson error structure. In this article, we develop a pseudo-penalized quasi-likelihood algorithm to account for the additional uncertainty when estimating regression parameters and associated measures of uncertainty. The method is applied to a point-to-point example assessing the relationship between low-birth weights and PM2.5 levels after the onset of the largest wildfire in Florida history, the Bugaboo scrub fire. A point-to-areal misalignment problem is presented where the relationship between asthma events in Florida's counties and PM2.5 levels after the onset of the fire is assessed. Finally, the method is evaluated using a simulation study. Our results indicate the method performs well in terms of coverage for 95% confidence intervals and naive methods that ignore the additional uncertainty tend to underestimate the variability associated with parameter estimates. The underestimation is most profound in Poisson regression models. © 2014, The International Biometric Society.

Determining the accuracy of maximum likelihood parameter estimates with colored residuals

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.; Klein, Vladislav

1994-01-01

An important part of building high fidelity mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of the accuracy of parameter estimates, the estimates themselves have limited value. In this work, an expression based on theoretical analysis was developed to properly compute parameter accuracy measures for maximum likelihood estimates with colored residuals. This result is important because experience from the analysis of measured data reveals that the residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Simulated data runs were used to show that the parameter accuracy measures computed with this technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for analysis of the output residuals in the frequency domain or heuristically determined multiplication factors. The result is general, although the application studied here is maximum likelihood estimation of aerodynamic model parameters from flight test data.

Analysis of energy-based algorithms for RNA secondary structure prediction

PubMed Central

2012-01-01

Background RNA molecules play critical roles in the cells of organisms, including roles in gene regulation, catalysis, and synthesis of proteins. Since RNA function depends in large part on its folded structures, much effort has been invested in developing accurate methods for prediction of RNA secondary structure from the base sequence. Minimum free energy (MFE) predictions are widely used, based on nearest neighbor thermodynamic parameters of Mathews, Turner et al. or those of Andronescu et al. Some recently proposed alternatives that leverage partition function calculations find the structure with maximum expected accuracy (MEA) or pseudo-expected accuracy (pseudo-MEA) methods. Advances in prediction methods are typically benchmarked using sensitivity, positive predictive value and their harmonic mean, namely F-measure, on datasets of known reference structures. Since such benchmarks document progress in improving accuracy of computational prediction methods, it is important to understand how measures of accuracy vary as a function of the reference datasets and whether advances in algorithms or thermodynamic parameters yield statistically significant improvements. Our work advances such understanding for the MFE and (pseudo-)MEA-based methods, with respect to the latest datasets and energy parameters. Results We present three main findings. First, using the bootstrap percentile method, we show that the average F-measure accuracy of the MFE and (pseudo-)MEA-based algorithms, as measured on our largest datasets with over 2000 RNAs from diverse families, is a reliable estimate (within a 2% range with high confidence) of the accuracy of a population of RNA molecules represented by this set. However, average accuracy on smaller classes of RNAs such as a class of 89 Group I introns used previously in benchmarking algorithm accuracy is not reliable enough to draw meaningful conclusions about the relative merits of the MFE and MEA-based algorithms. Second, on our large datasets, the algorithm with best overall accuracy is a pseudo MEA-based algorithm of Hamada et al. that uses a generalized centroid estimator of base pairs. However, between MFE and other MEA-based methods, there is no clear winner in the sense that the relative accuracy of the MFE versus MEA-based algorithms changes depending on the underlying energy parameters. Third, of the four parameter sets we considered, the best accuracy for the MFE-, MEA-based, and pseudo-MEA-based methods is 0.686, 0.680, and 0.711, respectively (on a scale from 0 to 1 with 1 meaning perfect structure predictions) and is obtained with a thermodynamic parameter set obtained by Andronescu et al. called BL* (named after the Boltzmann likelihood method by which the parameters were derived). Conclusions Large datasets should be used to obtain reliable measures of the accuracy of RNA structure prediction algorithms, and average accuracies on specific classes (such as Group I introns and Transfer RNAs) should be interpreted with caution, considering the relatively small size of currently available datasets for such classes. The accuracy of the MEA-based methods is significantly higher when using the BL* parameter set of Andronescu et al. than when using the parameters of Mathews and Turner, and there is no significant difference between the accuracy of MEA-based methods and MFE when using the BL* parameters. The pseudo-MEA-based method of Hamada et al. with the BL* parameter set significantly outperforms all other MFE and MEA-based algorithms on our large data sets. PMID:22296803

Analysis of energy-based algorithms for RNA secondary structure prediction.

PubMed

Hajiaghayi, Monir; Condon, Anne; Hoos, Holger H

2012-02-01

RNA molecules play critical roles in the cells of organisms, including roles in gene regulation, catalysis, and synthesis of proteins. Since RNA function depends in large part on its folded structures, much effort has been invested in developing accurate methods for prediction of RNA secondary structure from the base sequence. Minimum free energy (MFE) predictions are widely used, based on nearest neighbor thermodynamic parameters of Mathews, Turner et al. or those of Andronescu et al. Some recently proposed alternatives that leverage partition function calculations find the structure with maximum expected accuracy (MEA) or pseudo-expected accuracy (pseudo-MEA) methods. Advances in prediction methods are typically benchmarked using sensitivity, positive predictive value and their harmonic mean, namely F-measure, on datasets of known reference structures. Since such benchmarks document progress in improving accuracy of computational prediction methods, it is important to understand how measures of accuracy vary as a function of the reference datasets and whether advances in algorithms or thermodynamic parameters yield statistically significant improvements. Our work advances such understanding for the MFE and (pseudo-)MEA-based methods, with respect to the latest datasets and energy parameters. We present three main findings. First, using the bootstrap percentile method, we show that the average F-measure accuracy of the MFE and (pseudo-)MEA-based algorithms, as measured on our largest datasets with over 2000 RNAs from diverse families, is a reliable estimate (within a 2% range with high confidence) of the accuracy of a population of RNA molecules represented by this set. However, average accuracy on smaller classes of RNAs such as a class of 89 Group I introns used previously in benchmarking algorithm accuracy is not reliable enough to draw meaningful conclusions about the relative merits of the MFE and MEA-based algorithms. Second, on our large datasets, the algorithm with best overall accuracy is a pseudo MEA-based algorithm of Hamada et al. that uses a generalized centroid estimator of base pairs. However, between MFE and other MEA-based methods, there is no clear winner in the sense that the relative accuracy of the MFE versus MEA-based algorithms changes depending on the underlying energy parameters. Third, of the four parameter sets we considered, the best accuracy for the MFE-, MEA-based, and pseudo-MEA-based methods is 0.686, 0.680, and 0.711, respectively (on a scale from 0 to 1 with 1 meaning perfect structure predictions) and is obtained with a thermodynamic parameter set obtained by Andronescu et al. called BL* (named after the Boltzmann likelihood method by which the parameters were derived). Large datasets should be used to obtain reliable measures of the accuracy of RNA structure prediction algorithms, and average accuracies on specific classes (such as Group I introns and Transfer RNAs) should be interpreted with caution, considering the relatively small size of currently available datasets for such classes. The accuracy of the MEA-based methods is significantly higher when using the BL* parameter set of Andronescu et al. than when using the parameters of Mathews and Turner, and there is no significant difference between the accuracy of MEA-based methods and MFE when using the BL* parameters. The pseudo-MEA-based method of Hamada et al. with the BL* parameter set significantly outperforms all other MFE and MEA-based algorithms on our large data sets.

Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

PubMed

Rhodes, Kirsty M; Turner, Rebecca M; White, Ian R; Jackson, Dan; Spiegelhalter, David J; Higgins, Julian P T

2016-12-20

Many meta-analyses combine results from only a small number of studies, a situation in which the between-study variance is imprecisely estimated when standard methods are applied. Bayesian meta-analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta-analysis using data augmentation, in which we represent an informative conjugate prior for between-study variance by pseudo data and use meta-regression for estimation. To assist in this, we derive predictive inverse-gamma distributions for the between-study variance expected in future meta-analyses. These may serve as priors for heterogeneity in new meta-analyses. In a simulation study, we compare approximate Bayesian methods using meta-regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta-regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta-analysis is described. The proposed method facilitates Bayesian meta-analysis in a way that is accessible to applied researchers. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Applications of non-standard maximum likelihood techniques in energy and resource economics

NASA Astrophysics Data System (ADS)

Moeltner, Klaus

Two important types of non-standard maximum likelihood techniques, Simulated Maximum Likelihood (SML) and Pseudo-Maximum Likelihood (PML), have only recently found consideration in the applied economic literature. The objective of this thesis is to demonstrate how these methods can be successfully employed in the analysis of energy and resource models. Chapter I focuses on SML. It constitutes the first application of this technique in the field of energy economics. The framework is as follows: Surveys on the cost of power outages to commercial and industrial customers usually capture multiple observations on the dependent variable for a given firm. The resulting pooled data set is censored and exhibits cross-sectional heterogeneity. We propose a model that addresses these issues by allowing regression coefficients to vary randomly across respondents and by using the Geweke-Hajivassiliou-Keane simulator and Halton sequences to estimate high-order cumulative distribution terms. This adjustment requires the use of SML in the estimation process. Our framework allows for a more comprehensive analysis of outage costs than existing models, which rely on the assumptions of parameter constancy and cross-sectional homogeneity. Our results strongly reject both of these restrictions. The central topic of the second Chapter is the use of PML, a robust estimation technique, in count data analysis of visitor demand for a system of recreation sites. PML has been popular with researchers in this context, since it guards against many types of mis-specification errors. We demonstrate, however, that estimation results will generally be biased even if derived through PML if the recreation model is based on aggregate, or zonal data. To countervail this problem, we propose a zonal model of recreation that captures some of the underlying heterogeneity of individual visitors by incorporating distributional information on per-capita income into the aggregate demand function. This adjustment eliminates the unrealistic constraint of constant income across zonal residents, and thus reduces the risk of aggregation bias in estimated macro-parameters. The corrected aggregate specification reinstates the applicability of PML. It also increases model efficiency, and allows-for the generation of welfare estimates for population subgroups.

Using a pseudo-dynamic source inversion approach to improve earthquake source imaging

NASA Astrophysics Data System (ADS)

Zhang, Y.; Song, S. G.; Dalguer, L. A.; Clinton, J. F.

2014-12-01

Imaging a high-resolution spatio-temporal slip distribution of an earthquake rupture is a core research goal in seismology. In general we expect to obtain a higher quality source image by improving the observational input data (e.g. using more higher quality near-source stations). However, recent studies show that increasing the surface station density alone does not significantly improve source inversion results (Custodio et al. 2005; Zhang et al. 2014). We introduce correlation structures between the kinematic source parameters: slip, rupture velocity, and peak slip velocity (Song et al. 2009; Song and Dalguer 2013) in the non-linear source inversion. The correlation structures are physical constraints derived from rupture dynamics that effectively regularize the model space and may improve source imaging. We name this approach pseudo-dynamic source inversion. We investigate the effectiveness of this pseudo-dynamic source inversion method by inverting low frequency velocity waveforms from a synthetic dynamic rupture model of a buried vertical strike-slip event (Mw 6.5) in a homogeneous half space. In the inversion, we use a genetic algorithm in a Bayesian framework (Moneli et al. 2008), and a dynamically consistent regularized Yoffe function (Tinti, et al. 2005) was used for a single-window slip velocity function. We search for local rupture velocity directly in the inversion, and calculate the rupture time using a ray-tracing technique. We implement both auto- and cross-correlation of slip, rupture velocity, and peak slip velocity in the prior distribution. Our results suggest that kinematic source model estimates capture the major features of the target dynamic model. The estimated rupture velocity closely matches the target distribution from the dynamic rupture model, and the derived rupture time is smoother than the one we searched directly. By implementing both auto- and cross-correlation of kinematic source parameters, in comparison to traditional smoothing constraints, we are in effect regularizing the model space in a more physics-based manner without loosing resolution of the source image. Further investigation is needed to tune the related parameters of pseudo-dynamic source inversion and relative weighting between the prior and the likelihood function in the Bayesian inversion.

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.…

Approximate Bayesian computation in large-scale structure: constraining the galaxy-halo connection

NASA Astrophysics Data System (ADS)

Hahn, ChangHoon; Vakili, Mohammadjavad; Walsh, Kilian; Hearin, Andrew P.; Hogg, David W.; Campbell, Duncan

2017-08-01

Standard approaches to Bayesian parameter inference in large-scale structure assume a Gaussian functional form (chi-squared form) for the likelihood. This assumption, in detail, cannot be correct. Likelihood free inferences such as approximate Bayesian computation (ABC) relax these restrictions and make inference possible without making any assumptions on the likelihood. Instead ABC relies on a forward generative model of the data and a metric for measuring the distance between the model and data. In this work, we demonstrate that ABC is feasible for LSS parameter inference by using it to constrain parameters of the halo occupation distribution (HOD) model for populating dark matter haloes with galaxies. Using specific implementation of ABC supplemented with population Monte Carlo importance sampling, a generative forward model using HOD and a distance metric based on galaxy number density, two-point correlation function and galaxy group multiplicity function, we constrain the HOD parameters of mock observation generated from selected 'true' HOD parameters. The parameter constraints we obtain from ABC are consistent with the 'true' HOD parameters, demonstrating that ABC can be reliably used for parameter inference in LSS. Furthermore, we compare our ABC constraints to constraints we obtain using a pseudo-likelihood function of Gaussian form with MCMC and find consistent HOD parameter constraints. Ultimately, our results suggest that ABC can and should be applied in parameter inference for LSS analyses.

Two methods for parameter estimation using multiple-trait models and beef cattle field data.

PubMed

Bertrand, J K; Kriese, L A

1990-08-01

Two methods are presented for estimating variances and covariances from beef cattle field data using multiple-trait sire models. Both methods require that the first trait have no missing records and that the contemporary groups for the second trait be subsets of the contemporary groups for the first trait; however, the second trait may have missing records. One method uses pseudo expectations involving quadratics composed of the solutions and the right-hand sides of the mixed model equations. The other method is an extension of Henderson's Simple Method to the multiple trait case. Neither of these methods requires any inversions of large matrices in the computation of the parameters; therefore, both methods can handle very large sets of data. Four simulated data sets were generated to evaluate the methods. In general, both methods estimated genetic correlations and heritabilities that were close to the Restricted Maximum Likelihood estimates and the true data set values, even when selection within contemporary groups was practiced. The estimates of residual correlations by both methods, however, were biased by selection. These two methods can be useful in estimating variances and covariances from multiple-trait models in large populations that have undergone a minimal amount of selection within contemporary groups.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.

PubMed

Ding, A Adam; Wu, Hulin

2014-10-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression

PubMed Central

Ding, A. Adam; Wu, Hulin

2015-01-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method. PMID:26401093

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, Addendum

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1975-01-01

New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence.

Profile-likelihood Confidence Intervals in Item Response Theory Models.

PubMed

Chalmers, R Philip; Pek, Jolynn; Liu, Yang

2017-01-01

Confidence intervals (CIs) are fundamental inferential devices which quantify the sampling variability of parameter estimates. In item response theory, CIs have been primarily obtained from large-sample Wald-type approaches based on standard error estimates, derived from the observed or expected information matrix, after parameters have been estimated via maximum likelihood. An alternative approach to constructing CIs is to quantify sampling variability directly from the likelihood function with a technique known as profile-likelihood confidence intervals (PL CIs). In this article, we introduce PL CIs for item response theory models, compare PL CIs to classical large-sample Wald-type CIs, and demonstrate important distinctions among these CIs. CIs are then constructed for parameters directly estimated in the specified model and for transformed parameters which are often obtained post-estimation. Monte Carlo simulation results suggest that PL CIs perform consistently better than Wald-type CIs for both non-transformed and transformed parameters.

Bootstrap Standard Errors for Maximum Likelihood Ability Estimates When Item Parameters Are Unknown

ERIC Educational Resources Information Center

Patton, Jeffrey M.; Cheng, Ying; Yuan, Ke-Hai; Diao, Qi

2014-01-01

When item parameter estimates are used to estimate the ability parameter in item response models, the standard error (SE) of the ability estimate must be corrected to reflect the error carried over from item calibration. For maximum likelihood (ML) ability estimates, a corrected asymptotic SE is available, but it requires a long test and the…

Estimating Function Approaches for Spatial Point Processes

NASA Astrophysics Data System (ADS)

Deng, Chong

Spatial point pattern data consist of locations of events that are often of interest in biological and ecological studies. Such data are commonly viewed as a realization from a stochastic process called spatial point process. To fit a parametric spatial point process model to such data, likelihood-based methods have been widely studied. However, while maximum likelihood estimation is often too computationally intensive for Cox and cluster processes, pairwise likelihood methods such as composite likelihood, Palm likelihood usually suffer from the loss of information due to the ignorance of correlation among pairs. For many types of correlated data other than spatial point processes, when likelihood-based approaches are not desirable, estimating functions have been widely used for model fitting. In this dissertation, we explore the estimating function approaches for fitting spatial point process models. These approaches, which are based on the asymptotic optimal estimating function theories, can be used to incorporate the correlation among data and yield more efficient estimators. We conducted a series of studies to demonstrate that these estmating function approaches are good alternatives to balance the trade-off between computation complexity and estimating efficiency. First, we propose a new estimating procedure that improves the efficiency of pairwise composite likelihood method in estimating clustering parameters. Our approach combines estimating functions derived from pairwise composite likeli-hood estimation and estimating functions that account for correlations among the pairwise contributions. Our method can be used to fit a variety of parametric spatial point process models and can yield more efficient estimators for the clustering parameters than pairwise composite likelihood estimation. We demonstrate its efficacy through a simulation study and an application to the longleaf pine data. Second, we further explore the quasi-likelihood approach on fitting second-order intensity function of spatial point processes. However, the original second-order quasi-likelihood is barely feasible due to the intense computation and high memory requirement needed to solve a large linear system. Motivated by the existence of geometric regular patterns in the stationary point processes, we find a lower dimension representation of the optimal weight function and propose a reduced second-order quasi-likelihood approach. Through a simulation study, we show that the proposed method not only demonstrates superior performance in fitting the clustering parameter but also merits in the relaxation of the constraint of the tuning parameter, H. Third, we studied the quasi-likelihood type estimating funciton that is optimal in a certain class of first-order estimating functions for estimating the regression parameter in spatial point process models. Then, by using a novel spectral representation, we construct an implementation that is computationally much more efficient and can be applied to more general setup than the original quasi-likelihood method.

On non-parametric maximum likelihood estimation of the bivariate survivor function.

PubMed

Prentice, R L

The likelihood function for the bivariate survivor function F, under independent censorship, is maximized to obtain a non-parametric maximum likelihood estimator &Fcirc;. &Fcirc; may or may not be unique depending on the configuration of singly- and doubly-censored pairs. The likelihood function can be maximized by placing all mass on the grid formed by the uncensored failure times, or half lines beyond the failure time grid, or in the upper right quadrant beyond the grid. By accumulating the mass along lines (or regions) where the likelihood is flat, one obtains a partially maximized likelihood as a function of parameters that can be uniquely estimated. The score equations corresponding to these point mass parameters are derived, using a Lagrange multiplier technique to ensure unit total mass, and a modified Newton procedure is used to calculate the parameter estimates in some limited simulation studies. Some considerations for the further development of non-parametric bivariate survivor function estimators are briefly described.

Evaluation of weighted regression and sample size in developing a taper model for loblolly pine

Treesearch

Kenneth L. Cormier; Robin M. Reich; Raymond L. Czaplewski; William A. Bechtold

1992-01-01

A stem profile model, fit using pseudo-likelihood weighted regression, was used to estimate merchantable volume of loblolly pine (Pinus taeda L.) in the southeast. The weighted regression increased model fit marginally, but did not substantially increase model performance. In all cases, the unweighted regression models performed as well as the...

Recovery of Item Parameters in the Nominal Response Model: A Comparison of Marginal Maximum Likelihood Estimation and Markov Chain Monte Carlo Estimation.

ERIC Educational Resources Information Center

Wollack, James A.; Bolt, Daniel M.; Cohen, Allan S.; Lee, Young-Sun

2002-01-01

Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)

Likelihood-based methods for evaluating principal surrogacy in augmented vaccine trials.

PubMed

Liu, Wei; Zhang, Bo; Zhang, Hui; Zhang, Zhiwei

2017-04-01

There is growing interest in assessing immune biomarkers, which are quick to measure and potentially predictive of long-term efficacy, as surrogate endpoints in randomized, placebo-controlled vaccine trials. This can be done under a principal stratification approach, with principal strata defined using a subject's potential immune responses to vaccine and placebo (the latter may be assumed to be zero). In this context, principal surrogacy refers to the extent to which vaccine efficacy varies across principal strata. Because a placebo recipient's potential immune response to vaccine is unobserved in a standard vaccine trial, augmented vaccine trials have been proposed to produce the information needed to evaluate principal surrogacy. This article reviews existing methods based on an estimated likelihood and a pseudo-score (PS) and proposes two new methods based on a semiparametric likelihood (SL) and a pseudo-likelihood (PL), for analyzing augmented vaccine trials. Unlike the PS method, the SL method does not require a model for missingness, which can be advantageous when immune response data are missing by happenstance. The SL method is shown to be asymptotically efficient, and it performs similarly to the PS and PL methods in simulation experiments. The PL method appears to have a computational advantage over the PS and SL methods.

The Equivalence of Two Methods of Parameter Estimation for the Rasch Model.

ERIC Educational Resources Information Center

Blackwood, Larry G.; Bradley, Edwin L.

1989-01-01

Two methods of estimating parameters in the Rasch model are compared. The equivalence of likelihood estimations from the model of G. J. Mellenbergh and P. Vijn (1981) and from usual unconditional maximum likelihood (UML) estimation is demonstrated. Mellenbergh and Vijn's model is a convenient method of calculating UML estimates. (SLD)

Consistency of Rasch Model Parameter Estimation: A Simulation Study.

ERIC Educational Resources Information Center

van den Wollenberg, Arnold L.; And Others

1988-01-01

The unconditional--simultaneous--maximum likelihood (UML) estimation procedure for the one-parameter logistic model produces biased estimators. The UML method is inconsistent and is not a good alternative to conditional maximum likelihood method, at least with small numbers of items. The minimum Chi-square estimation procedure produces unbiased…

Bias correction in the hierarchical likelihood approach to the analysis of multivariate survival data.

PubMed

Jeon, Jihyoun; Hsu, Li; Gorfine, Malka

2012-07-01

Frailty models are useful for measuring unobserved heterogeneity in risk of failures across clusters, providing cluster-specific risk prediction. In a frailty model, the latent frailties shared by members within a cluster are assumed to act multiplicatively on the hazard function. In order to obtain parameter and frailty variate estimates, we consider the hierarchical likelihood (H-likelihood) approach (Ha, Lee and Song, 2001. Hierarchical-likelihood approach for frailty models. Biometrika 88, 233-243) in which the latent frailties are treated as "parameters" and estimated jointly with other parameters of interest. We find that the H-likelihood estimators perform well when the censoring rate is low, however, they are substantially biased when the censoring rate is moderate to high. In this paper, we propose a simple and easy-to-implement bias correction method for the H-likelihood estimators under a shared frailty model. We also extend the method to a multivariate frailty model, which incorporates complex dependence structure within clusters. We conduct an extensive simulation study and show that the proposed approach performs very well for censoring rates as high as 80%. We also illustrate the method with a breast cancer data set. Since the H-likelihood is the same as the penalized likelihood function, the proposed bias correction method is also applicable to the penalized likelihood estimators.

Cosmological parameter estimation using Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Prasad, J.; Souradeep, T.

2014-03-01

Constraining parameters of a theoretical model from observational data is an important exercise in cosmology. There are many theoretically motivated models, which demand greater number of cosmological parameters than the standard model of cosmology uses, and make the problem of parameter estimation challenging. It is a common practice to employ Bayesian formalism for parameter estimation for which, in general, likelihood surface is probed. For the standard cosmological model with six parameters, likelihood surface is quite smooth and does not have local maxima, and sampling based methods like Markov Chain Monte Carlo (MCMC) method are quite successful. However, when there are a large number of parameters or the likelihood surface is not smooth, other methods may be more effective. In this paper, we have demonstrated application of another method inspired from artificial intelligence, called Particle Swarm Optimization (PSO) for estimating cosmological parameters from Cosmic Microwave Background (CMB) data taken from the WMAP satellite.

Fuzzy multinomial logistic regression analysis: A multi-objective programming approach

NASA Astrophysics Data System (ADS)

Abdalla, Hesham A.; El-Sayed, Amany A.; Hamed, Ramadan

2017-05-01

Parameter estimation for multinomial logistic regression is usually based on maximizing the likelihood function. For large well-balanced datasets, Maximum Likelihood (ML) estimation is a satisfactory approach. Unfortunately, ML can fail completely or at least produce poor results in terms of estimated probabilities and confidence intervals of parameters, specially for small datasets. In this study, a new approach based on fuzzy concepts is proposed to estimate parameters of the multinomial logistic regression. The study assumes that the parameters of multinomial logistic regression are fuzzy. Based on the extension principle stated by Zadeh and Bárdossy's proposition, a multi-objective programming approach is suggested to estimate these fuzzy parameters. A simulation study is used to evaluate the performance of the new approach versus Maximum likelihood (ML) approach. Results show that the new proposed model outperforms ML in cases of small datasets.

IRT Item Parameter Recovery with Marginal Maximum Likelihood Estimation Using Loglinear Smoothing Models

ERIC Educational Resources Information Center

Casabianca, Jodi M.; Lewis, Charles

2015-01-01

Loglinear smoothing (LLS) estimates the latent trait distribution while making fewer assumptions about its form and maintaining parsimony, thus leading to more precise item response theory (IRT) item parameter estimates than standard marginal maximum likelihood (MML). This article provides the expectation-maximization algorithm for MML estimation…

An EM Algorithm for Maximum Likelihood Estimation of Process Factor Analysis Models

ERIC Educational Resources Information Center

Lee, Taehun

2010-01-01

In this dissertation, an Expectation-Maximization (EM) algorithm is developed and implemented to obtain maximum likelihood estimates of the parameters and the associated standard error estimates characterizing temporal flows for the latent variable time series following stationary vector ARMA processes, as well as the parameters defining the…

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

NASA Technical Reports Server (NTRS)

Grove, R. D.; Bowles, R. L.; Mayhew, S. C.

1972-01-01

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Estimating parameter of Rayleigh distribution by using Maximum Likelihood method and Bayes method

NASA Astrophysics Data System (ADS)

Ardianti, Fitri; Sutarman

2018-01-01

In this paper, we use Maximum Likelihood estimation and Bayes method under some risk function to estimate parameter of Rayleigh distribution to know the best method. The prior knowledge which used in Bayes method is Jeffrey’s non-informative prior. Maximum likelihood estimation and Bayes method under precautionary loss function, entropy loss function, loss function-L 1 will be compared. We compare these methods by bias and MSE value using R program. After that, the result will be displayed in tables to facilitate the comparisons.

Computing maximum-likelihood estimates for parameters of the National Descriptive Model of Mercury in Fish

USGS Publications Warehouse

Donato, David I.

2012-01-01

This report presents the mathematical expressions and the computational techniques required to compute maximum-likelihood estimates for the parameters of the National Descriptive Model of Mercury in Fish (NDMMF), a statistical model used to predict the concentration of methylmercury in fish tissue. The expressions and techniques reported here were prepared to support the development of custom software capable of computing NDMMF parameter estimates more quickly and using less computer memory than is currently possible with available general-purpose statistical software. Computation of maximum-likelihood estimates for the NDMMF by numerical solution of a system of simultaneous equations through repeated Newton-Raphson iterations is described. This report explains the derivation of the mathematical expressions required for computational parameter estimation in sufficient detail to facilitate future derivations for any revised versions of the NDMMF that may be developed.

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

NASA Technical Reports Server (NTRS)

Walker, H. F.

1976-01-01

Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate were considered. These equations suggest certain successive approximations iterative procedures for obtaining maximum likelihood estimates. The procedures, which are generalized steepest ascent (deflected gradient) procedures, contain those of Hosmer as a special case.

Recovery of Graded Response Model Parameters: A Comparison of Marginal Maximum Likelihood and Markov Chain Monte Carlo Estimation

ERIC Educational Resources Information Center

Kieftenbeld, Vincent; Natesan, Prathiba

2012-01-01

Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

Modeling of 2D diffusion processes based on microscopy data: parameter estimation and practical identifiability analysis.

PubMed

Hock, Sabrina; Hasenauer, Jan; Theis, Fabian J

2013-01-01

Diffusion is a key component of many biological processes such as chemotaxis, developmental differentiation and tissue morphogenesis. Since recently, the spatial gradients caused by diffusion can be assessed in-vitro and in-vivo using microscopy based imaging techniques. The resulting time-series of two dimensional, high-resolutions images in combination with mechanistic models enable the quantitative analysis of the underlying mechanisms. However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters. We introduce a likelihood function for image-based measurements with log-normal distributed noise. Based upon this likelihood function we formulate the maximum likelihood estimation problem, which is solved using PDE-constrained optimization methods. To assess the uncertainty and practical identifiability of the parameters we introduce profile likelihoods for diffusion processes. As proof of concept, we model certain aspects of the guidance of dendritic cells towards lymphatic vessels, an example for haptotaxis. Using a realistic set of artificial measurement data, we estimate the five kinetic parameters of this model and compute profile likelihoods. Our novel approach for the estimation of model parameters from image data as well as the proposed identifiability analysis approach is widely applicable to diffusion processes. The profile likelihood based method provides more rigorous uncertainty bounds in contrast to local approximation methods.

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.

Precision Parameter Estimation and Machine Learning

NASA Astrophysics Data System (ADS)

Wandelt, Benjamin D.

2008-12-01

I discuss the strategy of ``Acceleration by Parallel Precomputation and Learning'' (AP-PLe) that can vastly accelerate parameter estimation in high-dimensional parameter spaces and costly likelihood functions, using trivially parallel computing to speed up sequential exploration of parameter space. This strategy combines the power of distributed computing with machine learning and Markov-Chain Monte Carlo techniques efficiently to explore a likelihood function, posterior distribution or χ2-surface. This strategy is particularly successful in cases where computing the likelihood is costly and the number of parameters is moderate or large. We apply this technique to two central problems in cosmology: the solution of the cosmological parameter estimation problem with sufficient accuracy for the Planck data using PICo; and the detailed calculation of cosmological helium and hydrogen recombination with RICO. Since the APPLe approach is designed to be able to use massively parallel resources to speed up problems that are inherently serial, we can bring the power of distributed computing to bear on parameter estimation problems. We have demonstrated this with the CosmologyatHome project.

Estimating a Logistic Discrimination Functions When One of the Training Samples Is Subject to Misclassification: A Maximum Likelihood Approach.

PubMed

Nagelkerke, Nico; Fidler, Vaclav

2015-01-01

The problem of discrimination and classification is central to much of epidemiology. Here we consider the estimation of a logistic regression/discrimination function from training samples, when one of the training samples is subject to misclassification or mislabeling, e.g. diseased individuals are incorrectly classified/labeled as healthy controls. We show that this leads to zero-inflated binomial model with a defective logistic regression or discrimination function, whose parameters can be estimated using standard statistical methods such as maximum likelihood. These parameters can be used to estimate the probability of true group membership among those, possibly erroneously, classified as controls. Two examples are analyzed and discussed. A simulation study explores properties of the maximum likelihood parameter estimates and the estimates of the number of mislabeled observations.

Multiple robustness in factorized likelihood models.

PubMed

Molina, J; Rotnitzky, A; Sued, M; Robins, J M

2017-09-01

We consider inference under a nonparametric or semiparametric model with likelihood that factorizes as the product of two or more variation-independent factors. We are interested in a finite-dimensional parameter that depends on only one of the likelihood factors and whose estimation requires the auxiliary estimation of one or several nuisance functions. We investigate general structures conducive to the construction of so-called multiply robust estimating functions, whose computation requires postulating several dimension-reducing models but which have mean zero at the true parameter value provided one of these models is correct.

Cosmological parameters from a re-analysis of the WMAP 7 year low-resolution maps

NASA Astrophysics Data System (ADS)

Finelli, F.; De Rosa, A.; Gruppuso, A.; Paoletti, D.

2013-06-01

Cosmological parameters from Wilkinson Microwave Anisotropy Probe (WMAP) 7 year data are re-analysed by substituting a pixel-based likelihood estimator to the one delivered publicly by the WMAP team. Our pixel-based estimator handles exactly intensity and polarization in a joint manner, allowing us to use low-resolution maps and noise covariance matrices in T, Q, U at the same resolution, which in this work is 3.6°. We describe the features and the performances of the code implementing our pixel-based likelihood estimator. We perform a battery of tests on the application of our pixel-based likelihood routine to WMAP publicly available low-resolution foreground-cleaned products, in combination with the WMAP high-ℓ likelihood, reporting the differences on cosmological parameters evaluated by the full WMAP likelihood public package. The differences are not only due to the treatment of polarization, but also to the marginalization over monopole and dipole uncertainties present in the WMAP pixel likelihood code for temperature. The credible central value for the cosmological parameters change below the 1σ level with respect to the evaluation by the full WMAP 7 year likelihood code, with the largest difference in a shift to smaller values of the scalar spectral index nS.

Parameter estimation in astronomy through application of the likelihood ratio. [satellite data analysis techniques

NASA Technical Reports Server (NTRS)

Cash, W.

1979-01-01

Many problems in the experimental estimation of parameters for models can be solved through use of the likelihood ratio test. Applications of the likelihood ratio, with particular attention to photon counting experiments, are discussed. The procedures presented solve a greater range of problems than those currently in use, yet are no more difficult to apply. The procedures are proved analytically, and examples from current problems in astronomy are discussed.

An alternative method to measure the likelihood of a financial crisis in an emerging market

NASA Astrophysics Data System (ADS)

Özlale, Ümit; Metin-Özcan, Kıvılcım

2007-07-01

This paper utilizes an early warning system in order to measure the likelihood of a financial crisis in an emerging market economy. We introduce a methodology, where we can both obtain a likelihood series and analyze the time-varying effects of several macroeconomic variables on this likelihood. Since the issue is analyzed in a non-linear state space framework, the extended Kalman filter emerges as the optimal estimation algorithm. Taking the Turkish economy as our laboratory, the results indicate that both the derived likelihood measure and the estimated time-varying parameters are meaningful and can successfully explain the path that the Turkish economy had followed between 2000 and 2006. The estimated parameters also suggest that overvalued domestic currency, current account deficit and the increase in the default risk increase the likelihood of having an economic crisis in the economy. Overall, the findings in this paper suggest that the estimation methodology introduced in this paper can also be applied to other emerging market economies as well.

Use of Bayes theorem to correct size-specific sampling bias in growth data.

PubMed

Troynikov, V S

1999-03-01

The bayesian decomposition of posterior distribution was used to develop a likelihood function to correct bias in the estimates of population parameters from data collected randomly with size-specific selectivity. Positive distributions with time as a parameter were used for parametrization of growth data. Numerical illustrations are provided. The alternative applications of the likelihood to estimate selectivity parameters are discussed.

Fracture Characterization in Reactive Fluid-Fractured Rock Systems Using Tracer Transport Data

NASA Astrophysics Data System (ADS)

Mukhopadhyay, S.

2014-12-01

Fractures, whether natural or engineered, exert significant controls over resource exploitation from contemporary energy sources including enhanced geothermal systems and unconventional oil and gas reserves. Consequently, fracture characterization, i.e., estimating the permeability, connectivity, and spacing of the fractures is of critical importance for determining the viability of any energy recovery program. While some progress has recently been made towards estimating these critical fracture parameters, significant uncertainties still remain. A review of tracer technology, which has a long history in fracture characterization, reveals that uncertainties exist in the estimated parameters not only because of paucity of scale-specific data but also because of knowledge gaps in the interpretation methods, particularly in interpretation of tracer data in reactive fluid-rock systems. We have recently demonstrated that the transient tracer evolution signatures in reactive fluid-rock systems are significantly different from those in non-reactive systems (Mukhopadhyay et al., 2013, 2014). For example, the tracer breakthrough curves in reactive fluid-fractured rock systems are expected to exhibit a long pseudo-state condition, during which tracer concentration does not change by any appreciable amount with passage of time. Such a pseudo-steady state condition is not observed in a non-reactive system. In this paper, we show that the presence of this pseudo-steady state condition in tracer breakthrough patterns in reactive fluid-rock systems can have important connotations for fracture characterization. We show that the time of onset of the pseudo-steady state condition and the value of tracer concentration in the pseudo-state condition can be used to reliably estimate fracture spacing and fracture-matrix interface areas.

A simulation study to compare three self-controlled case series approaches: correction for violation of assumption and evaluation of bias.

PubMed

Hua, Wei; Sun, Guoying; Dodd, Caitlin N; Romio, Silvana A; Whitaker, Heather J; Izurieta, Hector S; Black, Steven; Sturkenboom, Miriam C J M; Davis, Robert L; Deceuninck, Genevieve; Andrews, N J

2013-08-01

The assumption that the occurrence of outcome event must not alter subsequent exposure probability is critical for preserving the validity of the self-controlled case series (SCCS) method. This assumption is violated in scenarios in which the event constitutes a contraindication for exposure. In this simulation study, we compared the performance of the standard SCCS approach and two alternative approaches when the event-independent exposure assumption was violated. Using the 2009 H1N1 and seasonal influenza vaccines and Guillain-Barré syndrome as a model, we simulated a scenario in which an individual may encounter multiple unordered exposures and each exposure may be contraindicated by the occurrence of outcome event. The degree of contraindication was varied at 0%, 50%, and 100%. The first alternative approach used only cases occurring after exposure with follow-up time starting from exposure. The second used a pseudo-likelihood method. When the event-independent exposure assumption was satisfied, the standard SCCS approach produced nearly unbiased relative incidence estimates. When this assumption was partially or completely violated, two alternative SCCS approaches could be used. While the post-exposure cases only approach could handle only one exposure, the pseudo-likelihood approach was able to correct bias for both exposures. Violation of the event-independent exposure assumption leads to an overestimation of relative incidence which could be corrected by alternative SCCS approaches. In multiple exposure situations, the pseudo-likelihood approach is optimal; the post-exposure cases only approach is limited in handling a second exposure and may introduce additional bias, thus should be used with caution. Copyright © 2013 John Wiley & Sons, Ltd.

Bias Correction for the Maximum Likelihood Estimate of Ability. Research Report. ETS RR-05-15

ERIC Educational Resources Information Center

Zhang, Jinming

2005-01-01

Lord's bias function and the weighted likelihood estimation method are effective in reducing the bias of the maximum likelihood estimate of an examinee's ability under the assumption that the true item parameters are known. This paper presents simulation studies to determine the effectiveness of these two methods in reducing the bias when the item…

Maximum likelihood estimates, from censored data, for mixed-Weibull distributions

NASA Astrophysics Data System (ADS)

Jiang, Siyuan; Kececioglu, Dimitri

1992-06-01

A new algorithm for estimating the parameters of mixed-Weibull distributions from censored data is presented. The algorithm follows the principle of maximum likelihood estimate (MLE) through the expectation and maximization (EM) algorithm, and it is derived for both postmortem and nonpostmortem time-to-failure data. It is concluded that the concept of the EM algorithm is easy to understand and apply (only elementary statistics and calculus are required). The log-likelihood function cannot decrease after an EM sequence; this important feature was observed in all of the numerical calculations. The MLEs of the nonpostmortem data were obtained successfully for mixed-Weibull distributions with up to 14 parameters in a 5-subpopulation, mixed-Weibull distribution. Numerical examples indicate that some of the log-likelihood functions of the mixed-Weibull distributions have multiple local maxima; therefore, the algorithm should start at several initial guesses of the parameter set.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1975-01-01

A general iterative procedure is given for determining the consistent maximum likelihood estimates of normal distributions. In addition, a local maximum of the log-likelihood function, Newtons's method, a method of scoring, and modifications of these procedures are discussed.

Improving and Evaluating Nested Sampling Algorithm for Marginal Likelihood Estimation

NASA Astrophysics Data System (ADS)

Ye, M.; Zeng, X.; Wu, J.; Wang, D.; Liu, J.

2016-12-01

With the growing impacts of climate change and human activities on the cycle of water resources, an increasing number of researches focus on the quantification of modeling uncertainty. Bayesian model averaging (BMA) provides a popular framework for quantifying conceptual model and parameter uncertainty. The ensemble prediction is generated by combining each plausible model's prediction, and each model is attached with a model weight which is determined by model's prior weight and marginal likelihood. Thus, the estimation of model's marginal likelihood is crucial for reliable and accurate BMA prediction. Nested sampling estimator (NSE) is a new proposed method for marginal likelihood estimation. The process of NSE is accomplished by searching the parameters' space from low likelihood area to high likelihood area gradually, and this evolution is finished iteratively via local sampling procedure. Thus, the efficiency of NSE is dominated by the strength of local sampling procedure. Currently, Metropolis-Hasting (M-H) algorithm is often used for local sampling. However, M-H is not an efficient sampling algorithm for high-dimensional or complicated parameter space. For improving the efficiency of NSE, it could be ideal to incorporate the robust and efficient sampling algorithm - DREAMzs into the local sampling of NSE. The comparison results demonstrated that the improved NSE could improve the efficiency of marginal likelihood estimation significantly. However, both improved and original NSEs suffer from heavy instability. In addition, the heavy computation cost of huge number of model executions is overcome by using an adaptive sparse grid surrogates.

Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions

PubMed Central

Barrett, Harrison H.; Dainty, Christopher; Lara, David

2008-01-01

Maximum-likelihood (ML) estimation in wavefront sensing requires careful attention to all noise sources and all factors that influence the sensor data. We present detailed probability density functions for the output of the image detector in a wavefront sensor, conditional not only on wavefront parameters but also on various nuisance parameters. Practical ways of dealing with nuisance parameters are described, and final expressions for likelihoods and Fisher information matrices are derived. The theory is illustrated by discussing Shack–Hartmann sensors, and computational requirements are discussed. Simulation results show that ML estimation can significantly increase the dynamic range of a Shack–Hartmann sensor with four detectors and that it can reduce the residual wavefront error when compared with traditional methods. PMID:17206255

Maximum likelihood solution for inclination-only data in paleomagnetism

NASA Astrophysics Data System (ADS)

Arason, P.; Levi, S.

2010-08-01

We have developed a new robust maximum likelihood method for estimating the unbiased mean inclination from inclination-only data. In paleomagnetic analysis, the arithmetic mean of inclination-only data is known to introduce a shallowing bias. Several methods have been introduced to estimate the unbiased mean inclination of inclination-only data together with measures of the dispersion. Some inclination-only methods were designed to maximize the likelihood function of the marginal Fisher distribution. However, the exact analytical form of the maximum likelihood function is fairly complicated, and all the methods require various assumptions and approximations that are often inappropriate. For some steep and dispersed data sets, these methods provide estimates that are significantly displaced from the peak of the likelihood function to systematically shallower inclination. The problem locating the maximum of the likelihood function is partly due to difficulties in accurately evaluating the function for all values of interest, because some elements of the likelihood function increase exponentially as precision parameters increase, leading to numerical instabilities. In this study, we succeeded in analytically cancelling exponential elements from the log-likelihood function, and we are now able to calculate its value anywhere in the parameter space and for any inclination-only data set. Furthermore, we can now calculate the partial derivatives of the log-likelihood function with desired accuracy, and locate the maximum likelihood without the assumptions required by previous methods. To assess the reliability and accuracy of our method, we generated large numbers of random Fisher-distributed data sets, for which we calculated mean inclinations and precision parameters. The comparisons show that our new robust Arason-Levi maximum likelihood method is the most reliable, and the mean inclination estimates are the least biased towards shallow values.

Finite mixture model: A maximum likelihood estimation approach on time series data

NASA Astrophysics Data System (ADS)

Yen, Phoong Seuk; Ismail, Mohd Tahir; Hamzah, Firdaus Mohamad

2014-09-01

Recently, statistician emphasized on the fitting of finite mixture model by using maximum likelihood estimation as it provides asymptotic properties. In addition, it shows consistency properties as the sample sizes increases to infinity. This illustrated that maximum likelihood estimation is an unbiased estimator. Moreover, the estimate parameters obtained from the application of maximum likelihood estimation have smallest variance as compared to others statistical method as the sample sizes increases. Thus, maximum likelihood estimation is adopted in this paper to fit the two-component mixture model in order to explore the relationship between rubber price and exchange rate for Malaysia, Thailand, Philippines and Indonesia. Results described that there is a negative effect among rubber price and exchange rate for all selected countries.

Constrained Maximum Likelihood Estimation for Two-Level Mean and Covariance Structure Models

ERIC Educational Resources Information Center

Bentler, Peter M.; Liang, Jiajuan; Tang, Man-Lai; Yuan, Ke-Hai

2011-01-01

Maximum likelihood is commonly used for the estimation of model parameters in the analysis of two-level structural equation models. Constraints on model parameters could be encountered in some situations such as equal factor loadings for different factors. Linear constraints are the most common ones and they are relatively easy to handle in…

An evaluation of percentile and maximum likelihood estimators of weibull paremeters

Treesearch

Stanley J. Zarnoch; Tommy R. Dell

1985-01-01

Two methods of estimating the three-parameter Weibull distribution were evaluated by computer simulation and field data comparison. Maximum likelihood estimators (MLB) with bias correction were calculated with the computer routine FITTER (Bailey 1974); percentile estimators (PCT) were those proposed by Zanakis (1979). The MLB estimators had superior smaller bias and...

Maximum likelihood estimation of signal-to-noise ratio and combiner weight

NASA Technical Reports Server (NTRS)

Kalson, S.; Dolinar, S. J.

1986-01-01

An algorithm for estimating signal to noise ratio and combiner weight parameters for a discrete time series is presented. The algorithm is based upon the joint maximum likelihood estimate of the signal and noise power. The discrete-time series are the sufficient statistics obtained after matched filtering of a biphase modulated signal in additive white Gaussian noise, before maximum likelihood decoding is performed.

Method and system for diagnostics of apparatus

NASA Technical Reports Server (NTRS)

Gorinevsky, Dimitry (Inventor)

2012-01-01

Proposed is a method, implemented in software, for estimating fault state of an apparatus outfitted with sensors. At each execution period the method processes sensor data from the apparatus to obtain a set of parity parameters, which are further used for estimating fault state. The estimation method formulates a convex optimization problem for each fault hypothesis and employs a convex solver to compute fault parameter estimates and fault likelihoods for each fault hypothesis. The highest likelihoods and corresponding parameter estimates are transmitted to a display device or an automated decision and control system. The obtained accurate estimate of fault state can be used to improve safety, performance, or maintenance processes for the apparatus.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1978-01-01

This paper addresses the problem of obtaining numerically maximum-likelihood estimates of the parameters for a mixture of normal distributions. In recent literature, a certain successive-approximations procedure, based on the likelihood equations, was shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, we introduce a general iterative procedure, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. We show that, with probability 1 as the sample size grows large, this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. We also show that the step-size which yields optimal local convergence rates for large samples is determined in a sense by the 'separation' of the component normal densities and is bounded below by a number between 1 and 2.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, 2

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1976-01-01

The problem of obtaining numerically maximum likelihood estimates of the parameters for a mixture of normal distributions is addressed. In recent literature, a certain successive approximations procedure, based on the likelihood equations, is shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, a general iterative procedure is introduced, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. With probability 1 as the sample size grows large, it is shown that this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. The step-size which yields optimal local convergence rates for large samples is determined in a sense by the separation of the component normal densities and is bounded below by a number between 1 and 2.

Likelihood of illegal alcohol sales at professional sport stadiums.

PubMed

Toomey, Traci L; Erickson, Darin J; Lenk, Kathleen M; Kilian, Gunna R

2008-11-01

Several studies have assessed the propensity for illegal alcohol sales at licensed alcohol establishments and community festivals, but no previous studies examined the propensity for these sales at professional sport stadiums. In this study, we assessed the likelihood of alcohol sales to both underage youth and obviously intoxicated patrons at professional sports stadiums across the United States, and assessed the factors related to likelihood of both types of alcohol sales. We conducted pseudo-underage (i.e., persons age 21 or older who appear under 21) and pseudo-intoxicated (i.e., persons feigning intoxication) alcohol purchase attempts at stadiums that house professional hockey, basketball, baseball, and football teams. We conducted the purchase attempts at 16 sport stadiums located in 5 states. We measured 2 outcome variables: pseudo-underage sale (yes, no) and pseudo-intoxicated sale (yes, no), and 3 types of independent variables: (1) seller characteristics, (2) purchase attempt characteristics, and (3) event characteristics. Following univariate and bivariate analyses, we a separate series of logistic generalized mixed regression models for each outcome variable. The overall sales rates to the pseudo-underage and pseudo-intoxicated buyers were 18% and 74%, respectively. In the multivariate logistic analyses, we found that the odds of a sale to a pseudo-underage buyer in the stands was 2.9 as large as the odds of a sale at the concession booths (30% vs. 13%; p = 0.01). The odds of a sale to an obviously intoxicated buyer in the stands was 2.9 as large as the odds of a sale at the concession booths (89% vs. 73%; p = 0.02). Similar to studies assessing illegal alcohol sales at licensed alcohol establishments and community festivals, findings from this study shows the need for interventions specifically focused on illegal alcohol sales at professional sporting events.

Stochastic control system parameter identifiability

NASA Technical Reports Server (NTRS)

Lee, C. H.; Herget, C. J.

1975-01-01

The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters.

Technical Note: Approximate Bayesian parameterization of a process-based tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2014-02-01

Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistical inversion methods require a particular metric, the probability of observing the data given the model parameters, known as the likelihood. For technical and computational reasons, likelihoods for process-based stochastic models are usually based on general assumptions about variability in the observed data, and not on the stochasticity generated by the model. Only in recent years have new methods become available that allow the generation of likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional Markov chain Monte Carlo (MCMC) sampler, performs well in retrieving known parameter values from virtual inventory data generated by the forest model. We analyze the results of the parameter estimation, examine its sensitivity to the choice and aggregation of model outputs and observed data (summary statistics), and demonstrate the application of this method by fitting the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss how this approach differs from approximate Bayesian computation (ABC), another method commonly used to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can be successfully applied to process-based models of high complexity. The methodology is particularly suitable for heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models.

Effect of formal and informal likelihood functions on uncertainty assessment in a single event rainfall-runoff model

NASA Astrophysics Data System (ADS)

Nourali, Mahrouz; Ghahraman, Bijan; Pourreza-Bilondi, Mohsen; Davary, Kamran

2016-09-01

In the present study, DREAM(ZS), Differential Evolution Adaptive Metropolis combined with both formal and informal likelihood functions, is used to investigate uncertainty of parameters of the HEC-HMS model in Tamar watershed, Golestan province, Iran. In order to assess the uncertainty of 24 parameters used in HMS, three flood events were used to calibrate and one flood event was used to validate the posterior distributions. Moreover, performance of seven different likelihood functions (L1-L7) was assessed by means of DREAM(ZS)approach. Four likelihood functions, L1-L4, Nash-Sutcliffe (NS) efficiency, Normalized absolute error (NAE), Index of agreement (IOA), and Chiew-McMahon efficiency (CM), is considered as informal, whereas remaining (L5-L7) is represented in formal category. L5 focuses on the relationship between the traditional least squares fitting and the Bayesian inference, and L6, is a hetereoscedastic maximum likelihood error (HMLE) estimator. Finally, in likelihood function L7, serial dependence of residual errors is accounted using a first-order autoregressive (AR) model of the residuals. According to the results, sensitivities of the parameters strongly depend on the likelihood function, and vary for different likelihood functions. Most of the parameters were better defined by formal likelihood functions L5 and L7 and showed a high sensitivity to model performance. Posterior cumulative distributions corresponding to the informal likelihood functions L1, L2, L3, L4 and the formal likelihood function L6 are approximately the same for most of the sub-basins, and these likelihood functions depict almost a similar effect on sensitivity of parameters. 95% total prediction uncertainty bounds bracketed most of the observed data. Considering all the statistical indicators and criteria of uncertainty assessment, including RMSE, KGE, NS, P-factor and R-factor, results showed that DREAM(ZS) algorithm performed better under formal likelihood functions L5 and L7, but likelihood function L5 may result in biased and unreliable estimation of parameters due to violation of the residualerror assumptions. Thus, likelihood function L7 provides posterior distribution of model parameters credibly and therefore can be employed for further applications.

A novel latent gaussian copula framework for modeling spatial correlation in quantized SAR imagery with applications to ATR

NASA Astrophysics Data System (ADS)

Thelen, Brian T.; Xique, Ismael J.; Burns, Joseph W.; Goley, G. Steven; Nolan, Adam R.; Benson, Jonathan W.

2017-04-01

With all of the new remote sensing modalities available, and with ever increasing capabilities and frequency of collection, there is a desire to fundamentally understand/quantify the information content in the collected image data relative to various exploitation goals, such as detection/classification. A fundamental approach for this is the framework of Bayesian decision theory, but a daunting challenge is to have significantly flexible and accurate multivariate models for the features and/or pixels that capture a wide assortment of distributions and dependen- cies. In addition, data can come in the form of both continuous and discrete representations, where the latter is often generated based on considerations of robustness to imaging conditions and occlusions/degradations. In this paper we propose a novel suite of "latent" models fundamentally based on multivariate Gaussian copula models that can be used for quantized data from SAR imagery. For this Latent Gaussian Copula (LGC) model, we derive an approximate, maximum-likelihood estimation algorithm and demonstrate very reasonable estimation performance even for the larger images with many pixels. However applying these LGC models to large dimen- sions/images within a Bayesian decision/classification theory is infeasible due to the computational/numerical issues in evaluating the true full likelihood, and we propose an alternative class of novel pseudo-likelihoood detection statistics that are computationally feasible. We show in a few simple examples that these statistics have the potential to provide very good and robust detection/classification performance. All of this framework is demonstrated on a simulated SLICY data set, and the results show the importance of modeling the dependencies, and of utilizing the pseudo-likelihood methods.

Aircraft parameter estimation

NASA Technical Reports Server (NTRS)

Iliff, Kenneth W.

1987-01-01

The aircraft parameter estimation problem is used to illustrate the utility of parameter estimation, which applies to many engineering and scientific fields. Maximum likelihood estimation has been used to extract stability and control derivatives from flight data for many years. This paper presents some of the basic concepts of aircraft parameter estimation and briefly surveys the literature in the field. The maximum likelihood estimator is discussed, and the basic concepts of minimization and estimation are examined for a simple simulated aircraft example. The cost functions that are to be minimized during estimation are defined and discussed. Graphic representations of the cost functions are given to illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Some of the major conclusions for the simulated example are also developed for the analysis of flight data from the F-14, highly maneuverable aircraft technology (HiMAT), and space shuttle vehicles.

Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models with Factor Structures

ERIC Educational Resources Information Center

Jeon, Minjeong; Rabe-Hesketh, Sophia

2012-01-01

In this article, the authors suggest a profile-likelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model. An important class of models that can be…

Approximate median regression for complex survey data with skewed response.

PubMed

Fraser, Raphael André; Lipsitz, Stuart R; Sinha, Debajyoti; Fitzmaurice, Garrett M; Pan, Yi

2016-12-01

The ready availability of public-use data from various large national complex surveys has immense potential for the assessment of population characteristics using regression models. Complex surveys can be used to identify risk factors for important diseases such as cancer. Existing statistical methods based on estimating equations and/or utilizing resampling methods are often not valid with survey data due to complex survey design features. That is, stratification, multistage sampling, and weighting. In this article, we accommodate these design features in the analysis of highly skewed response variables arising from large complex surveys. Specifically, we propose a double-transform-both-sides (DTBS)'based estimating equations approach to estimate the median regression parameters of the highly skewed response; the DTBS approach applies the same Box-Cox type transformation twice to both the outcome and regression function. The usual sandwich variance estimate can be used in our approach, whereas a resampling approach would be needed for a pseudo-likelihood based on minimizing absolute deviations (MAD). Furthermore, the approach is relatively robust to the true underlying distribution, and has much smaller mean square error than a MAD approach. The method is motivated by an analysis of laboratory data on urinary iodine (UI) concentration from the National Health and Nutrition Examination Survey. © 2016, The International Biometric Society.

Approximate Median Regression for Complex Survey Data with Skewed Response

PubMed Central

Fraser, Raphael André; Lipsitz, Stuart R.; Sinha, Debajyoti; Fitzmaurice, Garrett M.; Pan, Yi

2016-01-01

Summary The ready availability of public-use data from various large national complex surveys has immense potential for the assessment of population characteristics using regression models. Complex surveys can be used to identify risk factors for important diseases such as cancer. Existing statistical methods based on estimating equations and/or utilizing resampling methods are often not valid with survey data due to complex survey design features. That is, stratification, multistage sampling and weighting. In this paper, we accommodate these design features in the analysis of highly skewed response variables arising from large complex surveys. Specifically, we propose a double-transform-both-sides (DTBS) based estimating equations approach to estimate the median regression parameters of the highly skewed response; the DTBS approach applies the same Box-Cox type transformation twice to both the outcome and regression function. The usual sandwich variance estimate can be used in our approach, whereas a resampling approach would be needed for a pseudo-likelihood based on minimizing absolute deviations (MAD). Furthermore, the approach is relatively robust to the true underlying distribution, and has much smaller mean square error than a MAD approach. The method is motivated by an analysis of laboratory data on urinary iodine (UI) concentration from the National Health and Nutrition Examination Survey. PMID:27062562

Estimating population genetic parameters and comparing model goodness-of-fit using DNA sequences with error

PubMed Central

Liu, Xiaoming; Fu, Yun-Xin; Maxwell, Taylor J.; Boerwinkle, Eric

2010-01-01

It is known that sequencing error can bias estimation of evolutionary or population genetic parameters. This problem is more prominent in deep resequencing studies because of their large sample size n, and a higher probability of error at each nucleotide site. We propose a new method based on the composite likelihood of the observed SNP configurations to infer population mutation rate θ = 4Neμ, population exponential growth rate R, and error rate ɛ, simultaneously. Using simulation, we show the combined effects of the parameters, θ, n, ɛ, and R on the accuracy of parameter estimation. We compared our maximum composite likelihood estimator (MCLE) of θ with other θ estimators that take into account the error. The results show the MCLE performs well when the sample size is large or the error rate is high. Using parametric bootstrap, composite likelihood can also be used as a statistic for testing the model goodness-of-fit of the observed DNA sequences. The MCLE method is applied to sequence data on the ANGPTL4 gene in 1832 African American and 1045 European American individuals. PMID:19952140

Estimation of parameters of dose volume models and their confidence limits

NASA Astrophysics Data System (ADS)

van Luijk, P.; Delvigne, T. C.; Schilstra, C.; Schippers, J. M.

2003-07-01

Predictions of the normal-tissue complication probability (NTCP) for the ranking of treatment plans are based on fits of dose-volume models to clinical and/or experimental data. In the literature several different fit methods are used. In this work frequently used methods and techniques to fit NTCP models to dose response data for establishing dose-volume effects, are discussed. The techniques are tested for their usability with dose-volume data and NTCP models. Different methods to estimate the confidence intervals of the model parameters are part of this study. From a critical-volume (CV) model with biologically realistic parameters a primary dataset was generated, serving as the reference for this study and describable by the NTCP model. The CV model was fitted to this dataset. From the resulting parameters and the CV model, 1000 secondary datasets were generated by Monte Carlo simulation. All secondary datasets were fitted to obtain 1000 parameter sets of the CV model. Thus the 'real' spread in fit results due to statistical spreading in the data is obtained and has been compared with estimates of the confidence intervals obtained by different methods applied to the primary dataset. The confidence limits of the parameters of one dataset were estimated using the methods, employing the covariance matrix, the jackknife method and directly from the likelihood landscape. These results were compared with the spread of the parameters, obtained from the secondary parameter sets. For the estimation of confidence intervals on NTCP predictions, three methods were tested. Firstly, propagation of errors using the covariance matrix was used. Secondly, the meaning of the width of a bundle of curves that resulted from parameters that were within the one standard deviation region in the likelihood space was investigated. Thirdly, many parameter sets and their likelihood were used to create a likelihood-weighted probability distribution of the NTCP. It is concluded that for the type of dose response data used here, only a full likelihood analysis will produce reliable results. The often-used approximations, such as the usage of the covariance matrix, produce inconsistent confidence limits on both the parameter sets and the resulting NTCP values.

Development of advanced techniques for rotorcraft state estimation and parameter identification

NASA Technical Reports Server (NTRS)

Hall, W. E., Jr.; Bohn, J. G.; Vincent, J. H.

1980-01-01

An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases.

Can obviously intoxicated patrons still easily buy alcohol at on-premise establishments?

PubMed Central

Toomey, Traci L.; Lenk, Kathleen M.; Nederhoff, Dawn M.; Nelson, Toben F.; Ecklund, Alexandra M.; Horvath, Keith J.; Erickson, Darin J.

2015-01-01

Background Excessive alcohol consumption at licensed alcohol establishments (i.e., bars and restaurants) has been directly linked to alcohol-related problems such as traffic crashes and violence. Historically, alcohol establishments have had a high likelihood of selling alcohol to obviously intoxicated patrons (also referred to as “overservice”) despite laws prohibiting these sales. Given the risks associated with overservice and the need for up-to-date data, it is critical that we monitor the likelihood of sales to obviously intoxicated patrons. Methods To assess the current likelihood of a licensed alcohol establishment selling alcohol to an obviously intoxicated patron, we conducted pseudo-intoxicated purchase attempts (i.e., actors attempt to purchase alcohol while acting out obvious signs of intoxication) at 340 establishments in one Midwestern metropolitan area. We also measured characteristics of the establishments, the pseudo-intoxicated patrons, the servers, the managers, and the neighborhoods to assess whether these characteristics were associated with likelihood of sales of obviously intoxicated patrons. We assessed these associations with bivariate and multivariate regression models. Results Pseudo-intoxicated buyers were able to purchase alcohol at 82% of the establishments. In the fully adjusted multivariate regression model, only one of the characteristics we assessed was significantly associated with likelihood of selling to intoxicated patrons–establishments owned by a corporate entity had 3.6 greater odds of selling alcohol to a pseudo-intoxicated buyer compared to independently-owned establishments. Discussion Given the risks associated with overservice of alcohol, more resources should be devoted first to identify effective interventions for decreasing overservice of alcohol and then to educate practitioners who are working in their communities to address this public health problem. PMID:26891204

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis: A Comparison of Maximum Likelihood and Bayesian Estimations.

PubMed

Can, Seda; van de Schoot, Rens; Hox, Joop

2015-06-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions.

Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.

The Inverse Problem for Confined Aquifer Flow: Identification and Estimation With Extensions

NASA Astrophysics Data System (ADS)

Loaiciga, Hugo A.; MariñO, Miguel A.

1987-01-01

The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed-parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two-stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three-stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two-stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous-time solution to the flow equation, coping with noise-corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study.

Estimation Methods for One-Parameter Testlet Models

ERIC Educational Resources Information Center

Jiao, Hong; Wang, Shudong; He, Wei

2013-01-01

This study demonstrated the equivalence between the Rasch testlet model and the three-level one-parameter testlet model and explored the Markov Chain Monte Carlo (MCMC) method for model parameter estimation in WINBUGS. The estimation accuracy from the MCMC method was compared with those from the marginalized maximum likelihood estimation (MMLE)…

Maximum-Likelihood Estimation for Frequency-Modulated Continuous-Wave Laser Ranging Using Photon-Counting Detectors

DTIC Science & Technology

2013-01-01

are calculated from coherently -detected fields, e.g., coherent Doppler lidar . Our CRB results reveal that the best-case mean-square error scales as 1...1088 (2001). 7. K. Asaka, Y. Hirano, K. Tatsumi, K. Kasahara, and T. Tajime, “A pseudo-random frequency modulation continuous wave coherent lidar using...multiple returns,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 2170–2180 (2007). 11. T. J. Karr, “Atmospheric phase error in coherent laser radar

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics.

PubMed

Arampatzis, Georgios; Katsoulakis, Markos A; Rey-Bellet, Luc

2016-03-14

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

NASA Astrophysics Data System (ADS)

Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc

2016-03-01

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

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

Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc

2016-03-14

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systemsmore » with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.« less

Maximum likelihood method for estimating airplane stability and control parameters from flight data in frequency domain

NASA Technical Reports Server (NTRS)

Klein, V.

1980-01-01

A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.

Characterization, parameter estimation, and aircraft response statistics of atmospheric turbulence

NASA Technical Reports Server (NTRS)

Mark, W. D.

1981-01-01

A nonGaussian three component model of atmospheric turbulence is postulated that accounts for readily observable features of turbulence velocity records, their autocorrelation functions, and their spectra. Methods for computing probability density functions and mean exceedance rates of a generic aircraft response variable are developed using nonGaussian turbulence characterizations readily extracted from velocity recordings. A maximum likelihood method is developed for optimal estimation of the integral scale and intensity of records possessing von Karman transverse of longitudinal spectra. Formulas for the variances of such parameter estimates are developed. The maximum likelihood and least-square approaches are combined to yield a method for estimating the autocorrelation function parameters of a two component model for turbulence.

GRID-BASED EXPLORATION OF COSMOLOGICAL PARAMETER SPACE WITH SNAKE

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

Mikkelsen, K.; Næss, S. K.; Eriksen, H. K., E-mail: kristin.mikkelsen@astro.uio.no

2013-11-10

We present a fully parallelized grid-based parameter estimation algorithm for investigating multidimensional likelihoods called Snake, and apply it to cosmological parameter estimation. The basic idea is to map out the likelihood grid-cell by grid-cell according to decreasing likelihood, and stop when a certain threshold has been reached. This approach improves vastly on the 'curse of dimensionality' problem plaguing standard grid-based parameter estimation simply by disregarding grid cells with negligible likelihood. The main advantages of this method compared to standard Metropolis-Hastings Markov Chain Monte Carlo methods include (1) trivial extraction of arbitrary conditional distributions; (2) direct access to Bayesian evidences; (3)more » better sampling of the tails of the distribution; and (4) nearly perfect parallelization scaling. The main disadvantage is, as in the case of brute-force grid-based evaluation, a dependency on the number of parameters, N{sub par}. One of the main goals of the present paper is to determine how large N{sub par} can be, while still maintaining reasonable computational efficiency; we find that N{sub par} = 12 is well within the capabilities of the method. The performance of the code is tested by comparing cosmological parameters estimated using Snake and the WMAP-7 data with those obtained using CosmoMC, the current standard code in the field. We find fully consistent results, with similar computational expenses, but shorter wall time due to the perfect parallelization scheme.« less

Linear and non-linear regression analysis for the sorption kinetics of methylene blue onto activated carbon.

PubMed

Kumar, K Vasanth

2006-10-11

Batch kinetic experiments were carried out for the sorption of methylene blue onto activated carbon. The experimental kinetics were fitted to the pseudo first-order and pseudo second-order kinetics by linear and a non-linear method. The five different types of Ho pseudo second-order expression have been discussed. A comparison of linear least-squares method and a trial and error non-linear method of estimating the pseudo second-order rate kinetic parameters were examined. The sorption process was found to follow a both pseudo first-order kinetic and pseudo second-order kinetic model. Present investigation showed that it is inappropriate to use a type 1 and type pseudo second-order expressions as proposed by Ho and Blanachard et al. respectively for predicting the kinetic rate constants and the initial sorption rate for the studied system. Three correct possible alternate linear expressions (type 2 to type 4) to better predict the initial sorption rate and kinetic rate constants for the studied system (methylene blue/activated carbon) was proposed. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Non-linear regression method was found to be the more appropriate method to determine the rate kinetic parameters.

PERIODIC AUTOREGRESSIVE-MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES.

USGS Publications Warehouse

Vecchia, A.V.

1985-01-01

Results involving correlation properties and parameter estimation for autogressive-moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum-likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time series.

Comparing Three Estimation Methods for the Three-Parameter Logistic IRT Model

ERIC Educational Resources Information Center

Lamsal, Sunil

2015-01-01

Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each…

Estimation of Dynamic Discrete Choice Models by Maximum Likelihood and the Simulated Method of Moments

PubMed Central

Eisenhauer, Philipp; Heckman, James J.; Mosso, Stefano

2015-01-01

We compare the performance of maximum likelihood (ML) and simulated method of moments (SMM) estimation for dynamic discrete choice models. We construct and estimate a simplified dynamic structural model of education that captures some basic features of educational choices in the United States in the 1980s and early 1990s. We use estimates from our model to simulate a synthetic dataset and assess the ability of ML and SMM to recover the model parameters on this sample. We investigate the performance of alternative tuning parameters for SMM. PMID:26494926

Maximum likelihood estimation of signal detection model parameters for the assessment of two-stage diagnostic strategies.

PubMed

Lirio, R B; Dondériz, I C; Pérez Abalo, M C

1992-08-01

The methodology of Receiver Operating Characteristic curves based on the signal detection model is extended to evaluate the accuracy of two-stage diagnostic strategies. A computer program is developed for the maximum likelihood estimation of parameters that characterize the sensitivity and specificity of two-stage classifiers according to this extended methodology. Its use is briefly illustrated with data collected in a two-stage screening for auditory defects.

Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Ben Abdessalem, Anis; Dervilis, Nikolaos; Wagg, David; Worden, Keith

2018-01-01

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours.

Program for Weibull Analysis of Fatigue Data

NASA Technical Reports Server (NTRS)

Krantz, Timothy L.

2005-01-01

A Fortran computer program has been written for performing statistical analyses of fatigue-test data that are assumed to be adequately represented by a two-parameter Weibull distribution. This program calculates the following: (1) Maximum-likelihood estimates of the Weibull distribution; (2) Data for contour plots of relative likelihood for two parameters; (3) Data for contour plots of joint confidence regions; (4) Data for the profile likelihood of the Weibull-distribution parameters; (5) Data for the profile likelihood of any percentile of the distribution; and (6) Likelihood-based confidence intervals for parameters and/or percentiles of the distribution. The program can account for tests that are suspended without failure (the statistical term for such suspension of tests is "censoring"). The analytical approach followed in this program for the software is valid for type-I censoring, which is the removal of unfailed units at pre-specified times. Confidence regions and intervals are calculated by use of the likelihood-ratio method.

A black box optimization approach to parameter estimation in a model for long/short term variations dynamics of commodity prices

NASA Astrophysics Data System (ADS)

De Santis, Alberto; Dellepiane, Umberto; Lucidi, Stefano

2012-11-01

In this paper we investigate the estimation problem for a model of the commodity prices. This model is a stochastic state space dynamical model and the problem unknowns are the state variables and the system parameters. Data are represented by the commodity spot prices, very seldom time series of Futures contracts are available for free. Both the system joint likelihood function (state variables and parameters) and the system marginal likelihood (the state variables are eliminated) function are addressed.

Pseudo-radar algorithms with two extremely wet months of disdrometer data in the Paris area

NASA Astrophysics Data System (ADS)

Gires, A.; Tchiguirinskaia, I.; Schertzer, D.

2018-05-01

Disdrometer data collected during the two extremely wet months of May and June 2016 at the Ecole des Ponts ParisTech are used to get insights on radar algorithms. The rain rate and pseudo-radar quantities (horizontal and vertical reflectivity, specific differential phase shift) are all estimated over several durations with the help of drop size distributions (DSD) collected at 30 s time steps. The pseudo-radar quantities are defined with simplifying hypotheses, in particular on the DSD homogeneity. First it appears that the parameters of the standard radar relations Zh - R, R - Kdp and R - Zh - Zdr for these pseudo-radar quantities exhibit strong variability between events and even within an event. Second an innovative methodology that relies on checking the ability of a given algorithm to reproduce the good scale invariant multifractal behaviour (on scales 30 s - few h) observed on rainfall time series is implemented. In this framework, the classical hybrid model (Zh - R for low rain rates and R - Kdp for great ones) performs best, as well as the local estimates of the radar relations' parameters. However, we emphasise that due to the hypotheses on which they rely these observations cannot be straightforwardly extended to real radar quantities.

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

NASA Technical Reports Server (NTRS)

Walker, H. F.

1976-01-01

Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate are considered. These equations, suggest certain successive-approximations iterative procedures for obtaining maximum-likelihood estimates. These are generalized steepest ascent (deflected gradient) procedures. It is shown that, with probability 1 as N sub 0 approaches infinity (regardless of the relative sizes of N sub 0 and N sub 1, i=1,...,m), these procedures converge locally to the strongly consistent maximum-likelihood estimates whenever the step size is between 0 and 2. Furthermore, the value of the step size which yields optimal local convergence rates is bounded from below by a number which always lies between 1 and 2.

Signal detection theory and vestibular perception: III. Estimating unbiased fit parameters for psychometric functions.

PubMed

Chaudhuri, Shomesh E; Merfeld, Daniel M

2013-03-01

Psychophysics generally relies on estimating a subject's ability to perform a specific task as a function of an observed stimulus. For threshold studies, the fitted functions are called psychometric functions. While fitting psychometric functions to data acquired using adaptive sampling procedures (e.g., "staircase" procedures), investigators have encountered a bias in the spread ("slope" or "threshold") parameter that has been attributed to the serial dependency of the adaptive data. Using simulations, we confirm this bias for cumulative Gaussian parametric maximum likelihood fits on data collected via adaptive sampling procedures, and then present a bias-reduced maximum likelihood fit that substantially reduces the bias without reducing the precision of the spread parameter estimate and without reducing the accuracy or precision of the other fit parameters. As a separate topic, we explain how to implement this bias reduction technique using generalized linear model fits as well as other numeric maximum likelihood techniques such as the Nelder-Mead simplex. We then provide a comparison of the iterative bootstrap and observed information matrix techniques for estimating parameter fit variance from adaptive sampling procedure data sets. The iterative bootstrap technique is shown to be slightly more accurate; however, the observed information technique executes in a small fraction (0.005 %) of the time required by the iterative bootstrap technique, which is an advantage when a real-time estimate of parameter fit variance is required.

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data

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

West, R. Derek; Gunther, Jacob H.; Moon, Todd K.

In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts tomore » a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.« less

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data

DOE PAGES

West, R. Derek; Gunther, Jacob H.; Moon, Todd K.

2016-12-01

In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts tomore » a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.« less

Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin; Feeney, Stephen

2018-07-01

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data space suffers from the curse of dimensionality and requires compression of the data to a small number of summary statistics to be tractable. In this paper, we use massive asymptotically optimal data compression to reduce the dimensionality of the data space to just one number per parameter, providing a natural and optimal framework for summary statistic choice for likelihood-free inference. Secondly, we present the first cosmological application of Density Estimation Likelihood-Free Inference (DELFI), which learns a parametrized model for joint distribution of data and parameters, yielding both the parameter posterior and the model evidence. This approach is conceptually simple, requires less tuning than traditional Approximate Bayesian Computation approaches to likelihood-free inference and can give high-fidelity posteriors from orders of magnitude fewer forward simulations. As an additional bonus, it enables parameter inference and Bayesian model comparison simultaneously. We demonstrate DELFI with massive data compression on an analysis of the joint light-curve analysis supernova data, as a simple validation case study. We show that high-fidelity posterior inference is possible for full-scale cosmological data analyses with as few as ˜104 simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological data sets.

Maximum-likelihood estimation of parameterized wavefronts from multifocal data

PubMed Central

Sakamoto, Julia A.; Barrett, Harrison H.

2012-01-01

A method for determining the pupil phase distribution of an optical system is demonstrated. Coefficients in a wavefront expansion were estimated using likelihood methods, where the data consisted of multiple irradiance patterns near focus. Proof-of-principle results were obtained in both simulation and experiment. Large-aberration wavefronts were handled in the numerical study. Experimentally, we discuss the handling of nuisance parameters. Fisher information matrices, Cramér-Rao bounds, and likelihood surfaces are examined. ML estimates were obtained by simulated annealing to deal with numerous local extrema in the likelihood function. Rapid processing techniques were employed to reduce the computational time. PMID:22772282

Maintained Individual Data Distributed Likelihood Estimation (MIDDLE)

PubMed Central

Boker, Steven M.; Brick, Timothy R.; Pritikin, Joshua N.; Wang, Yang; von Oertzen, Timo; Brown, Donald; Lach, John; Estabrook, Ryne; Hunter, Michael D.; Maes, Hermine H.; Neale, Michael C.

2015-01-01

Maintained Individual Data Distributed Likelihood Estimation (MIDDLE) is a novel paradigm for research in the behavioral, social, and health sciences. The MIDDLE approach is based on the seemingly-impossible idea that data can be privately maintained by participants and never revealed to researchers, while still enabling statistical models to be fit and scientific hypotheses tested. MIDDLE rests on the assumption that participant data should belong to, be controlled by, and remain in the possession of the participants themselves. Distributed likelihood estimation refers to fitting statistical models by sending an objective function and vector of parameters to each participants’ personal device (e.g., smartphone, tablet, computer), where the likelihood of that individual’s data is calculated locally. Only the likelihood value is returned to the central optimizer. The optimizer aggregates likelihood values from responding participants and chooses new vectors of parameters until the model converges. A MIDDLE study provides significantly greater privacy for participants, automatic management of opt-in and opt-out consent, lower cost for the researcher and funding institute, and faster determination of results. Furthermore, if a participant opts into several studies simultaneously and opts into data sharing, these studies automatically have access to individual-level longitudinal data linked across all studies. PMID:26717128

Gaussian copula as a likelihood function for environmental models

NASA Astrophysics Data System (ADS)

Wani, O.; Espadas, G.; Cecinati, F.; Rieckermann, J.

2017-12-01

Parameter estimation of environmental models always comes with uncertainty. To formally quantify this parametric uncertainty, a likelihood function needs to be formulated, which is defined as the probability of observations given fixed values of the parameter set. A likelihood function allows us to infer parameter values from observations using Bayes' theorem. The challenge is to formulate a likelihood function that reliably describes the error generating processes which lead to the observed monitoring data, such as rainfall and runoff. If the likelihood function is not representative of the error statistics, the parameter inference will give biased parameter values. Several uncertainty estimation methods that are currently being used employ Gaussian processes as a likelihood function, because of their favourable analytical properties. Box-Cox transformation is suggested to deal with non-symmetric and heteroscedastic errors e.g. for flow data which are typically more uncertain in high flows than in periods with low flows. Problem with transformations is that the results are conditional on hyper-parameters, for which it is difficult to formulate the analyst's belief a priori. In an attempt to address this problem, in this research work we suggest learning the nature of the error distribution from the errors made by the model in the "past" forecasts. We use a Gaussian copula to generate semiparametric error distributions . 1) We show that this copula can be then used as a likelihood function to infer parameters, breaking away from the practice of using multivariate normal distributions. Based on the results from a didactical example of predicting rainfall runoff, 2) we demonstrate that the copula captures the predictive uncertainty of the model. 3) Finally, we find that the properties of autocorrelation and heteroscedasticity of errors are captured well by the copula, eliminating the need to use transforms. In summary, our findings suggest that copulas are an interesting departure from the usage of fully parametric distributions as likelihood functions - and they could help us to better capture the statistical properties of errors and make more reliable predictions.

The Maximum Likelihood Solution for Inclination-only Data

NASA Astrophysics Data System (ADS)

Arason, P.; Levi, S.

2006-12-01

The arithmetic means of inclination-only data are known to introduce a shallowing bias. Several methods have been proposed to estimate unbiased means of the inclination along with measures of the precision. Most of the inclination-only methods were designed to maximize the likelihood function of the marginal Fisher distribution. However, the exact analytical form of the maximum likelihood function is fairly complicated, and all these methods require various assumptions and approximations that are inappropriate for many data sets. For some steep and dispersed data sets, the estimates provided by these methods are significantly displaced from the peak of the likelihood function to systematically shallower inclinations. The problem in locating the maximum of the likelihood function is partly due to difficulties in accurately evaluating the function for all values of interest. This is because some elements of the log-likelihood function increase exponentially as precision parameters increase, leading to numerical instabilities. In this study we succeeded in analytically cancelling exponential elements from the likelihood function, and we are now able to calculate its value for any location in the parameter space and for any inclination-only data set, with full accuracy. Furtermore, we can now calculate the partial derivatives of the likelihood function with desired accuracy. Locating the maximum likelihood without the assumptions required by previous methods is now straight forward. The information to separate the mean inclination from the precision parameter will be lost for very steep and dispersed data sets. It is worth noting that the likelihood function always has a maximum value. However, for some dispersed and steep data sets with few samples, the likelihood function takes its highest value on the boundary of the parameter space, i.e. at inclinations of +/- 90 degrees, but with relatively well defined dispersion. Our simulations indicate that this occurs quite frequently for certain data sets, and relatively small perturbations in the data will drive the maxima to the boundary. We interpret this to indicate that, for such data sets, the information needed to separate the mean inclination and the precision parameter is permanently lost. To assess the reliability and accuracy of our method we generated large number of random Fisher-distributed data sets and used seven methods to estimate the mean inclination and precision paramenter. These comparisons are described by Levi and Arason at the 2006 AGU Fall meeting. The results of the various methods is very favourable to our new robust maximum likelihood method, which, on average, is the most reliable, and the mean inclination estimates are the least biased toward shallow values. Further information on our inclination-only analysis can be obtained from: http://www.vedur.is/~arason/paleomag

Likelihood-based confidence intervals for estimating floods with given return periods

NASA Astrophysics Data System (ADS)

Martins, Eduardo Sávio P. R.; Clarke, Robin T.

1993-06-01

This paper discusses aspects of the calculation of likelihood-based confidence intervals for T-year floods, with particular reference to (1) the two-parameter gamma distribution; (2) the Gumbel distribution; (3) the two-parameter log-normal distribution, and other distributions related to the normal by Box-Cox transformations. Calculation of the confidence limits is straightforward using the Nelder-Mead algorithm with a constraint incorporated, although care is necessary to ensure convergence either of the Nelder-Mead algorithm, or of the Newton-Raphson calculation of maximum-likelihood estimates. Methods are illustrated using records from 18 gauging stations in the basin of the River Itajai-Acu, State of Santa Catarina, southern Brazil. A small and restricted simulation compared likelihood-based confidence limits with those given by use of the central limit theorem; for the same confidence probability, the confidence limits of the simulation were wider than those of the central limit theorem, which failed more frequently to contain the true quantile being estimated. The paper discusses possible applications of likelihood-based confidence intervals in other areas of hydrological analysis.

Maximum likelihood estimation for life distributions with competing failure modes

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1979-01-01

Systems which are placed on test at time zero, function for a period and die at some random time were studied. Failure may be due to one of several causes or modes. The parameters of the life distribution may depend upon the levels of various stress variables the item is subject to. Maximum likelihood estimation methods are discussed. Specific methods are reported for the smallest extreme-value distributions of life. Monte-Carlo results indicate the methods to be promising. Under appropriate conditions, the location parameters are nearly unbiased, the scale parameter is slight biased, and the asymptotic covariances are rapidly approached.

SMURC: High-Dimension Small-Sample Multivariate Regression With Covariance Estimation.

PubMed

Bayar, Belhassen; Bouaynaya, Nidhal; Shterenberg, Roman

2017-03-01

We consider a high-dimension low sample-size multivariate regression problem that accounts for correlation of the response variables. The system is underdetermined as there are more parameters than samples. We show that the maximum likelihood approach with covariance estimation is senseless because the likelihood diverges. We subsequently propose a normalization of the likelihood function that guarantees convergence. We call this method small-sample multivariate regression with covariance (SMURC) estimation. We derive an optimization problem and its convex approximation to compute SMURC. Simulation results show that the proposed algorithm outperforms the regularized likelihood estimator with known covariance matrix and the sparse conditional Gaussian graphical model. We also apply SMURC to the inference of the wing-muscle gene network of the Drosophila melanogaster (fruit fly).

Bayesian model selection: Evidence estimation based on DREAM simulation and bridge sampling

NASA Astrophysics Data System (ADS)

Volpi, Elena; Schoups, Gerrit; Firmani, Giovanni; Vrugt, Jasper A.

2017-04-01

Bayesian inference has found widespread application in Earth and Environmental Systems Modeling, providing an effective tool for prediction, data assimilation, parameter estimation, uncertainty analysis and hypothesis testing. Under multiple competing hypotheses, the Bayesian approach also provides an attractive alternative to traditional information criteria (e.g. AIC, BIC) for model selection. The key variable for Bayesian model selection is the evidence (or marginal likelihood) that is the normalizing constant in the denominator of Bayes theorem; while it is fundamental for model selection, the evidence is not required for Bayesian inference. It is computed for each hypothesis (model) by averaging the likelihood function over the prior parameter distribution, rather than maximizing it as by information criteria; the larger a model evidence the more support it receives among a collection of hypothesis as the simulated values assign relatively high probability density to the observed data. Hence, the evidence naturally acts as an Occam's razor, preferring simpler and more constrained models against the selection of over-fitted ones by information criteria that incorporate only the likelihood maximum. Since it is not particularly easy to estimate the evidence in practice, Bayesian model selection via the marginal likelihood has not yet found mainstream use. We illustrate here the properties of a new estimator of the Bayesian model evidence, which provides robust and unbiased estimates of the marginal likelihood; the method is coined Gaussian Mixture Importance Sampling (GMIS). GMIS uses multidimensional numerical integration of the posterior parameter distribution via bridge sampling (a generalization of importance sampling) of a mixture distribution fitted to samples of the posterior distribution derived from the DREAM algorithm (Vrugt et al., 2008; 2009). Some illustrative examples are presented to show the robustness and superiority of the GMIS estimator with respect to other commonly used approaches in the literature.

An architecture for efficient gravitational wave parameter estimation with multimodal linear surrogate models

NASA Astrophysics Data System (ADS)

O'Shaughnessy, Richard; Blackman, Jonathan; Field, Scott E.

2017-07-01

The recent direct observation of gravitational waves has further emphasized the desire for fast, low-cost, and accurate methods to infer the parameters of gravitational wave sources. Due to expense in waveform generation and data handling, the cost of evaluating the likelihood function limits the computational performance of these calculations. Building on recently developed surrogate models and a novel parameter estimation pipeline, we show how to quickly generate the likelihood function as an analytic, closed-form expression. Using a straightforward variant of a production-scale parameter estimation code, we demonstrate our method using surrogate models of effective-one-body and numerical relativity waveforms. Our study is the first time these models have been used for parameter estimation and one of the first ever parameter estimation calculations with multi-modal numerical relativity waveforms, which include all \\ell ≤slant 4 modes. Our grid-free method enables rapid parameter estimation for any waveform with a suitable reduced-order model. The methods described in this paper may also find use in other data analysis studies, such as vetting coincident events or the computation of the coalescing-compact-binary detection statistic.

Speech processing using maximum likelihood continuity mapping

DOEpatents

Hogden, John E.

2000-01-01

Speech processing is obtained that, given a probabilistic mapping between static speech sounds and pseudo-articulator positions, allows sequences of speech sounds to be mapped to smooth sequences of pseudo-articulator positions. In addition, a method for learning a probabilistic mapping between static speech sounds and pseudo-articulator position is described. The method for learning the mapping between static speech sounds and pseudo-articulator position uses a set of training data composed only of speech sounds. The said speech processing can be applied to various speech analysis tasks, including speech recognition, speaker recognition, speech coding, speech synthesis, and voice mimicry.

Speech processing using maximum likelihood continuity mapping

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

Hogden, J.E.

Speech processing is obtained that, given a probabilistic mapping between static speech sounds and pseudo-articulator positions, allows sequences of speech sounds to be mapped to smooth sequences of pseudo-articulator positions. In addition, a method for learning a probabilistic mapping between static speech sounds and pseudo-articulator position is described. The method for learning the mapping between static speech sounds and pseudo-articulator position uses a set of training data composed only of speech sounds. The said speech processing can be applied to various speech analysis tasks, including speech recognition, speaker recognition, speech coding, speech synthesis, and voice mimicry.

Parameter Estimation and Model Selection for Indoor Environments Based on Sparse Observations

NASA Astrophysics Data System (ADS)

Dehbi, Y.; Loch-Dehbi, S.; Plümer, L.

2017-09-01

This paper presents a novel method for the parameter estimation and model selection for the reconstruction of indoor environments based on sparse observations. While most approaches for the reconstruction of indoor models rely on dense observations, we predict scenes of the interior with high accuracy in the absence of indoor measurements. We use a model-based top-down approach and incorporate strong but profound prior knowledge. The latter includes probability density functions for model parameters and sparse observations such as room areas and the building footprint. The floorplan model is characterized by linear and bi-linear relations with discrete and continuous parameters. We focus on the stochastic estimation of model parameters based on a topological model derived by combinatorial reasoning in a first step. A Gauss-Markov model is applied for estimation and simulation of the model parameters. Symmetries are represented and exploited during the estimation process. Background knowledge as well as observations are incorporated in a maximum likelihood estimation and model selection is performed with AIC/BIC. The likelihood is also used for the detection and correction of potential errors in the topological model. Estimation results are presented and discussed.

Simple Penalties on Maximum-Likelihood Estimates of Genetic Parameters to Reduce Sampling Variation

PubMed Central

Meyer, Karin

2016-01-01

Multivariate estimates of genetic parameters are subject to substantial sampling variation, especially for smaller data sets and more than a few traits. A simple modification of standard, maximum-likelihood procedures for multivariate analyses to estimate genetic covariances is described, which can improve estimates by substantially reducing their sampling variances. This is achieved by maximizing the likelihood subject to a penalty. Borrowing from Bayesian principles, we propose a mild, default penalty—derived assuming a Beta distribution of scale-free functions of the covariance components to be estimated—rather than laboriously attempting to determine the stringency of penalization from the data. An extensive simulation study is presented, demonstrating that such penalties can yield very worthwhile reductions in loss, i.e., the difference from population values, for a wide range of scenarios and without distorting estimates of phenotypic covariances. Moreover, mild default penalties tend not to increase loss in difficult cases and, on average, achieve reductions in loss of similar magnitude to computationally demanding schemes to optimize the degree of penalization. Pertinent details required for the adaptation of standard algorithms to locate the maximum of the likelihood function are outlined. PMID:27317681

Estimation of Time-Varying Pilot Model Parameters

NASA Technical Reports Server (NTRS)

Zaal, Peter M. T.; Sweet, Barbara T.

2011-01-01

Human control behavior is rarely completely stationary over time due to fatigue or loss of attention. In addition, there are many control tasks for which human operators need to adapt their control strategy to vehicle dynamics that vary in time. In previous studies on the identification of time-varying pilot control behavior wavelets were used to estimate the time-varying frequency response functions. However, the estimation of time-varying pilot model parameters was not considered. Estimating these parameters can be a valuable tool for the quantification of different aspects of human time-varying manual control. This paper presents two methods for the estimation of time-varying pilot model parameters, a two-step method using wavelets and a windowed maximum likelihood estimation method. The methods are evaluated using simulations of a closed-loop control task with time-varying pilot equalization and vehicle dynamics. Simulations are performed with and without remnant. Both methods give accurate results when no pilot remnant is present. The wavelet transform is very sensitive to measurement noise, resulting in inaccurate parameter estimates when considerable pilot remnant is present. Maximum likelihood estimation is less sensitive to pilot remnant, but cannot detect fast changes in pilot control behavior.

A Penalized Likelihood Framework For High-Dimensional Phylogenetic Comparative Methods And An Application To New-World Monkeys Brain Evolution.

PubMed

Julien, Clavel; Leandro, Aristide; Hélène, Morlon

2018-06-19

Working with high-dimensional phylogenetic comparative datasets is challenging because likelihood-based multivariate methods suffer from low statistical performances as the number of traits p approaches the number of species n and because some computational complications occur when p exceeds n. Alternative phylogenetic comparative methods have recently been proposed to deal with the large p small n scenario but their use and performances are limited. Here we develop a penalized likelihood framework to deal with high-dimensional comparative datasets. We propose various penalizations and methods for selecting the intensity of the penalties. We apply this general framework to the estimation of parameters (the evolutionary trait covariance matrix and parameters of the evolutionary model) and model comparison for the high-dimensional multivariate Brownian (BM), Early-burst (EB), Ornstein-Uhlenbeck (OU) and Pagel's lambda models. We show using simulations that our penalized likelihood approach dramatically improves the estimation of evolutionary trait covariance matrices and model parameters when p approaches n, and allows for their accurate estimation when p equals or exceeds n. In addition, we show that penalized likelihood models can be efficiently compared using Generalized Information Criterion (GIC). We implement these methods, as well as the related estimation of ancestral states and the computation of phylogenetic PCA in the R package RPANDA and mvMORPH. Finally, we illustrate the utility of the new proposed framework by evaluating evolutionary models fit, analyzing integration patterns, and reconstructing evolutionary trajectories for a high-dimensional 3-D dataset of brain shape in the New World monkeys. We find a clear support for an Early-burst model suggesting an early diversification of brain morphology during the ecological radiation of the clade. Penalized likelihood offers an efficient way to deal with high-dimensional multivariate comparative data.

Gaussian process inference for estimating pharmacokinetic parameters of dynamic contrast-enhanced MR images.

PubMed

Wang, Shijun; Liu, Peter; Turkbey, Baris; Choyke, Peter; Pinto, Peter; Summers, Ronald M

2012-01-01

In this paper, we propose a new pharmacokinetic model for parameter estimation of dynamic contrast-enhanced (DCE) MRI by using Gaussian process inference. Our model is based on the Tofts dual-compartment model for the description of tracer kinetics and the observed time series from DCE-MRI is treated as a Gaussian stochastic process. The parameter estimation is done through a maximum likelihood approach and we propose a variant of the coordinate descent method to solve this likelihood maximization problem. The new model was shown to outperform a baseline method on simulated data. Parametric maps generated on prostate DCE data with the new model also provided better enhancement of tumors, lower intensity on false positives, and better boundary delineation when compared with the baseline method. New statistical parameter maps from the process model were also found to be informative, particularly when paired with the PK parameter maps.

Lateral stability and control derivatives of a jet fighter airplane extracted from flight test data by utilizing maximum likelihood estimation

NASA Technical Reports Server (NTRS)

Parrish, R. V.; Steinmetz, G. G.

1972-01-01

A method of parameter extraction for stability and control derivatives of aircraft from flight test data, implementing maximum likelihood estimation, has been developed and successfully applied to actual lateral flight test data from a modern sophisticated jet fighter. This application demonstrates the important role played by the analyst in combining engineering judgment and estimator statistics to yield meaningful results. During the analysis, the problems of uniqueness of the extracted set of parameters and of longitudinal coupling effects were encountered and resolved. The results for all flight runs are presented in tabular form and as time history comparisons between the estimated states and the actual flight test data.

Likelihoods for fixed rank nomination networks

PubMed Central

HOFF, PETER; FOSDICK, BAILEY; VOLFOVSKY, ALEX; STOVEL, KATHERINE

2014-01-01

Many studies that gather social network data use survey methods that lead to censored, missing, or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and businesses, asks study participants to nominate and rank at most a small number of contacts or friends, leaving the existence of other relations uncertain. However, most statistical models are formulated in terms of completely observed binary networks. Statistical analyses of FRN data with such models ignore the censored and ranked nature of the data and could potentially result in misleading statistical inference. To investigate this possibility, we compare Bayesian parameter estimates obtained from a likelihood for complete binary networks with those obtained from likelihoods that are derived from the FRN scheme, and therefore accommodate the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, particularly for certain model parameters that relate network ties to characteristics of individuals and pairs of individuals. We also compare these different likelihoods in a data analysis of several adolescent social networks. For some of these networks, the parameter estimates from the binary and FRN likelihoods lead to different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design. PMID:25110586

On the Nature of SEM Estimates of ARMA Parameters.

ERIC Educational Resources Information Center

Hamaker, Ellen L.; Dolan, Conor V.; Molenaar, Peter C. M.

2002-01-01

Reexamined the nature of structural equation modeling (SEM) estimates of autoregressive moving average (ARMA) models, replicated the simulation experiments of P. Molenaar, and examined the behavior of the log-likelihood ratio test. Simulation studies indicate that estimates of ARMA parameters observed with SEM software are identical to those…

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables.

ERIC Educational Resources Information Center

Ethington, Corinna A.

1987-01-01

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical variables. The analysis of mixed matrices produced estimates that closely approximated the model parameters except where dichotomous variables were…

Computing Maximum Likelihood Estimates of Loglinear Models from Marginal Sums with Special Attention to Loglinear Item Response Theory.

ERIC Educational Resources Information Center

Kelderman, Henk

1992-01-01

Describes algorithms used in the computer program LOGIMO for obtaining maximum likelihood estimates of the parameters in loglinear models. These algorithms are also useful for the analysis of loglinear item-response theory models. Presents modified versions of the iterative proportional fitting and Newton-Raphson algorithms. Simulated data…

Estimation of Two-Parameter Logistic Item Response Curves. Research Report 83-1. Mathematical Sciences Technical Report No. 130.

ERIC Educational Resources Information Center

Tsutakawa, Robert K.

This paper presents a method for estimating certain characteristics of test items which are designed to measure ability, or knowledge, in a particular area. Under the assumption that ability parameters are sampled from a normal distribution, the EM algorithm is used to derive maximum likelihood estimates to item parameters of the two-parameter…

A Solution to Separation and Multicollinearity in Multiple Logistic Regression

PubMed Central

Shen, Jianzhao; Gao, Sujuan

2010-01-01

In dementia screening tests, item selection for shortening an existing screening test can be achieved using multiple logistic regression. However, maximum likelihood estimates for such logistic regression models often experience serious bias or even non-existence because of separation and multicollinearity problems resulting from a large number of highly correlated items. Firth (1993, Biometrika, 80(1), 27–38) proposed a penalized likelihood estimator for generalized linear models and it was shown to reduce bias and the non-existence problems. The ridge regression has been used in logistic regression to stabilize the estimates in cases of multicollinearity. However, neither solves the problems for each other. In this paper, we propose a double penalized maximum likelihood estimator combining Firth’s penalized likelihood equation with a ridge parameter. We present a simulation study evaluating the empirical performance of the double penalized likelihood estimator in small to moderate sample sizes. We demonstrate the proposed approach using a current screening data from a community-based dementia study. PMID:20376286

A Solution to Separation and Multicollinearity in Multiple Logistic Regression.

PubMed

Shen, Jianzhao; Gao, Sujuan

2008-10-01

In dementia screening tests, item selection for shortening an existing screening test can be achieved using multiple logistic regression. However, maximum likelihood estimates for such logistic regression models often experience serious bias or even non-existence because of separation and multicollinearity problems resulting from a large number of highly correlated items. Firth (1993, Biometrika, 80(1), 27-38) proposed a penalized likelihood estimator for generalized linear models and it was shown to reduce bias and the non-existence problems. The ridge regression has been used in logistic regression to stabilize the estimates in cases of multicollinearity. However, neither solves the problems for each other. In this paper, we propose a double penalized maximum likelihood estimator combining Firth's penalized likelihood equation with a ridge parameter. We present a simulation study evaluating the empirical performance of the double penalized likelihood estimator in small to moderate sample sizes. We demonstrate the proposed approach using a current screening data from a community-based dementia study.

Refinement of a Bias-Correction Procedure for the Weighted Likelihood Estimator of Ability. Research Report. ETS RR-07-23

ERIC Educational Resources Information Center

Zhang, Jinming; Lu, Ting

2007-01-01

In practical applications of item response theory (IRT), item parameters are usually estimated first from a calibration sample. After treating these estimates as fixed and known, ability parameters are then estimated. However, the statistical inferences based on the estimated abilities can be misleading if the uncertainty of the item parameter…

Bayesian logistic regression approaches to predict incorrect DRG assignment.

PubMed

Suleiman, Mani; Demirhan, Haydar; Boyd, Leanne; Girosi, Federico; Aksakalli, Vural

2018-05-07

Episodes of care involving similar diagnoses and treatments and requiring similar levels of resource utilisation are grouped to the same Diagnosis-Related Group (DRG). In jurisdictions which implement DRG based payment systems, DRGs are a major determinant of funding for inpatient care. Hence, service providers often dedicate auditing staff to the task of checking that episodes have been coded to the correct DRG. The use of statistical models to estimate an episode's probability of DRG error can significantly improve the efficiency of clinical coding audits. This study implements Bayesian logistic regression models with weakly informative prior distributions to estimate the likelihood that episodes require a DRG revision, comparing these models with each other and to classical maximum likelihood estimates. All Bayesian approaches had more stable model parameters than maximum likelihood. The best performing Bayesian model improved overall classification per- formance by 6% compared to maximum likelihood, with a 34% gain compared to random classification, respectively. We found that the original DRG, coder and the day of coding all have a significant effect on the likelihood of DRG error. Use of Bayesian approaches has improved model parameter stability and classification accuracy. This method has already lead to improved audit efficiency in an operational capacity.

Coupled semivariogram uncertainty of hydrogeological and geophysical data on capture zone uncertainty analysis

USGS Publications Warehouse

Rahman, A.; Tsai, F.T.-C.; White, C.D.; Willson, C.S.

2008-01-01

This study investigates capture zone uncertainty that relates to the coupled semivariogram uncertainty of hydrogeological and geophysical data. Semivariogram uncertainty is represented by the uncertainty in structural parameters (range, sill, and nugget). We used the beta distribution function to derive the prior distributions of structural parameters. The probability distributions of structural parameters were further updated through the Bayesian approach with the Gaussian likelihood functions. Cokriging of noncollocated pumping test data and electrical resistivity data was conducted to better estimate hydraulic conductivity through autosemivariograms and pseudo-cross-semivariogram. Sensitivities of capture zone variability with respect to the spatial variability of hydraulic conductivity, porosity and aquifer thickness were analyzed using ANOVA. The proposed methodology was applied to the analysis of capture zone uncertainty at the Chicot aquifer in Southwestern Louisiana, where a regional groundwater flow model was developed. MODFLOW-MODPATH was adopted to delineate the capture zone. The ANOVA results showed that both capture zone area and compactness were sensitive to hydraulic conductivity variation. We concluded that the capture zone uncertainty due to the semivariogram uncertainty is much higher than that due to the kriging uncertainty for given semivariograms. In other words, the sole use of conditional variances of kriging may greatly underestimate the flow response uncertainty. Semivariogram uncertainty should also be taken into account in the uncertainty analysis. ?? 2008 ASCE.

Empirical Likelihood in Nonignorable Covariate-Missing Data Problems.

PubMed

Xie, Yanmei; Zhang, Biao

2017-04-20

Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. We study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. We adopt the semiparametric perspective of Bartlett et al. (Improving upon the efficiency of complete case analysis when covariates are MNAR. Biostatistics 2014;15:719-30) on regression analyses with nonignorable missing covariates, in which they have introduced the use of two working models, the working probability model of missingness and the working conditional score model. In this paper, we study an empirical likelihood approach to nonignorable covariate-missing data problems with the objective of effectively utilizing the two working models in the analysis of covariate-missing data. We propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. One useful feature of these unbiased estimating equations is that they naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. We apply the general methodology of empirical likelihood to optimally combine these unbiased estimating equations. We propose three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. We present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. The proposed empirical likelihood method is also illustrated by an analysis of a data set from the US National Health and Nutrition Examination Survey (NHANES).

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis

PubMed Central

van de Schoot, Rens; Hox, Joop

2014-01-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions. PMID:29795827

The Asymptotic Distribution of Ability Estimates: Beyond Dichotomous Items and Unidimensional IRT Models

ERIC Educational Resources Information Center

Sinharay, Sandip

2015-01-01

The maximum likelihood estimate (MLE) of the ability parameter of an item response theory model with known item parameters was proved to be asymptotically normally distributed under a set of regularity conditions for tests involving dichotomous items and a unidimensional ability parameter (Klauer, 1990; Lord, 1983). This article first considers…

Predictive Uncertainty And Parameter Sensitivity Of A Sediment-Flux Model: Nitrogen Flux and Sediment Oxygen Demand

EPA Science Inventory

Estimating model predictive uncertainty is imperative to informed environmental decision making and management of water resources. This paper applies the Generalized Sensitivity Analysis (GSA) to examine parameter sensitivity and the Generalized Likelihood Uncertainty Estimation...

Likelihood parameter estimation for calibrating a soil moisture using radar backscatter

USDA-ARS?s Scientific Manuscript database

Assimilating soil moisture information contained in synthetic aperture radar imagery into land surface model predictions can be done using a calibration, or parameter estimation, approach. The presence of speckle, however, necessitates aggregating backscatter measurements over large land areas in or...

On Obtaining Estimates of the Fraction of Missing Information from Full Information Maximum Likelihood

ERIC Educational Resources Information Center

Savalei, Victoria; Rhemtulla, Mijke

2012-01-01

Fraction of missing information [lambda][subscript j] is a useful measure of the impact of missing data on the quality of estimation of a particular parameter. This measure can be computed for all parameters in the model, and it communicates the relative loss of efficiency in the estimation of a particular parameter due to missing data. It has…

Comparing Different Approaches of Bias Correction for Ability Estimation in IRT Models. Research Report. ETS RR-08-13

ERIC Educational Resources Information Center

Lee, Yi-Hsuan; Zhang, Jinming

2008-01-01

The method of maximum-likelihood is typically applied to item response theory (IRT) models when the ability parameter is estimated while conditioning on the true item parameters. In practice, the item parameters are unknown and need to be estimated first from a calibration sample. Lewis (1985) and Zhang and Lu (2007) proposed the expected response…

Spatial design and strength of spatial signal: Effects on covariance estimation

USGS Publications Warehouse

Irvine, Kathryn M.; Gitelman, Alix I.; Hoeting, Jennifer A.

2007-01-01

In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the influence of the strength of spatial dependence on maximum likelihood (ML) and restricted maximum likelihood (REML) estimates of covariance parameters in an exponential-with-nugget model, and we also examine these influences under different sampling designs—specifically, lattice designs and more realistic random and cluster designs—at differing intensities of sampling (n=144 and 361). We find that neither ML nor REML estimates perform well when the range parameter and/or the nugget-to-sill ratio is large—ML tends to underestimate the autocorrelation function and REML produces highly variable estimates of the autocorrelation function. The best estimates of both the covariance parameters and the autocorrelation function come under the cluster sampling design and large sample sizes. As a motivating example, we consider a spatial model for stream sulfate concentration.

Systems identification using a modified Newton-Raphson method: A FORTRAN program

NASA Technical Reports Server (NTRS)

Taylor, L. W., Jr.; Iliff, K. W.

1972-01-01

A FORTRAN program is offered which computes a maximum likelihood estimate of the parameters of any linear, constant coefficient, state space model. For the case considered, the maximum likelihood estimate can be identical to that which minimizes simultaneously the weighted mean square difference between the computed and measured response of a system and the weighted square of the difference between the estimated and a priori parameter values. A modified Newton-Raphson or quasilinearization method is used to perform the minimization which typically requires several iterations. A starting technique is used which insures convergence for any initial values of the unknown parameters. The program and its operation are described in sufficient detail to enable the user to apply the program to his particular problem with a minimum of difficulty.

Estimating cellular parameters through optimization procedures: elementary principles and applications.

PubMed

Kimura, Akatsuki; Celani, Antonio; Nagao, Hiromichi; Stasevich, Timothy; Nakamura, Kazuyuki

2015-01-01

Construction of quantitative models is a primary goal of quantitative biology, which aims to understand cellular and organismal phenomena in a quantitative manner. In this article, we introduce optimization procedures to search for parameters in a quantitative model that can reproduce experimental data. The aim of optimization is to minimize the sum of squared errors (SSE) in a prediction or to maximize likelihood. A (local) maximum of likelihood or (local) minimum of the SSE can efficiently be identified using gradient approaches. Addition of a stochastic process enables us to identify the global maximum/minimum without becoming trapped in local maxima/minima. Sampling approaches take advantage of increasing computational power to test numerous sets of parameters in order to determine the optimum set. By combining Bayesian inference with gradient or sampling approaches, we can estimate both the optimum parameters and the form of the likelihood function related to the parameters. Finally, we introduce four examples of research that utilize parameter optimization to obtain biological insights from quantified data: transcriptional regulation, bacterial chemotaxis, morphogenesis, and cell cycle regulation. With practical knowledge of parameter optimization, cell and developmental biologists can develop realistic models that reproduce their observations and thus, obtain mechanistic insights into phenomena of interest.

Maximum Likelihood Estimation with Emphasis on Aircraft Flight Data

NASA Technical Reports Server (NTRS)

Iliff, K. W.; Maine, R. E.

1985-01-01

Accurate modeling of flexible space structures is an important field that is currently under investigation. Parameter estimation, using methods such as maximum likelihood, is one of the ways that the model can be improved. The maximum likelihood estimator has been used to extract stability and control derivatives from flight data for many years. Most of the literature on aircraft estimation concentrates on new developments and applications, assuming familiarity with basic estimation concepts. Some of these basic concepts are presented. The maximum likelihood estimator and the aircraft equations of motion that the estimator uses are briefly discussed. The basic concepts of minimization and estimation are examined for a simple computed aircraft example. The cost functions that are to be minimized during estimation are defined and discussed. Graphic representations of the cost functions are given to help illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Specific examples of estimation of structural dynamics are included. Some of the major conclusions for the computed example are also developed for the analysis of flight data.

Generalized Likelihood Uncertainty Estimation (GLUE) Using Multi-Optimization Algorithm as Sampling Method

NASA Astrophysics Data System (ADS)

Wang, Z.

2015-12-01

For decades, distributed and lumped hydrological models have furthered our understanding of hydrological system. The development of hydrological simulation in large scale and high precision elaborated the spatial descriptions and hydrological behaviors. Meanwhile, the new trend is also followed by the increment of model complexity and number of parameters, which brings new challenges of uncertainty quantification. Generalized Likelihood Uncertainty Estimation (GLUE) has been widely used in uncertainty analysis for hydrological models referring to Monte Carlo method coupled with Bayesian estimation. However, the stochastic sampling method of prior parameters adopted by GLUE appears inefficient, especially in high dimensional parameter space. The heuristic optimization algorithms utilizing iterative evolution show better convergence speed and optimality-searching performance. In light of the features of heuristic optimization algorithms, this study adopted genetic algorithm, differential evolution, shuffled complex evolving algorithm to search the parameter space and obtain the parameter sets of large likelihoods. Based on the multi-algorithm sampling, hydrological model uncertainty analysis is conducted by the typical GLUE framework. To demonstrate the superiority of the new method, two hydrological models of different complexity are examined. The results shows the adaptive method tends to be efficient in sampling and effective in uncertainty analysis, providing an alternative path for uncertainty quantilization.

Estimation of modal parameters using bilinear joint time frequency distributions

NASA Astrophysics Data System (ADS)

Roshan-Ghias, A.; Shamsollahi, M. B.; Mobed, M.; Behzad, M.

2007-07-01

In this paper, a new method is proposed for modal parameter estimation using time-frequency representations. Smoothed Pseudo Wigner-Ville distribution which is a member of the Cohen's class distributions is used to decouple vibration modes completely in order to study each mode separately. This distribution reduces cross-terms which are troublesome in Wigner-Ville distribution and retains the resolution as well. The method was applied to highly damped systems, and results were superior to those obtained via other conventional methods.

COSMIC MICROWAVE BACKGROUND LIKELIHOOD APPROXIMATION FOR BANDED PROBABILITY DISTRIBUTIONS

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

Gjerløw, E.; Mikkelsen, K.; Eriksen, H. K.

We investigate sets of random variables that can be arranged sequentially such that a given variable only depends conditionally on its immediate predecessor. For such sets, we show that the full joint probability distribution may be expressed exclusively in terms of uni- and bivariate marginals. Under the assumption that the cosmic microwave background (CMB) power spectrum likelihood only exhibits correlations within a banded multipole range, Δl{sub C}, we apply this expression to two outstanding problems in CMB likelihood analysis. First, we derive a statistically well-defined hybrid likelihood estimator, merging two independent (e.g., low- and high-l) likelihoods into a single expressionmore » that properly accounts for correlations between the two. Applying this expression to the Wilkinson Microwave Anisotropy Probe (WMAP) likelihood, we verify that the effect of correlations on cosmological parameters in the transition region is negligible in terms of cosmological parameters for WMAP; the largest relative shift seen for any parameter is 0.06σ. However, because this may not hold for other experimental setups (e.g., for different instrumental noise properties or analysis masks), but must rather be verified on a case-by-case basis, we recommend our new hybridization scheme for future experiments for statistical self-consistency reasons. Second, we use the same expression to improve the convergence rate of the Blackwell-Rao likelihood estimator, reducing the required number of Monte Carlo samples by several orders of magnitude, and thereby extend it to high-l applications.« less

Nonlinear Spatial Inversion Without Monte Carlo Sampling

NASA Astrophysics Data System (ADS)

Curtis, A.; Nawaz, A.

2017-12-01

High-dimensional, nonlinear inverse or inference problems usually have non-unique solutions. The distribution of solutions are described by probability distributions, and these are usually found using Monte Carlo (MC) sampling methods. These take pseudo-random samples of models in parameter space, calculate the probability of each sample given available data and other information, and thus map out high or low probability values of model parameters. However, such methods would converge to the solution only as the number of samples tends to infinity; in practice, MC is found to be slow to converge, convergence is not guaranteed to be achieved in finite time, and detection of convergence requires the use of subjective criteria. We propose a method for Bayesian inversion of categorical variables such as geological facies or rock types in spatial problems, which requires no sampling at all. The method uses a 2-D Hidden Markov Model over a grid of cells, where observations represent localized data constraining the model in each cell. The data in our example application are seismic properties such as P- and S-wave impedances or rock density; our model parameters are the hidden states and represent the geological rock types in each cell. The observations at each location are assumed to depend on the facies at that location only - an assumption referred to as `localized likelihoods'. However, the facies at a location cannot be determined solely by the observation at that location as it also depends on prior information concerning its correlation with the spatial distribution of facies elsewhere. Such prior information is included in the inversion in the form of a training image which represents a conceptual depiction of the distribution of local geologies that might be expected, but other forms of prior information can be used in the method as desired. The method provides direct (pseudo-analytic) estimates of posterior marginal probability distributions over each variable, so these do not need to be estimated from samples as is required in MC methods. On a 2-D test example the method is shown to outperform previous methods significantly, and at a fraction of the computational cost. In many foreseeable applications there are therefore no serious impediments to extending the method to 3-D spatial models.

Approximated maximum likelihood estimation in multifractal random walks

NASA Astrophysics Data System (ADS)

Løvsletten, O.; Rypdal, M.

2012-04-01

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.64.026103 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the r computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.

Ramsay-Curve Item Response Theory for the Three-Parameter Logistic Item Response Model

ERIC Educational Resources Information Center

Woods, Carol M.

2008-01-01

In Ramsay-curve item response theory (RC-IRT), the latent variable distribution is estimated simultaneously with the item parameters of a unidimensional item response model using marginal maximum likelihood estimation. This study evaluates RC-IRT for the three-parameter logistic (3PL) model with comparisons to the normal model and to the empirical…

Bayesian experimental design for models with intractable likelihoods.

PubMed

Drovandi, Christopher C; Pettitt, Anthony N

2013-12-01

In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables. © 2013, The International Biometric Society.

User's manual for MMLE3, a general FORTRAN program for maximum likelihood parameter estimation

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1980-01-01

A user's manual for the FORTRAN IV computer program MMLE3 is described. It is a maximum likelihood parameter estimation program capable of handling general bilinear dynamic equations of arbitrary order with measurement noise and/or state noise (process noise). The theory and use of the program is described. The basic MMLE3 program is quite general and, therefore, applicable to a wide variety of problems. The basic program can interact with a set of user written problem specific routines to simplify the use of the program on specific systems. A set of user routines for the aircraft stability and control derivative estimation problem is provided with the program.

Validation of the alternating conditional estimation algorithm for estimation of flexible extensions of Cox's proportional hazards model with nonlinear constraints on the parameters.

PubMed

Wynant, Willy; Abrahamowicz, Michal

2016-11-01

Standard optimization algorithms for maximizing likelihood may not be applicable to the estimation of those flexible multivariable models that are nonlinear in their parameters. For applications where the model's structure permits separating estimation of mutually exclusive subsets of parameters into distinct steps, we propose the alternating conditional estimation (ACE) algorithm. We validate the algorithm, in simulations, for estimation of two flexible extensions of Cox's proportional hazards model where the standard maximum partial likelihood estimation does not apply, with simultaneous modeling of (1) nonlinear and time-dependent effects of continuous covariates on the hazard, and (2) nonlinear interaction and main effects of the same variable. We also apply the algorithm in real-life analyses to estimate nonlinear and time-dependent effects of prognostic factors for mortality in colon cancer. Analyses of both simulated and real-life data illustrate good statistical properties of the ACE algorithm and its ability to yield new potentially useful insights about the data structure. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Parameter Estimation for Thurstone Choice Models

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

Vojnovic, Milan; Yun, Seyoung

We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates the well-known choice models such as the Luce choice model for comparison sets of two or more items and the Bradley-Terry model for pair comparisons. We provide a tight characterization of the mean squared error of the maximum likelihood parameter estimator. We also provide similar characterizations for parameter estimators defined by a rank-breaking method, which amounts to deducing one ormore » more pair comparisons from a comparison of two or more items, assuming independence of these pair comparisons, and maximizing a likelihood function derived under these assumptions. We also consider a related binary classification problem where each individual parameter takes value from a set of two possible values and the goal is to correctly classify all items within a prescribed classification error. The results of this paper shed light on how the parameter estimation accuracy depends on given Thurstone choice model and the structure of comparison sets. In particular, we found that for unbiased input comparison sets of a given cardinality, when in expectation each comparison set of given cardinality occurs the same number of times, for a broad class of Thurstone choice models, the mean squared error decreases with the cardinality of comparison sets, but only marginally according to a diminishing returns relation. On the other hand, we found that there exist Thurstone choice models for which the mean squared error of the maximum likelihood parameter estimator can decrease much faster with the cardinality of comparison sets. We report empirical evaluation of some claims and key parameters revealed by theory using both synthetic and real-world input data from some popular sport competitions and online labor platforms.« less

On the Existence and Uniqueness of JML Estimates for the Partial Credit Model

ERIC Educational Resources Information Center

Bertoli-Barsotti, Lucio

2005-01-01

A necessary and sufficient condition is given in this paper for the existence and uniqueness of the maximum likelihood (the so-called joint maximum likelihood) estimate of the parameters of the Partial Credit Model. This condition is stated in terms of a structural property of the pattern of the data matrix that can be easily verified on the basis…

Marginal Maximum A Posteriori Item Parameter Estimation for the Generalized Graded Unfolding Model

ERIC Educational Resources Information Center

Roberts, James S.; Thompson, Vanessa M.

2011-01-01

A marginal maximum a posteriori (MMAP) procedure was implemented to estimate item parameters in the generalized graded unfolding model (GGUM). Estimates from the MMAP method were compared with those derived from marginal maximum likelihood (MML) and Markov chain Monte Carlo (MCMC) procedures in a recovery simulation that varied sample size,…

A spatially explicit capture-recapture estimator for single-catch traps.

PubMed

Distiller, Greg; Borchers, David L

2015-11-01

Single-catch traps are frequently used in live-trapping studies of small mammals. Thus far, a likelihood for single-catch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capture-recapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. We build on a recently developed continuous-time model for SECR to derive a likelihood for single-catch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height of the detection function. By contrast, the single-catch estimators of density, distribution, and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constant over the survey region, then the multicatch estimator performs well with single-catch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the single-catch estimator when trap saturation is above about 60%. The estimator's performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a single-catch likelihood with unknown capture times remains intractable for now, researchers using single-catch traps should aim to incorporate timing devices with their traps.

Estimating Model Probabilities using Thermodynamic Markov Chain Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Ye, M.; Liu, P.; Beerli, P.; Lu, D.; Hill, M. C.

2014-12-01

Markov chain Monte Carlo (MCMC) methods are widely used to evaluate model probability for quantifying model uncertainty. In a general procedure, MCMC simulations are first conducted for each individual model, and MCMC parameter samples are then used to approximate marginal likelihood of the model by calculating the geometric mean of the joint likelihood of the model and its parameters. It has been found the method of evaluating geometric mean suffers from the numerical problem of low convergence rate. A simple test case shows that even millions of MCMC samples are insufficient to yield accurate estimation of the marginal likelihood. To resolve this problem, a thermodynamic method is used to have multiple MCMC runs with different values of a heating coefficient between zero and one. When the heating coefficient is zero, the MCMC run is equivalent to a random walk MC in the prior parameter space; when the heating coefficient is one, the MCMC run is the conventional one. For a simple case with analytical form of the marginal likelihood, the thermodynamic method yields more accurate estimate than the method of using geometric mean. This is also demonstrated for a case of groundwater modeling with consideration of four alternative models postulated based on different conceptualization of a confining layer. This groundwater example shows that model probabilities estimated using the thermodynamic method are more reasonable than those obtained using the geometric method. The thermodynamic method is general, and can be used for a wide range of environmental problem for model uncertainty quantification.

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1972-01-01

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Maximum Likelihood Estimations and EM Algorithms with Length-biased Data

PubMed Central

Qin, Jing; Ning, Jing; Liu, Hao; Shen, Yu

2012-01-01

SUMMARY Length-biased sampling has been well recognized in economics, industrial reliability, etiology applications, epidemiological, genetic and cancer screening studies. Length-biased right-censored data have a unique data structure different from traditional survival data. The nonparametric and semiparametric estimations and inference methods for traditional survival data are not directly applicable for length-biased right-censored data. We propose new expectation-maximization algorithms for estimations based on full likelihoods involving infinite dimensional parameters under three settings for length-biased data: estimating nonparametric distribution function, estimating nonparametric hazard function under an increasing failure rate constraint, and jointly estimating baseline hazards function and the covariate coefficients under the Cox proportional hazards model. Extensive empirical simulation studies show that the maximum likelihood estimators perform well with moderate sample sizes and lead to more efficient estimators compared to the estimating equation approaches. The proposed estimates are also more robust to various right-censoring mechanisms. We prove the strong consistency properties of the estimators, and establish the asymptotic normality of the semi-parametric maximum likelihood estimators under the Cox model using modern empirical processes theory. We apply the proposed methods to a prevalent cohort medical study. Supplemental materials are available online. PMID:22323840

Transmuted of Rayleigh Distribution with Estimation and Application on Noise Signal

NASA Astrophysics Data System (ADS)

Ahmed, Suhad; Qasim, Zainab

2018-05-01

This paper deals with transforming one parameter Rayleigh distribution, into transmuted probability distribution through introducing a new parameter (λ), since this studied distribution is necessary in representing signal data distribution and failure data model the value of this transmuted parameter |λ| ≤ 1, is also estimated as well as the original parameter (⊖) by methods of moments and maximum likelihood using different sample size (n=25, 50, 75, 100) and comparing the results of estimation by statistical measure (mean square error, MSE).

WEIGHTED LIKELIHOOD ESTIMATION UNDER TWO-PHASE SAMPLING

PubMed Central

Saegusa, Takumi; Wellner, Jon A.

2013-01-01

We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process tools are developed including a Glivenko–Cantelli theorem, a theorem for rates of convergence of M-estimators, and a Donsker theorem for the inverse probability weighted empirical processes under two-phase sampling and sampling without replacement at the second phase. Using these general results, we derive asymptotic distributions of the WLE of a finite-dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is estimable either at regular or nonregular rates. We illustrate these results and methods in the Cox model with right censoring and interval censoring. We compare the methods via their asymptotic variances under both sampling without replacement and the more usual (and easier to analyze) assumption of Bernoulli sampling at the second phase. PMID:24563559

A modified Leslie-Gower predator-prey interaction model and parameter identifiability

NASA Astrophysics Data System (ADS)

Tripathi, Jai Prakash; Meghwani, Suraj S.; Thakur, Manoj; Abbas, Syed

2018-01-01

In this work, bifurcation and a systematic approach for estimation of identifiable parameters of a modified Leslie-Gower predator-prey system with Crowley-Martin functional response and prey refuge is discussed. Global asymptotic stability is discussed by applying fluctuation lemma. The system undergoes into Hopf bifurcation with respect to parameters intrinsic growth rate of predators (s) and prey reserve (m). The stability of Hopf bifurcation is also discussed by calculating Lyapunov number. The sensitivity analysis of the considered model system with respect to all variables is performed which also supports our theoretical study. To estimate the unknown parameter from the data, an optimization procedure (pseudo-random search algorithm) is adopted. System responses and phase plots for estimated parameters are also compared with true noise free data. It is found that the system dynamics with true set of parametric values is similar to the estimated parametric values. Numerical simulations are presented to substantiate the analytical findings.

Comparison of stability and control parameters for a light, single-engine, high-winged aircraft using different flight test and parameter estimation techniques

NASA Technical Reports Server (NTRS)

Suit, W. T.; Cannaday, R. L.

1979-01-01

The longitudinal and lateral stability and control parameters for a high wing, general aviation, airplane are examined. Estimations using flight data obtained at various flight conditions within the normal range of the aircraft are presented. The estimations techniques, an output error technique (maximum likelihood) and an equation error technique (linear regression), are presented. The longitudinal static parameters are estimated from climbing, descending, and quasi steady state flight data. The lateral excitations involve a combination of rudder and ailerons. The sensitivity of the aircraft modes of motion to variations in the parameter estimates are discussed.

Determination of stability and control parameters of a light airplane from flight data using two estimation methods. [equation error and maximum likelihood methods

NASA Technical Reports Server (NTRS)

Klein, V.

1979-01-01

Two identification methods, the equation error method and the output error method, are used to estimate stability and control parameter values from flight data for a low-wing, single-engine, general aviation airplane. The estimated parameters from both methods are in very good agreement primarily because of sufficient accuracy of measured data. The estimated static parameters also agree with the results from steady flights. The effect of power different input forms are demonstrated. Examination of all results available gives the best values of estimated parameters and specifies their accuracies.

Detecting changes in ultrasound backscattered statistics by using Nakagami parameters: Comparisons of moment-based and maximum likelihood estimators.

PubMed

Lin, Jen-Jen; Cheng, Jung-Yu; Huang, Li-Fei; Lin, Ying-Hsiu; Wan, Yung-Liang; Tsui, Po-Hsiang

2017-05-01

The Nakagami distribution is an approximation useful to the statistics of ultrasound backscattered signals for tissue characterization. Various estimators may affect the Nakagami parameter in the detection of changes in backscattered statistics. In particular, the moment-based estimator (MBE) and maximum likelihood estimator (MLE) are two primary methods used to estimate the Nakagami parameters of ultrasound signals. This study explored the effects of the MBE and different MLE approximations on Nakagami parameter estimations. Ultrasound backscattered signals of different scatterer number densities were generated using a simulation model, and phantom experiments and measurements of human liver tissues were also conducted to acquire real backscattered echoes. Envelope signals were employed to estimate the Nakagami parameters by using the MBE, first- and second-order approximations of MLE (MLE 1 and MLE 2 , respectively), and Greenwood approximation (MLE gw ) for comparisons. The simulation results demonstrated that, compared with the MBE and MLE 1 , the MLE 2 and MLE gw enabled more stable parameter estimations with small sample sizes. Notably, the required data length of the envelope signal was 3.6 times the pulse length. The phantom and tissue measurement results also showed that the Nakagami parameters estimated using the MLE 2 and MLE gw could simultaneously differentiate various scatterer concentrations with lower standard deviations and reliably reflect physical meanings associated with the backscattered statistics. Therefore, the MLE 2 and MLE gw are suggested as estimators for the development of Nakagami-based methodologies for ultrasound tissue characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

The Atacama Cosmology Telescope: Likelihood for Small-Scale CMB Data

NASA Technical Reports Server (NTRS)

Dunkley, J.; Calabrese, E.; Sievers, J.; Addison, G. E.; Battaglia, N.; Battistelli, E. S.; Bond, J. R.; Das, S.; Devlin, M. J.; Dunner, R.;

Maximum likelihood estimation for Cox's regression model under nested case-control sampling.

PubMed

Scheike, Thomas H; Juul, Anders

2004-04-01

Nested case-control sampling is designed to reduce the costs of large cohort studies. It is important to estimate the parameters of interest as efficiently as possible. We present a new maximum likelihood estimator (MLE) for nested case-control sampling in the context of Cox's proportional hazards model. The MLE is computed by the EM-algorithm, which is easy to implement in the proportional hazards setting. Standard errors are estimated by a numerical profile likelihood approach based on EM aided differentiation. The work was motivated by a nested case-control study that hypothesized that insulin-like growth factor I was associated with ischemic heart disease. The study was based on a population of 3784 Danes and 231 cases of ischemic heart disease where controls were matched on age and gender. We illustrate the use of the MLE for these data and show how the maximum likelihood framework can be used to obtain information additional to the relative risk estimates of covariates.

New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology.

PubMed

Han, Jubong; Lee, K B; Lee, Jong-Man; Park, Tae Soon; Oh, J S; Oh, Pil-Jei

2016-03-01

We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods. Copyright © 2015. Published by Elsevier Ltd.

Quasar microlensing models with constraints on the Quasar light curves

NASA Astrophysics Data System (ADS)

Tie, S. S.; Kochanek, C. S.

2018-01-01

Quasar microlensing analyses implicitly generate a model of the variability of the source quasar. The implied source variability may be unrealistic yet its likelihood is generally not evaluated. We used the damped random walk (DRW) model for quasar variability to evaluate the likelihood of the source variability and applied the revized algorithm to a microlensing analysis of the lensed quasar RX J1131-1231. We compared estimates of the size of the quasar disc and the average stellar mass of the lens galaxy with and without applying the DRW likelihoods for the source variability model and found no significant effect on the estimated physical parameters. The most likely explanation is that unreliastic source light-curve models are generally associated with poor microlensing fits that already make a negligible contribution to the probability distributions of the derived parameters.

Mortality table construction

NASA Astrophysics Data System (ADS)

Sutawanir

2015-12-01

Mortality tables play important role in actuarial studies such as life annuities, premium determination, premium reserve, valuation pension plan, pension funding. Some known mortality tables are CSO mortality table, Indonesian Mortality Table, Bowers mortality table, Japan Mortality table. For actuary applications some tables are constructed with different environment such as single decrement, double decrement, and multiple decrement. There exist two approaches in mortality table construction : mathematics approach and statistical approach. Distribution model and estimation theory are the statistical concepts that are used in mortality table construction. This article aims to discuss the statistical approach in mortality table construction. The distributional assumptions are uniform death distribution (UDD) and constant force (exponential). Moment estimation and maximum likelihood are used to estimate the mortality parameter. Moment estimation methods are easier to manipulate compared to maximum likelihood estimation (mle). However, the complete mortality data are not used in moment estimation method. Maximum likelihood exploited all available information in mortality estimation. Some mle equations are complicated and solved using numerical methods. The article focus on single decrement estimation using moment and maximum likelihood estimation. Some extension to double decrement will introduced. Simple dataset will be used to illustrated the mortality estimation, and mortality table.

A Comparative Study of Co-Channel Interference Suppression Techniques

NASA Technical Reports Server (NTRS)

Hamkins, Jon; Satorius, Ed; Paparisto, Gent; Polydoros, Andreas

1997-01-01

We describe three methods of combatting co-channel interference (CCI): a cross-coupled phase-locked loop (CCPLL); a phase-tracking circuit (PTC), and joint Viterbi estimation based on the maximum likelihood principle. In the case of co-channel FM-modulated voice signals, the CCPLL and PTC methods typically outperform the maximum likelihood estimators when the modulation parameters are dissimilar. However, as the modulation parameters become identical, joint Viterbi estimation provides for a more robust estimate of the co-channel signals and does not suffer as much from "signal switching" which especially plagues the CCPLL approach. Good performance for the PTC requires both dissimilar modulation parameters and a priori knowledge of the co-channel signal amplitudes. The CCPLL and joint Viterbi estimators, on the other hand, incorporate accurate amplitude estimates. In addition, application of the joint Viterbi algorithm to demodulating co-channel digital (BPSK) signals in a multipath environment is also discussed. It is shown in this case that if the interference is sufficiently small, a single trellis model is most effective in demodulating the co-channel signals.

Genetic and phenotypic parameter estimates for feed intake and other traits in growing beef cattle

USDA-ARS?s Scientific Manuscript database

Genetic parameters for dry matter intake (DMI), residual feed intake (RFI), average daily gain (ADG), mid-period body weight (MBW), gain to feed ratio (G:F) and flight speed (FS) were estimated using 1165 steers from a mixed-breed population using restricted maximum likelihood methodology applied to...

Case-Deletion Diagnostics for Maximum Likelihood Multipoint Quantitative Trait Locus Linkage Analysis

PubMed Central

Mendoza, Maria C.B.; Burns, Trudy L.; Jones, Michael P.

2009-01-01

Objectives Case-deletion diagnostic methods are tools that allow identification of influential observations that may affect parameter estimates and model fitting conclusions. The goal of this paper was to develop two case-deletion diagnostics, the exact case deletion (ECD) and the empirical influence function (EIF), for detecting outliers that can affect results of sib-pair maximum likelihood quantitative trait locus (QTL) linkage analysis. Methods Subroutines to compute the ECD and EIF were incorporated into the maximum likelihood QTL variance estimation components of the linkage analysis program MAPMAKER/SIBS. Performance of the diagnostics was compared in simulation studies that evaluated the proportion of outliers correctly identified (sensitivity), and the proportion of non-outliers correctly identified (specificity). Results Simulations involving nuclear family data sets with one outlier showed EIF sensitivities approximated ECD sensitivities well for outlier-affected parameters. Sensitivities were high, indicating the outlier was identified a high proportion of the time. Simulations also showed the enormous computational time advantage of the EIF. Diagnostics applied to body mass index in nuclear families detected observations influential on the lod score and model parameter estimates. Conclusions The EIF is a practical diagnostic tool that has the advantages of high sensitivity and quick computation. PMID:19172086

Period Estimation for Sparsely-sampled Quasi-periodic Light Curves Applied to Miras

NASA Astrophysics Data System (ADS)

He, Shiyuan; Yuan, Wenlong; Huang, Jianhua Z.; Long, James; Macri, Lucas M.

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequency parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period-luminosity relations.

Mixture class recovery in GMM under varying degrees of class separation: frequentist versus Bayesian estimation.

PubMed

Depaoli, Sarah

2013-06-01

Growth mixture modeling (GMM) represents a technique that is designed to capture change over time for unobserved subgroups (or latent classes) that exhibit qualitatively different patterns of growth. The aim of the current article was to explore the impact of latent class separation (i.e., how similar growth trajectories are across latent classes) on GMM performance. Several estimation conditions were compared: maximum likelihood via the expectation maximization (EM) algorithm and the Bayesian framework implementing diffuse priors, "accurate" informative priors, weakly informative priors, data-driven informative priors, priors reflecting partial-knowledge of parameters, and "inaccurate" (but informative) priors. The main goal was to provide insight about the optimal estimation condition under different degrees of latent class separation for GMM. Results indicated that optimal parameter recovery was obtained though the Bayesian approach using "accurate" informative priors, and partial-knowledge priors showed promise for the recovery of the growth trajectory parameters. Maximum likelihood and the remaining Bayesian estimation conditions yielded poor parameter recovery for the latent class proportions and the growth trajectories. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Maximum likelihood-based analysis of single-molecule photon arrival trajectories

NASA Astrophysics Data System (ADS)

Hajdziona, Marta; Molski, Andrzej

2011-02-01

In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 103 photons. When the intensity levels are well-separated and 104 photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.

Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices

PubMed Central

Meyer, Karin; Kirkpatrick, Mark

2005-01-01

Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of genetic correlation, a subset of the principal component generally suffices to capture the bulk of genetic variation. Corresponding estimates of genetic covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from k(k + 1)/2 to m(2k - m + 1)/2 for k effects and m principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the genetic covariance matrix, via restricted maximum likelihood using derivatives of the likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given. PMID:15588566

A simulation study on Bayesian Ridge regression models for several collinearity levels

NASA Astrophysics Data System (ADS)

Efendi, Achmad; Effrihan

2017-12-01

When analyzing data with multiple regression model if there are collinearities, then one or several predictor variables are usually omitted from the model. However, there sometimes some reasons, for instance medical or economic reasons, the predictors are all important and should be included in the model. Ridge regression model is not uncommon in some researches to use to cope with collinearity. Through this modeling, weights for predictor variables are used for estimating parameters. The next estimation process could follow the concept of likelihood. Furthermore, for the estimation nowadays the Bayesian version could be an alternative. This estimation method does not match likelihood one in terms of popularity due to some difficulties; computation and so forth. Nevertheless, with the growing improvement of computational methodology recently, this caveat should not at the moment become a problem. This paper discusses about simulation process for evaluating the characteristic of Bayesian Ridge regression parameter estimates. There are several simulation settings based on variety of collinearity levels and sample sizes. The results show that Bayesian method gives better performance for relatively small sample sizes, and for other settings the method does perform relatively similar to the likelihood method.

Parameter estimation of history-dependent leaky integrate-and-fire neurons using maximum-likelihood methods

PubMed Central

Dong, Yi; Mihalas, Stefan; Russell, Alexander; Etienne-Cummings, Ralph; Niebur, Ernst

2012-01-01

When a neuronal spike train is observed, what can we say about the properties of the neuron that generated it? A natural way to answer this question is to make an assumption about the type of neuron, select an appropriate model for this type, and then to choose the model parameters as those that are most likely to generate the observed spike train. This is the maximum likelihood method. If the neuron obeys simple integrate and fire dynamics, Paninski, Pillow, and Simoncelli (2004) showed that its negative log-likelihood function is convex and that its unique global minimum can thus be found by gradient descent techniques. The global minimum property requires independence of spike time intervals. Lack of history dependence is, however, an important constraint that is not fulfilled in many biological neurons which are known to generate a rich repertoire of spiking behaviors that are incompatible with history independence. Therefore, we expanded the integrate and fire model by including one additional variable, a variable threshold (Mihalas & Niebur, 2009) allowing for history-dependent firing patterns. This neuronal model produces a large number of spiking behaviors while still being linear. Linearity is important as it maintains the distribution of the random variables and still allows for maximum likelihood methods to be used. In this study we show that, although convexity of the negative log-likelihood is not guaranteed for this model, the minimum of the negative log-likelihood function yields a good estimate for the model parameters, in particular if the noise level is treated as a free parameter. Furthermore, we show that a nonlinear function minimization method (r-algorithm with space dilation) frequently reaches the global minimum. PMID:21851282

An Optimization-based Framework to Learn Conditional Random Fields for Multi-label Classification

PubMed Central

Naeini, Mahdi Pakdaman; Batal, Iyad; Liu, Zitao; Hong, CharmGil; Hauskrecht, Milos

2015-01-01

This paper studies multi-label classification problem in which data instances are associated with multiple, possibly high-dimensional, label vectors. This problem is especially challenging when labels are dependent and one cannot decompose the problem into a set of independent classification problems. To address the problem and properly represent label dependencies we propose and study a pairwise conditional random Field (CRF) model. We develop a new approach for learning the structure and parameters of the CRF from data. The approach maximizes the pseudo likelihood of observed labels and relies on the fast proximal gradient descend for learning the structure and limited memory BFGS for learning the parameters of the model. Empirical results on several datasets show that our approach outperforms several multi-label classification baselines, including recently published state-of-the-art methods. PMID:25927015

Critically evaluating the theory and performance of Bayesian analysis of macroevolutionary mixtures

PubMed Central

Moore, Brian R.; Höhna, Sebastian; May, Michael R.; Rannala, Bruce; Huelsenbeck, John P.

2016-01-01

Bayesian analysis of macroevolutionary mixtures (BAMM) has recently taken the study of lineage diversification by storm. BAMM estimates the diversification-rate parameters (speciation and extinction) for every branch of a study phylogeny and infers the number and location of diversification-rate shifts across branches of a tree. Our evaluation of BAMM reveals two major theoretical errors: (i) the likelihood function (which estimates the model parameters from the data) is incorrect, and (ii) the compound Poisson process prior model (which describes the prior distribution of diversification-rate shifts across branches) is incoherent. Using simulation, we demonstrate that these theoretical issues cause statistical pathologies; posterior estimates of the number of diversification-rate shifts are strongly influenced by the assumed prior, and estimates of diversification-rate parameters are unreliable. Moreover, the inability to correctly compute the likelihood or to correctly specify the prior for rate-variable trees precludes the use of Bayesian approaches for testing hypotheses regarding the number and location of diversification-rate shifts using BAMM. PMID:27512038

Computing Maximum Likelihood Estimates of Loglinear Models from Marginal Sums with Special Attention to Loglinear Item Response Theory. [Project Psychometric Aspects of Item Banking No. 53.] Research Report 91-1.

ERIC Educational Resources Information Center

Kelderman, Henk

In this paper, algorithms are described for obtaining the maximum likelihood estimates of the parameters in log-linear models. Modified versions of the iterative proportional fitting and Newton-Raphson algorithms are described that work on the minimal sufficient statistics rather than on the usual counts in the full contingency table. This is…

Standard and goodness-of-fit parameter estimation methods for the three-parameter lognormal distribution

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

Kane, V.E.

1982-01-01

A class of goodness-of-fit estimators is found to provide a useful alternative in certain situations to the standard maximum likelihood method which has some undesirable estimation characteristics for estimation from the three-parameter lognormal distribution. The class of goodness-of-fit tests considered include the Shapiro-Wilk and Filliben tests which reduce to a weighted linear combination of the order statistics that can be maximized in estimation problems. The weighted order statistic estimators are compared to the standard procedures in Monte Carlo simulations. Robustness of the procedures are examined and example data sets analyzed.

Model-based estimation with boundary side information or boundary regularization [cardiac emission CT].

PubMed

Chiao, P C; Rogers, W L; Fessler, J A; Clinthorne, N H; Hero, A O

1994-01-01

The authors have previously developed a model-based strategy for joint estimation of myocardial perfusion and boundaries using ECT (emission computed tomography). They have also reported difficulties with boundary estimation in low contrast and low count rate situations. Here they propose using boundary side information (obtainable from high resolution MRI and CT images) or boundary regularization to improve both perfusion and boundary estimation in these situations. To fuse boundary side information into the emission measurements, the authors formulate a joint log-likelihood function to include auxiliary boundary measurements as well as ECT projection measurements. In addition, they introduce registration parameters to align auxiliary boundary measurements with ECT measurements and jointly estimate these parameters with other parameters of interest from the composite measurements. In simulated PET O-15 water myocardial perfusion studies using a simplified model, the authors show that the joint estimation improves perfusion estimation performance and gives boundary alignment accuracy of <0.5 mm even at 0.2 million counts. They implement boundary regularization through formulating a penalized log-likelihood function. They also demonstrate in simulations that simultaneous regularization of the epicardial boundary and myocardial thickness gives comparable perfusion estimation accuracy with the use of boundary side information.

Using an EM Covariance Matrix to Estimate Structural Equation Models with Missing Data: Choosing an Adjusted Sample Size to Improve the Accuracy of Inferences

ERIC Educational Resources Information Center

Enders, Craig K.; Peugh, James L.

2004-01-01

Two methods, direct maximum likelihood (ML) and the expectation maximization (EM) algorithm, can be used to obtain ML parameter estimates for structural equation models with missing data (MD). Although the 2 methods frequently produce identical parameter estimates, it may be easier to satisfy missing at random assumptions using EM. However, no…

Multiple-hit parameter estimation in monolithic detectors.

PubMed

Hunter, William C J; Barrett, Harrison H; Lewellen, Tom K; Miyaoka, Robert S

2013-02-01

We examine a maximum-a-posteriori method for estimating the primary interaction position of gamma rays with multiple interaction sites (hits) in a monolithic detector. In assessing the performance of a multiple-hit estimator over that of a conventional one-hit estimator, we consider a few different detector and readout configurations of a 50-mm-wide square cerium-doped lutetium oxyorthosilicate block. For this study, we use simulated data from SCOUT, a Monte-Carlo tool for photon tracking and modeling scintillation- camera output. With this tool, we determine estimate bias and variance for a multiple-hit estimator and compare these with similar metrics for a one-hit maximum-likelihood estimator, which assumes full energy deposition in one hit. We also examine the effect of event filtering on these metrics; for this purpose, we use a likelihood threshold to reject signals that are not likely to have been produced under the assumed likelihood model. Depending on detector design, we observe a 1%-12% improvement of intrinsic resolution for a 1-or-2-hit estimator as compared with a 1-hit estimator. We also observe improved differentiation of photopeak events using a 1-or-2-hit estimator as compared with the 1-hit estimator; more than 6% of photopeak events that were rejected by likelihood filtering for the 1-hit estimator were accurately identified as photopeak events and positioned without loss of resolution by a 1-or-2-hit estimator; for PET, this equates to at least a 12% improvement in coincidence-detection efficiency with likelihood filtering applied.

Task Performance with List-Mode Data

NASA Astrophysics Data System (ADS)

Caucci, Luca

This dissertation investigates the application of list-mode data to detection, estimation, and image reconstruction problems, with an emphasis on emission tomography in medical imaging. We begin by introducing a theoretical framework for list-mode data and we use it to define two observers that operate on list-mode data. These observers are applied to the problem of detecting a signal (known in shape and location) buried in a random lumpy background. We then consider maximum-likelihood methods for the estimation of numerical parameters from list-mode data, and we characterize the performance of these estimators via the so-called Fisher information matrix. Reconstruction from PET list-mode data is then considered. In a process we called "double maximum-likelihood" reconstruction, we consider a simple PET imaging system and we use maximum-likelihood methods to first estimate a parameter vector for each pair of gamma-ray photons that is detected by the hardware. The collection of these parameter vectors forms a list, which is then fed to another maximum-likelihood algorithm for volumetric reconstruction over a grid of voxels. Efficient parallel implementation of the algorithms discussed above is then presented. In this work, we take advantage of two low-cost, mass-produced computing platforms that have recently appeared on the market, and we provide some details on implementing our algorithms on these devices. We conclude this dissertation work by elaborating on a possible application of list-mode data to X-ray digital mammography. We argue that today's CMOS detectors and computing platforms have become fast enough to make X-ray digital mammography list-mode data acquisition and processing feasible.

Factors associated with over-serving at drinking establishments.

PubMed

Buvik, Kristin; Rossow, Ingeborg

2015-04-01

To address characteristics of drinking establishments, bartenders and patrons that may affect the likelihood of over-serving. A systematic examination of 425 purchase attempts with pseudo-intoxicated patrons enacting scripts that, according to the law, should lead to the denial of alcohol sales. Drinking establishments in the three largest cities in Norway (Trondheim, Bergen and Oslo) were visited by male and female actors aged 20-30 years on weekend nights, with a total of 425 purchase items. Over-serving was recorded when the pseudo-intoxicated patron was served alcohol. Characteristics of the drinking establishment, the bartender and the pseudo-intoxicated patron were recorded systematically. Pseudo-intoxicated patrons were served in 347 of 425 purchase attempts (82%). In bivariate analyses, the over-serving rate increased with venue characteristics, music/noise level and intoxication level among patrons. These factors were intercorrelated and correlated with poor lighting. The over-serving rate was also higher when the pseudo-intoxicated patron was female and when the purchase attempt occurred after midnight. In multi-variate analyses, two factors increased the likelihood of over-serving significantly: a high problematic bar indicator score (poor lighting, high music/noise level and high intoxication level among patrons) [adjusted odds ratio (OR) = 3.5, 95% confidence interval (CI) = 1.9, 6.4] and female gender of pseudo-intoxicated patrons (adjusted OR = 2.6, 95% CI = 1.4, 4.7). The rate of over-serving was 95% when both risk factors were present and 67% when both factors were absent. In urban settings in Norway, it is likely that over-serving occurs frequently, and is increased by the risk factors of poor lighting, loud music and high intoxication level among patrons. © 2015 Society for the Study of Addiction.

F-8C adaptive flight control extensions. [for maximum likelihood estimation

NASA Technical Reports Server (NTRS)

Stein, G.; Hartmann, G. L.

1977-01-01

An adaptive concept which combines gain-scheduled control laws with explicit maximum likelihood estimation (MLE) identification to provide the scheduling values is described. The MLE algorithm was improved by incorporating attitude data, estimating gust statistics for setting filter gains, and improving parameter tracking during changing flight conditions. A lateral MLE algorithm was designed to improve true air speed and angle of attack estimates during lateral maneuvers. Relationships between the pitch axis sensors inherent in the MLE design were examined and used for sensor failure detection. Design details and simulation performance are presented for each of the three areas investigated.

Population genetics of polymorphism and divergence for diploid selection models with arbitrary dominance.

PubMed

Williamson, Scott; Fledel-Alon, Adi; Bustamante, Carlos D

2004-09-01

We develop a Poisson random-field model of polymorphism and divergence that allows arbitrary dominance relations in a diploid context. This model provides a maximum-likelihood framework for estimating both selection and dominance parameters of new mutations using information on the frequency spectrum of sequence polymorphisms. This is the first DNA sequence-based estimator of the dominance parameter. Our model also leads to a likelihood-ratio test for distinguishing nongenic from genic selection; simulations indicate that this test is quite powerful when a large number of segregating sites are available. We also use simulations to explore the bias in selection parameter estimates caused by unacknowledged dominance relations. When inference is based on the frequency spectrum of polymorphisms, genic selection estimates of the selection parameter can be very strongly biased even for minor deviations from the genic selection model. Surprisingly, however, when inference is based on polymorphism and divergence (McDonald-Kreitman) data, genic selection estimates of the selection parameter are nearly unbiased, even for completely dominant or recessive mutations. Further, we find that weak overdominant selection can increase, rather than decrease, the substitution rate relative to levels of polymorphism. This nonintuitive result has major implications for the interpretation of several popular tests of neutrality.

Proceedings of the Antenna Applications Symposium (32nd) Held in Monticello, Illinois on 16-18 September 2008. Volume 1

DTIC Science & Technology

2008-12-20

Equation 6 for the sample likelihood function gives a “concentrated likelihood function,” which depends on correlation parameters θh and ph. This...step one and estimates correlation parameters using the new data set including all previous sample points and the new data point x. The algorithm...Unclassified b. ABSTRACT Unclassified c. THIS PAGE Unclassified UU 279 19b. TELEPHONE NUMBER (include area code ) N/A

A composite likelihood approach for spatially correlated survival data

PubMed Central

Paik, Jane; Ying, Zhiliang

2013-01-01

The aim of this paper is to provide a composite likelihood approach to handle spatially correlated survival data using pairwise joint distributions. With e-commerce data, a recent question of interest in marketing research has been to describe spatially clustered purchasing behavior and to assess whether geographic distance is the appropriate metric to describe purchasing dependence. We present a model for the dependence structure of time-to-event data subject to spatial dependence to characterize purchasing behavior from the motivating example from e-commerce data. We assume the Farlie-Gumbel-Morgenstern (FGM) distribution and then model the dependence parameter as a function of geographic and demographic pairwise distances. For estimation of the dependence parameters, we present pairwise composite likelihood equations. We prove that the resulting estimators exhibit key properties of consistency and asymptotic normality under certain regularity conditions in the increasing-domain framework of spatial asymptotic theory. PMID:24223450

A composite likelihood approach for spatially correlated survival data.

PubMed

Paik, Jane; Ying, Zhiliang

2013-01-01

The aim of this paper is to provide a composite likelihood approach to handle spatially correlated survival data using pairwise joint distributions. With e-commerce data, a recent question of interest in marketing research has been to describe spatially clustered purchasing behavior and to assess whether geographic distance is the appropriate metric to describe purchasing dependence. We present a model for the dependence structure of time-to-event data subject to spatial dependence to characterize purchasing behavior from the motivating example from e-commerce data. We assume the Farlie-Gumbel-Morgenstern (FGM) distribution and then model the dependence parameter as a function of geographic and demographic pairwise distances. For estimation of the dependence parameters, we present pairwise composite likelihood equations. We prove that the resulting estimators exhibit key properties of consistency and asymptotic normality under certain regularity conditions in the increasing-domain framework of spatial asymptotic theory.

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

NASA Technical Reports Server (NTRS)

Shantaram, S. Pai; Gyekenyesi, John P.

1989-01-01

The calculation of shape and scale parametes of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by using the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.

Improvement and comparison of likelihood functions for model calibration and parameter uncertainty analysis within a Markov chain Monte Carlo scheme

NASA Astrophysics Data System (ADS)

Cheng, Qin-Bo; Chen, Xi; Xu, Chong-Yu; Reinhardt-Imjela, Christian; Schulte, Achim

2014-11-01

In this study, the likelihood functions for uncertainty analysis of hydrological models are compared and improved through the following steps: (1) the equivalent relationship between the Nash-Sutcliffe Efficiency coefficient (NSE) and the likelihood function with Gaussian independent and identically distributed residuals is proved; (2) a new estimation method of the Box-Cox transformation (BC) parameter is developed to improve the effective elimination of the heteroscedasticity of model residuals; and (3) three likelihood functions-NSE, Generalized Error Distribution with BC (BC-GED) and Skew Generalized Error Distribution with BC (BC-SGED)-are applied for SWAT-WB-VSA (Soil and Water Assessment Tool - Water Balance - Variable Source Area) model calibration in the Baocun watershed, Eastern China. Performances of calibrated models are compared using the observed river discharges and groundwater levels. The result shows that the minimum variance constraint can effectively estimate the BC parameter. The form of the likelihood function significantly impacts on the calibrated parameters and the simulated results of high and low flow components. SWAT-WB-VSA with the NSE approach simulates flood well, but baseflow badly owing to the assumption of Gaussian error distribution, where the probability of the large error is low, but the small error around zero approximates equiprobability. By contrast, SWAT-WB-VSA with the BC-GED or BC-SGED approach mimics baseflow well, which is proved in the groundwater level simulation. The assumption of skewness of the error distribution may be unnecessary, because all the results of the BC-SGED approach are nearly the same as those of the BC-GED approach.

Temporal gravity field modeling based on least square collocation with short-arc approach

NASA Astrophysics Data System (ADS)

ran, jiangjun; Zhong, Min; Xu, Houze; Liu, Chengshu; Tangdamrongsub, Natthachet

2014-05-01

After the launch of the Gravity Recovery And Climate Experiment (GRACE) in 2002, several research centers have attempted to produce the finest gravity model based on different approaches. In this study, we present an alternative approach to derive the Earth's gravity field, and two main objectives are discussed. Firstly, we seek the optimal method to estimate the accelerometer parameters, and secondly, we intend to recover the monthly gravity model based on least square collocation method. The method has been paid less attention compared to the least square adjustment method because of the massive computational resource's requirement. The positions of twin satellites are treated as pseudo-observations and unknown parameters at the same time. The variance covariance matrices of the pseudo-observations and the unknown parameters are valuable information to improve the accuracy of the estimated gravity solutions. Our analyses showed that introducing a drift parameter as an additional accelerometer parameter, compared to using only a bias parameter, leads to a significant improvement of our estimated monthly gravity field. The gravity errors outside the continents are significantly reduced based on the selected set of the accelerometer parameters. We introduced the improved gravity model namely the second version of Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG-CAS 02). The accuracy of IGG-CAS 02 model is comparable to the gravity solutions computed from the Geoforschungszentrum (GFZ), the Center for Space Research (CSR) and the NASA Jet Propulsion Laboratory (JPL). In term of the equivalent water height, the correlation coefficients over the study regions (the Yangtze River valley, the Sahara desert, and the Amazon) among four gravity models are greater than 0.80.

Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model

ERIC Educational Resources Information Center

de la Torre, Jimmy; Stark, Stephen; Chernyshenko, Oleksandr S.

2006-01-01

The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…

Pseudo Bayes Estimates for Test Score Distributions and Chained Equipercentile Equating. Research Report. ETS RR-09-47

ERIC Educational Resources Information Center

Moses, Tim; Oh, Hyeonjoo J.

2009-01-01

Pseudo Bayes probability estimates are weighted averages of raw and modeled probabilities; these estimates have been studied primarily in nonpsychometric contexts. The purpose of this study was to evaluate pseudo Bayes probability estimates as applied to the estimation of psychometric test score distributions and chained equipercentile equating…

An Analysis on a Dynamic Amplifier and Calibration Methods for a Pseudo-Differential Dynamic Comparator

NASA Astrophysics Data System (ADS)

Paik, Daehwa; Miyahara, Masaya; Matsuzawa, Akira

This paper analyzes a pseudo-differential dynamic comparator with a dynamic pre-amplifier. The transient gain of a dynamic pre-amplifier is derived and applied to equations of the thermal noise and the regeneration time of a comparator. This analysis enhances understanding of the roles of transistor's parameters in pre-amplifier's gain. Based on the calculated gain, two calibration methods are also analyzed. One is calibration of a load capacitance and the other is calibration of a bypass current. The analysis helps designers' estimation for the accuracy of calibration, dead-zone of a comparator with a calibration circuit, and the influence of PVT variation. The analyzed comparator uses 90-nm CMOS technology as an example and each estimation is compared with simulation results.

Using the β-binomial distribution to characterize forest health

Treesearch

S.J. Zarnoch; R.L. Anderson; R.M. Sheffield

1995-01-01

The β-binomial distribution is suggested as a model for describing and analyzing the dichotomous data obtained from programs monitoring the health of forests in the United States. Maximum likelihood estimation of the parameters is given as well as asymptotic likelihood ratio tests. The procedure is illustrated with data on dogwood anthracnose infection (caused...

A likelihood-based time series modeling approach for application in dendrochronology to examine the growth-climate relations and forest disturbance history

EPA Science Inventory

A time series intervention analysis (TSIA) of dendrochronological data to infer the tree growth-climate-disturbance relations and forest disturbance history is described. Maximum likelihood is used to estimate the parameters of a structural time series model with components for ...

A New Distribution Family for Microarray Data †

PubMed Central

Kelmansky, Diana Mabel; Ricci, Lila

2017-01-01

The traditional approach with microarray data has been to apply transformations that approximately normalize them, with the drawback of losing the original scale. The alternative standpoint taken here is to search for models that fit the data, characterized by the presence of negative values, preserving their scale; one advantage of this strategy is that it facilitates a direct interpretation of the results. A new family of distributions named gpower-normal indexed by p∈R is introduced and it is proven that these variables become normal or truncated normal when a suitable gpower transformation is applied. Expressions are given for moments and quantiles, in terms of the truncated normal density. This new family can be used to model asymmetric data that include non-positive values, as required for microarray analysis. Moreover, it has been proven that the gpower-normal family is a special case of pseudo-dispersion models, inheriting all the good properties of these models, such as asymptotic normality for small variances. A combined maximum likelihood method is proposed to estimate the model parameters, and it is applied to microarray and contamination data. R codes are available from the authors upon request. PMID:28208652

A New Distribution Family for Microarray Data.

PubMed

Kelmansky, Diana Mabel; Ricci, Lila

2017-02-10

The traditional approach with microarray data has been to apply transformations that approximately normalize them, with the drawback of losing the original scale. The alternative stand point taken here is to search for models that fit the data, characterized by the presence of negative values, preserving their scale; one advantage of this strategy is that it facilitates a direct interpretation of the results. A new family of distributions named gpower-normal indexed by p∈R is introduced and it is proven that these variables become normal or truncated normal when a suitable gpower transformation is applied. Expressions are given for moments and quantiles, in terms of the truncated normal density. This new family can be used to model asymmetric data that include non-positive values, as required for microarray analysis. Moreover, it has been proven that the gpower-normal family is a special case of pseudo-dispersion models, inheriting all the good properties of these models, such as asymptotic normality for small variances. A combined maximum likelihood method is proposed to estimate the model parameters, and it is applied to microarray and contamination data. Rcodes are available from the authors upon request.

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times.

PubMed

dos Reis, Mario; Yang, Ziheng

2011-07-01

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.

Estimation of correlation functions by stochastic approximation.

NASA Technical Reports Server (NTRS)

Habibi, A.; Wintz, P. A.

1972-01-01

Consideration of the autocorrelation function of a zero-mean stationary random process. The techniques are applicable to processes with nonzero mean provided the mean is estimated first and subtracted. Two recursive techniques are proposed, both of which are based on the method of stochastic approximation and assume a functional form for the correlation function that depends on a number of parameters that are recursively estimated from successive records. One technique uses a standard point estimator of the correlation function to provide estimates of the parameters that minimize the mean-square error between the point estimates and the parametric function. The other technique provides estimates of the parameters that maximize a likelihood function relating the parameters of the function to the random process. Examples are presented.

Statistical methods for the beta-binomial model in teratology.

PubMed Central

Yamamoto, E; Yanagimoto, T

1994-01-01

The beta-binomial model is widely used for analyzing teratological data involving littermates. Recent developments in statistical analyses of teratological data are briefly reviewed with emphasis on the model. For statistical inference of the parameters in the beta-binomial distribution, separation of the likelihood introduces an likelihood inference. This leads to reducing biases of estimators and also to improving accuracy of empirical significance levels of tests. Separate inference of the parameters can be conducted in a unified way. PMID:8187716

An Improved Nested Sampling Algorithm for Model Selection and Assessment

NASA Astrophysics Data System (ADS)

Zeng, X.; Ye, M.; Wu, J.; WANG, D.

2017-12-01

Multimodel strategy is a general approach for treating model structure uncertainty in recent researches. The unknown groundwater system is represented by several plausible conceptual models. Each alternative conceptual model is attached with a weight which represents the possibility of this model. In Bayesian framework, the posterior model weight is computed as the product of model prior weight and marginal likelihood (or termed as model evidence). As a result, estimating marginal likelihoods is crucial for reliable model selection and assessment in multimodel analysis. Nested sampling estimator (NSE) is a new proposed algorithm for marginal likelihood estimation. The implementation of NSE comprises searching the parameters' space from low likelihood area to high likelihood area gradually, and this evolution is finished iteratively via local sampling procedure. Thus, the efficiency of NSE is dominated by the strength of local sampling procedure. Currently, Metropolis-Hasting (M-H) algorithm and its variants are often used for local sampling in NSE. However, M-H is not an efficient sampling algorithm for high-dimensional or complex likelihood function. For improving the performance of NSE, it could be feasible to integrate more efficient and elaborated sampling algorithm - DREAMzs into the local sampling. In addition, in order to overcome the computation burden problem of large quantity of repeating model executions in marginal likelihood estimation, an adaptive sparse grid stochastic collocation method is used to build the surrogates for original groundwater model.

Multiple-Hit Parameter Estimation in Monolithic Detectors

PubMed Central

Barrett, Harrison H.; Lewellen, Tom K.; Miyaoka, Robert S.

2014-01-01

We examine a maximum-a-posteriori method for estimating the primary interaction position of gamma rays with multiple interaction sites (hits) in a monolithic detector. In assessing the performance of a multiple-hit estimator over that of a conventional one-hit estimator, we consider a few different detector and readout configurations of a 50-mm-wide square cerium-doped lutetium oxyorthosilicate block. For this study, we use simulated data from SCOUT, a Monte-Carlo tool for photon tracking and modeling scintillation- camera output. With this tool, we determine estimate bias and variance for a multiple-hit estimator and compare these with similar metrics for a one-hit maximum-likelihood estimator, which assumes full energy deposition in one hit. We also examine the effect of event filtering on these metrics; for this purpose, we use a likelihood threshold to reject signals that are not likely to have been produced under the assumed likelihood model. Depending on detector design, we observe a 1%–12% improvement of intrinsic resolution for a 1-or-2-hit estimator as compared with a 1-hit estimator. We also observe improved differentiation of photopeak events using a 1-or-2-hit estimator as compared with the 1-hit estimator; more than 6% of photopeak events that were rejected by likelihood filtering for the 1-hit estimator were accurately identified as photopeak events and positioned without loss of resolution by a 1-or-2-hit estimator; for PET, this equates to at least a 12% improvement in coincidence-detection efficiency with likelihood filtering applied. PMID:23193231

Parameter Estimation in Epidemiology: from Simple to Complex Dynamics

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Ballesteros, Sebastién; Boto, João Pedro; Kooi, Bob W.; Mateus, Luís; Stollenwerk, Nico

2011-09-01

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models like multi-strain dynamics to describe the virus-host interaction in dengue fever, even most recently developed parameter estimation techniques, like maximum likelihood iterated filtering, come to their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

Equivalence between Step Selection Functions and Biased Correlated Random Walks for Statistical Inference on Animal Movement.

PubMed

Duchesne, Thierry; Fortin, Daniel; Rivest, Louis-Paul

2015-01-01

Animal movement has a fundamental impact on population and community structure and dynamics. Biased correlated random walks (BCRW) and step selection functions (SSF) are commonly used to study movements. Because no studies have contrasted the parameters and the statistical properties of their estimators for models constructed under these two Lagrangian approaches, it remains unclear whether or not they allow for similar inference. First, we used the Weak Law of Large Numbers to demonstrate that the log-likelihood function for estimating the parameters of BCRW models can be approximated by the log-likelihood of SSFs. Second, we illustrated the link between the two approaches by fitting BCRW with maximum likelihood and with SSF to simulated movement data in virtual environments and to the trajectory of bison (Bison bison L.) trails in natural landscapes. Using simulated and empirical data, we found that the parameters of a BCRW estimated directly from maximum likelihood and by fitting an SSF were remarkably similar. Movement analysis is increasingly used as a tool for understanding the influence of landscape properties on animal distribution. In the rapidly developing field of movement ecology, management and conservation biologists must decide which method they should implement to accurately assess the determinants of animal movement. We showed that BCRW and SSF can provide similar insights into the environmental features influencing animal movements. Both techniques have advantages. BCRW has already been extended to allow for multi-state modeling. Unlike BCRW, however, SSF can be estimated using most statistical packages, it can simultaneously evaluate habitat selection and movement biases, and can easily integrate a large number of movement taxes at multiple scales. SSF thus offers a simple, yet effective, statistical technique to identify movement taxis.

Variational Bayesian Parameter Estimation Techniques for the General Linear Model

PubMed Central

Starke, Ludger; Ostwald, Dirk

2017-01-01

Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation techniques are rarely covered in introductory statistical texts. Because of the widespread practical use of VB, VML, ReML, and ML in the neuroimaging community, we reasoned that a theoretical treatment of their relationships and their application in a basic modeling scenario may be helpful for both neuroimaging novices and practitioners alike. In this technical study, we thus revisit the conceptual and formal underpinnings of VB, VML, ReML, and ML and provide a detailed account of their mathematical relationships and implementational details. We further apply VB, VML, ReML, and ML to the general linear model (GLM) with non-spherical error covariance as commonly encountered in the first-level analysis of fMRI data. To this end, we explicitly derive the corresponding free energy objective functions and ensuing iterative algorithms. Finally, in the applied part of our study, we evaluate the parameter and model recovery properties of VB, VML, ReML, and ML, first in an exemplary setting and then in the analysis of experimental fMRI data acquired from a single participant under visual stimulation. PMID:28966572

Estimating ambiguity preferences and perceptions in multiple prior models: Evidence from the field.

PubMed

Dimmock, Stephen G; Kouwenberg, Roy; Mitchell, Olivia S; Peijnenburg, Kim

2015-12-01

We develop a tractable method to estimate multiple prior models of decision-making under ambiguity. In a representative sample of the U.S. population, we measure ambiguity attitudes in the gain and loss domains. We find that ambiguity aversion is common for uncertain events of moderate to high likelihood involving gains, but ambiguity seeking prevails for low likelihoods and for losses. We show that choices made under ambiguity in the gain domain are best explained by the α-MaxMin model, with one parameter measuring ambiguity aversion (ambiguity preferences) and a second parameter quantifying the perceived degree of ambiguity (perceptions about ambiguity). The ambiguity aversion parameter α is constant and prior probability sets are asymmetric for low and high likelihood events. The data reject several other models, such as MaxMin and MaxMax, as well as symmetric probability intervals. Ambiguity aversion and the perceived degree of ambiguity are both higher for men and for the college-educated. Ambiguity aversion (but not perceived ambiguity) is also positively related to risk aversion. In the loss domain, we find evidence of reflection, implying that ambiguity aversion for gains tends to reverse into ambiguity seeking for losses. Our model's estimates for preferences and perceptions about ambiguity can be used to analyze the economic and financial implications of such preferences.

The Importance of Behavioral Thresholds and Objective Functions in Contaminant Transport Uncertainty Analysis

NASA Astrophysics Data System (ADS)

Sykes, J. F.; Kang, M.; Thomson, N. R.

2007-12-01

The TCE release from The Lockformer Company in Lisle Illinois resulted in a plume in a confined aquifer that is more than 4 km long and impacted more than 300 residential wells. Many of the wells are on the fringe of the plume and have concentrations that did not exceed 5 ppb. The settlement for the Chapter 11 bankruptcy protection of Lockformer involved the establishment of a trust fund that compensates individuals with cancers with payments being based on cancer type, estimated TCE concentration in the well and the duration of exposure to TCE. The estimation of early arrival times and hence low likelihood events is critical in the determination of the eligibility of an individual for compensation. Thus, an emphasis must be placed on the accuracy of the leading tail region in the likelihood distribution of possible arrival times at a well. The estimation of TCE arrival time, using a three-dimensional analytical solution, involved parameter estimation and uncertainty analysis. Parameters in the model included TCE source parameters, groundwater velocities, dispersivities and the TCE decay coefficient for both the confining layer and the bedrock aquifer. Numerous objective functions, which include the well-known L2-estimator, robust estimators (L1-estimators and M-estimators), penalty functions, and dead zones, were incorporated in the parameter estimation process to treat insufficiencies in both the model and observational data due to errors, biases, and limitations. The concept of equifinality was adopted and multiple maximum likelihood parameter sets were accepted if pre-defined physical criteria were met. The criteria ensured that a valid solution predicted TCE concentrations for all TCE impacted areas. Monte Carlo samples are found to be inadequate for uncertainty analysis of this case study due to its inability to find parameter sets that meet the predefined physical criteria. Successful results are achieved using a Dynamically-Dimensioned Search sampling methodology that inherently accounts for parameter correlations and does not require assumptions regarding parameter distributions. For uncertainty analysis, multiple parameter sets were obtained using a modified Cauchy's M-estimator. Penalty functions had to be incorporated into the objective function definitions to generate a sufficient number of acceptable parameter sets. The combined effect of optimization and the application of the physical criteria perform the function of behavioral thresholds by reducing anomalies and by removing parameter sets with high objective function values. The factors that are important to the creation of an uncertainty envelope for TCE arrival at wells are outlined in the work. In general, greater uncertainty appears to be present at the tails of the distribution. For a refinement of the uncertainty envelopes, the application of additional physical criteria or behavioral thresholds is recommended.

PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS

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

He, Shiyuan; Huang, Jianhua Z.; Long, James

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequencymore » parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period–luminosity relations.« less

Efficient estimation of Pareto model: Some modified percentile estimators.

PubMed

Bhatti, Sajjad Haider; Hussain, Shahzad; Ahmad, Tanvir; Aslam, Muhammad; Aftab, Muhammad; Raza, Muhammad Ali

2018-01-01

The article proposes three modified percentile estimators for parameter estimation of the Pareto distribution. These modifications are based on median, geometric mean and expectation of empirical cumulative distribution function of first-order statistic. The proposed modified estimators are compared with traditional percentile estimators through a Monte Carlo simulation for different parameter combinations with varying sample sizes. Performance of different estimators is assessed in terms of total mean square error and total relative deviation. It is determined that modified percentile estimator based on expectation of empirical cumulative distribution function of first-order statistic provides efficient and precise parameter estimates compared to other estimators considered. The simulation results were further confirmed using two real life examples where maximum likelihood and moment estimators were also considered.

Effects of control inputs on the estimation of stability and control parameters of a light airplane

NASA Technical Reports Server (NTRS)

Cannaday, R. L.; Suit, W. T.

1977-01-01

The maximum likelihood parameter estimation technique was used to determine the values of stability and control derivatives from flight test data for a low-wing, single-engine, light airplane. Several input forms were used during the tests to investigate the consistency of parameter estimates as it relates to inputs. These consistencies were compared by using the ensemble variance and estimated Cramer-Rao lower bound. In addition, the relationship between inputs and parameter correlations was investigated. Results from the stabilator inputs are inconclusive but the sequence of rudder input followed by aileron input or aileron followed by rudder gave more consistent estimates than did rudder or ailerons individually. Also, square-wave inputs appeared to provide slightly improved consistency in the parameter estimates when compared to sine-wave inputs.

The concordance index C and the Mann-Whitney parameter Pr(X>Y) with randomly censored data.

PubMed

Koziol, James A; Jia, Zhenyu

2009-06-01

Harrell's c-index or concordance C has been widely used as a measure of separation of two survival distributions. In the absence of censored data, the c-index estimates the Mann-Whitney parameter Pr(X>Y), which has been repeatedly utilized in various statistical contexts. In the presence of randomly censored data, the c-index no longer estimates Pr(X>Y); rather, a parameter that involves the underlying censoring distributions. This is in contrast to Efron's maximum likelihood estimator of the Mann-Whitney parameter, which is recommended in the setting of random censorship.

A Test-Length Correction to the Estimation of Extreme Proficiency Levels

ERIC Educational Resources Information Center

Magis, David; Beland, Sebastien; Raiche, Gilles

2011-01-01

In this study, the estimation of extremely large or extremely small proficiency levels, given the item parameters of a logistic item response model, is investigated. On one hand, the estimation of proficiency levels by maximum likelihood (ML), despite being asymptotically unbiased, may yield infinite estimates. On the other hand, with an…

Temporal rainfall estimation using input data reduction and model inversion

NASA Astrophysics Data System (ADS)

Wright, A. J.; Vrugt, J. A.; Walker, J. P.; Pauwels, V. R. N.

2016-12-01

Floods are devastating natural hazards. To provide accurate, precise and timely flood forecasts there is a need to understand the uncertainties associated with temporal rainfall and model parameters. The estimation of temporal rainfall and model parameter distributions from streamflow observations in complex dynamic catchments adds skill to current areal rainfall estimation methods, allows for the uncertainty of rainfall input to be considered when estimating model parameters and provides the ability to estimate rainfall from poorly gauged catchments. Current methods to estimate temporal rainfall distributions from streamflow are unable to adequately explain and invert complex non-linear hydrologic systems. This study uses the Discrete Wavelet Transform (DWT) to reduce rainfall dimensionality for the catchment of Warwick, Queensland, Australia. The reduction of rainfall to DWT coefficients allows the input rainfall time series to be simultaneously estimated along with model parameters. The estimation process is conducted using multi-chain Markov chain Monte Carlo simulation with the DREAMZS algorithm. The use of a likelihood function that considers both rainfall and streamflow error allows for model parameter and temporal rainfall distributions to be estimated. Estimation of the wavelet approximation coefficients of lower order decomposition structures was able to estimate the most realistic temporal rainfall distributions. These rainfall estimates were all able to simulate streamflow that was superior to the results of a traditional calibration approach. It is shown that the choice of wavelet has a considerable impact on the robustness of the inversion. The results demonstrate that streamflow data contains sufficient information to estimate temporal rainfall and model parameter distributions. The extent and variance of rainfall time series that are able to simulate streamflow that is superior to that simulated by a traditional calibration approach is a demonstration of equifinality. The use of a likelihood function that considers both rainfall and streamflow error combined with the use of the DWT as a model data reduction technique allows the joint inference of hydrologic model parameters along with rainfall.

An algorithm for computing moments-based flood quantile estimates when historical flood information is available

USGS Publications Warehouse

Cohn, T.A.; Lane, W.L.; Baier, W.G.

1997-01-01

This paper presents the expected moments algorithm (EMA), a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies. EMA can utilize three types of at-site flood information: systematic stream gage record; information about the magnitude of historical floods; and knowledge of the number of years in the historical period when no large flood occurred. EMA employs an iterative procedure to compute method-of-moments parameter estimates. Initial parameter estimates are calculated from systematic stream gage data. These moments are then updated by including the measured historical peaks and the expected moments, given the previously estimated parameters, of the below-threshold floods from the historical period. The updated moments result in new parameter estimates, and the last two steps are repeated until the algorithm converges. Monte Carlo simulations compare EMA, Bulletin 17B's [United States Water Resources Council, 1982] historically weighted moments adjustment, and maximum likelihood estimators when fitting the three parameters of the log-Pearson type III distribution. These simulations demonstrate that EMA is more efficient than the Bulletin 17B method, and that it is nearly as efficient as maximum likelihood estimation (MLE). The experiments also suggest that EMA has two advantages over MLE when dealing with the log-Pearson type III distribution: It appears that EMA estimates always exist and that they are unique, although neither result has been proven. EMA can be used with binomial or interval-censored data and with any distributional family amenable to method-of-moments estimation.

An algorithm for computing moments-based flood quantile estimates when historical flood information is available

NASA Astrophysics Data System (ADS)

Cohn, T. A.; Lane, W. L.; Baier, W. G.

This paper presents the expected moments algorithm (EMA), a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies. EMA can utilize three types of at-site flood information: systematic stream gage record; information about the magnitude of historical floods; and knowledge of the number of years in the historical period when no large flood occurred. EMA employs an iterative procedure to compute method-of-moments parameter estimates. Initial parameter estimates are calculated from systematic stream gage data. These moments are then updated by including the measured historical peaks and the expected moments, given the previously estimated parameters, of the below-threshold floods from the historical period. The updated moments result in new parameter estimates, and the last two steps are repeated until the algorithm converges. Monte Carlo simulations compare EMA, Bulletin 17B's [United States Water Resources Council, 1982] historically weighted moments adjustment, and maximum likelihood estimators when fitting the three parameters of the log-Pearson type III distribution. These simulations demonstrate that EMA is more efficient than the Bulletin 17B method, and that it is nearly as efficient as maximum likelihood estimation (MLE). The experiments also suggest that EMA has two advantages over MLE when dealing with the log-Pearson type III distribution: It appears that EMA estimates always exist and that they are unique, although neither result has been proven. EMA can be used with binomial or interval-censored data and with any distributional family amenable to method-of-moments estimation.

Maximum likelihood-based analysis of single-molecule photon arrival trajectories.

PubMed

Hajdziona, Marta; Molski, Andrzej

2011-02-07

In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 10(3) photons. When the intensity levels are well-separated and 10(4) photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.

cosmoabc: Likelihood-free inference for cosmology

NASA Astrophysics Data System (ADS)

Ishida, Emille E. O.; Vitenti, Sandro D. P.; Penna-Lima, Mariana; Trindade, Arlindo M.; Cisewski, Jessi; M.; de Souza, Rafael; Cameron, Ewan; Busti, Vinicius C.

2015-05-01

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogs. cosmoabc is a Python Approximate Bayesian Computation (ABC) sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code can be coupled to an external simulator to allow incorporation of arbitrary distance and prior functions. When coupled with the numcosmo library, it has been used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function.

A study of parameter identification

NASA Technical Reports Server (NTRS)

Herget, C. J.; Patterson, R. E., III

1978-01-01

A set of definitions for deterministic parameter identification ability were proposed. Deterministic parameter identificability properties are presented based on four system characteristics: direct parameter recoverability, properties of the system transfer function, properties of output distinguishability, and uniqueness properties of a quadratic cost functional. Stochastic parameter identifiability was defined in terms of the existence of an estimation sequence for the unknown parameters which is consistent in probability. Stochastic parameter identifiability properties are presented based on the following characteristics: convergence properties of the maximum likelihood estimate, properties of the joint probability density functions of the observations, and properties of the information matrix.

Inverse statistical estimation via order statistics: a resolution of the ill-posed inverse problem of PERT scheduling

NASA Astrophysics Data System (ADS)

Pickard, William F.

2004-10-01

The classical PERT inverse statistics problem requires estimation of the mean, \\skew1\\bar{m} , and standard deviation, s, of a unimodal distribution given estimates of its mode, m, and of the smallest, a, and largest, b, values likely to be encountered. After placing the problem in historical perspective and showing that it is ill-posed because it is underdetermined, this paper offers an approach to resolve the ill-posedness: (a) by interpreting a and b modes of order statistic distributions; (b) by requiring also an estimate of the number of samples, N, considered in estimating the set {m, a, b}; and (c) by maximizing a suitable likelihood, having made the traditional assumption that the underlying distribution is beta. Exact formulae relating the four parameters of the beta distribution to {m, a, b, N} and the assumed likelihood function are then used to compute the four underlying parameters of the beta distribution; and from them, \\skew1\\bar{m} and s are computed using exact formulae.

Estimation and Identifiability of Model Parameters in Human Nociceptive Processing Using Yes-No Detection Responses to Electrocutaneous Stimulation.

PubMed

Yang, Huan; Meijer, Hil G E; Buitenweg, Jan R; van Gils, Stephan A

2016-01-01

Healthy or pathological states of nociceptive subsystems determine different stimulus-response relations measured from quantitative sensory testing. In turn, stimulus-response measurements may be used to assess these states. In a recently developed computational model, six model parameters characterize activation of nerve endings and spinal neurons. However, both model nonlinearity and limited information in yes-no detection responses to electrocutaneous stimuli challenge to estimate model parameters. Here, we address the question whether and how one can overcome these difficulties for reliable parameter estimation. First, we fit the computational model to experimental stimulus-response pairs by maximizing the likelihood. To evaluate the balance between model fit and complexity, i.e., the number of model parameters, we evaluate the Bayesian Information Criterion. We find that the computational model is better than a conventional logistic model regarding the balance. Second, our theoretical analysis suggests to vary the pulse width among applied stimuli as a necessary condition to prevent structural non-identifiability. In addition, the numerically implemented profile likelihood approach reveals structural and practical non-identifiability. Our model-based approach with integration of psychophysical measurements can be useful for a reliable assessment of states of the nociceptive system.

Modeling, estimation and identification methods for static shape determination of flexible structures. [for large space structure design

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1986-01-01

This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.

Statistical modeling of ecosystem respiration using eddy covariance data: Maximum likelihood parameter estimation, and Monte Carlo simulation of model and parameter uncertainty, applied to three simple models

Treesearch

Andrew D. Richardson; David Y. Hollinger; David Y. Hollinger

2005-01-01

Whether the goal is to fill gaps in the flux record, or to extract physiological parameters from eddy covariance data, researchers are frequently interested in fitting simple models of ecosystem physiology to measured data. Presently, there is no consensus on the best models to use, or the ideal optimization criteria. We demonstrate that, given our estimates of the...

Using genetic data to estimate diffusion rates in heterogeneous landscapes.

PubMed

Roques, L; Walker, E; Franck, P; Soubeyrand, S; Klein, E K

2016-08-01

Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to increase the survival of endangered species. In this paper, we propose a mechanistic-statistical method to estimate space-dependent diffusion parameters of spatially-explicit models based on stochastic differential equations, using genetic data. Dividing the total population into subpopulations corresponding to different habitat patches with known allele frequencies, the expected proportions of individuals from each subpopulation at each position is computed by solving a system of reaction-diffusion equations. Modelling the capture and genotyping of the individuals with a statistical approach, we derive a numerically tractable formula for the likelihood function associated with the diffusion parameters. In a simulated environment made of three types of regions, each associated with a different diffusion coefficient, we successfully estimate the diffusion parameters with a maximum-likelihood approach. Although higher genetic differentiation among subpopulations leads to more accurate estimations, once a certain level of differentiation has been reached, the finite size of the genotyped population becomes the limiting factor for accurate estimation.

Model-based estimation for dynamic cardiac studies using ECT.

PubMed

Chiao, P C; Rogers, W L; Clinthorne, N H; Fessler, J A; Hero, A O

1994-01-01

The authors develop a strategy for joint estimation of physiological parameters and myocardial boundaries using ECT (emission computed tomography). They construct an observation model to relate parameters of interest to the projection data and to account for limited ECT system resolution and measurement noise. The authors then use a maximum likelihood (ML) estimator to jointly estimate all the parameters directly from the projection data without reconstruction of intermediate images. They also simulate myocardial perfusion studies based on a simplified heart model to evaluate the performance of the model-based joint ML estimator and compare this performance to the Cramer-Rao lower bound. Finally, the authors discuss model assumptions and potential uses of the joint estimation strategy.

Additive hazards regression and partial likelihood estimation for ecological monitoring data across space.

PubMed

Lin, Feng-Chang; Zhu, Jun

2012-01-01

We develop continuous-time models for the analysis of environmental or ecological monitoring data such that subjects are observed at multiple monitoring time points across space. Of particular interest are additive hazards regression models where the baseline hazard function can take on flexible forms. We consider time-varying covariates and take into account spatial dependence via autoregression in space and time. We develop statistical inference for the regression coefficients via partial likelihood. Asymptotic properties, including consistency and asymptotic normality, are established for parameter estimates under suitable regularity conditions. Feasible algorithms utilizing existing statistical software packages are developed for computation. We also consider a simpler additive hazards model with homogeneous baseline hazard and develop hypothesis testing for homogeneity. A simulation study demonstrates that the statistical inference using partial likelihood has sound finite-sample properties and offers a viable alternative to maximum likelihood estimation. For illustration, we analyze data from an ecological study that monitors bark beetle colonization of red pines in a plantation of Wisconsin.

Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

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

Hock, Kiel; Earle, Keith

2016-02-06

In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. In conclusion, the posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.

Fast automated analysis of strong gravitational lenses with convolutional neural networks.

PubMed

Hezaveh, Yashar D; Levasseur, Laurence Perreault; Marshall, Philip J

2017-08-30

Quantifying image distortions caused by strong gravitational lensing-the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures-and estimating the corresponding matter distribution of these structures (the 'gravitational lens') has primarily been performed using maximum likelihood modelling of observations. This procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physical processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys. Here we report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis of multi-filter imaging data. Our networks can recover the parameters of the 'singular isothermal ellipsoid' density profile, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

NASA Technical Reports Server (NTRS)

Pai, Shantaram S.; Gyekenyesi, John P.

1988-01-01

The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.

Estimating temporary emigration and breeding proportions using capture-recapture data with Pollock's robust design

USGS Publications Warehouse

Kendall, W.L.; Nichols, J.D.; Hines, J.E.

1997-01-01

Statistical inference for capture-recapture studies of open animal populations typically relies on the assumption that all emigration from the studied population is permanent. However, there are many instances in which this assumption is unlikely to be met. We define two general models for the process of temporary emigration, completely random and Markovian. We then consider effects of these two types of temporary emigration on Jolly-Seber (Seber 1982) estimators and on estimators arising from the full-likelihood approach of Kendall et al. (1995) to robust design data. Capture-recapture data arising from Pollock's (1982) robust design provide the basis for obtaining unbiased estimates of demographic parameters in the presence of temporary emigration and for estimating the probability of temporary emigration. We present a likelihood-based approach to dealing with temporary emigration that permits estimation under different models of temporary emigration and yields tests for completely random and Markovian emigration. In addition, we use the relationship between capture probability estimates based on closed and open models under completely random temporary emigration to derive three ad hoc estimators for the probability of temporary emigration, two of which should be especially useful in situations where capture probabilities are heterogeneous among individual animals. Ad hoc and full-likelihood estimators are illustrated for small mammal capture-recapture data sets. We believe that these models and estimators will be useful for testing hypotheses about the process of temporary emigration, for estimating demographic parameters in the presence of temporary emigration, and for estimating probabilities of temporary emigration. These latter estimates are frequently of ecological interest as indicators of animal movement and, in some sampling situations, as direct estimates of breeding probabilities and proportions.

A single-index threshold Cox proportional hazard model for identifying a treatment-sensitive subset based on multiple biomarkers.

PubMed

He, Ye; Lin, Huazhen; Tu, Dongsheng

2018-06-04

In this paper, we introduce a single-index threshold Cox proportional hazard model to select and combine biomarkers to identify patients who may be sensitive to a specific treatment. A penalized smoothed partial likelihood is proposed to estimate the parameters in the model. A simple, efficient, and unified algorithm is presented to maximize this likelihood function. The estimators based on this likelihood function are shown to be consistent and asymptotically normal. Under mild conditions, the proposed estimators also achieve the oracle property. The proposed approach is evaluated through simulation analyses and application to the analysis of data from two clinical trials, one involving patients with locally advanced or metastatic pancreatic cancer and one involving patients with resectable lung cancer. Copyright © 2018 John Wiley & Sons, Ltd.

A maximum likelihood algorithm for genome mapping of cytogenetic loci from meiotic configuration data.

PubMed Central

Reyes-Valdés, M H; Stelly, D M

1995-01-01

Frequencies of meiotic configurations in cytogenetic stocks are dependent on chiasma frequencies in segments defined by centromeres, breakpoints, and telomeres. The expectation maximization algorithm is proposed as a general method to perform maximum likelihood estimations of the chiasma frequencies in the intervals between such locations. The estimates can be translated via mapping functions into genetic maps of cytogenetic landmarks. One set of observational data was analyzed to exemplify application of these methods, results of which were largely concordant with other comparable data. The method was also tested by Monte Carlo simulation of frequencies of meiotic configurations from a monotelodisomic translocation heterozygote, assuming six different sample sizes. The estimate averages were always close to the values given initially to the parameters. The maximum likelihood estimation procedures can be extended readily to other kinds of cytogenetic stocks and allow the pooling of diverse cytogenetic data to collectively estimate lengths of segments, arms, and chromosomes. Images Fig. 1 PMID:7568226

The effect of high leverage points on the logistic ridge regression estimator having multicollinearity

NASA Astrophysics Data System (ADS)

Ariffin, Syaiba Balqish; Midi, Habshah

2014-06-01

This article is concerned with the performance of logistic ridge regression estimation technique in the presence of multicollinearity and high leverage points. In logistic regression, multicollinearity exists among predictors and in the information matrix. The maximum likelihood estimator suffers a huge setback in the presence of multicollinearity which cause regression estimates to have unduly large standard errors. To remedy this problem, a logistic ridge regression estimator is put forward. It is evident that the logistic ridge regression estimator outperforms the maximum likelihood approach for handling multicollinearity. The effect of high leverage points are then investigated on the performance of the logistic ridge regression estimator through real data set and simulation study. The findings signify that logistic ridge regression estimator fails to provide better parameter estimates in the presence of both high leverage points and multicollinearity.

Stochastic capture zone analysis of an arsenic-contaminated well using the generalized likelihood uncertainty estimator (GLUE) methodology

NASA Astrophysics Data System (ADS)

Morse, Brad S.; Pohll, Greg; Huntington, Justin; Rodriguez Castillo, Ramiro

2003-06-01

In 1992, Mexican researchers discovered concentrations of arsenic in excess of World Heath Organization (WHO) standards in several municipal wells in the Zimapan Valley of Mexico. This study describes a method to delineate a capture zone for one of the most highly contaminated wells to aid in future well siting. A stochastic approach was used to model the capture zone because of the high level of uncertainty in several input parameters. Two stochastic techniques were performed and compared: "standard" Monte Carlo analysis and the generalized likelihood uncertainty estimator (GLUE) methodology. The GLUE procedure differs from standard Monte Carlo analysis in that it incorporates a goodness of fit (termed a likelihood measure) in evaluating the model. This allows for more information (in this case, head data) to be used in the uncertainty analysis, resulting in smaller prediction uncertainty. Two likelihood measures are tested in this study to determine which are in better agreement with the observed heads. While the standard Monte Carlo approach does not aid in parameter estimation, the GLUE methodology indicates best fit models when hydraulic conductivity is approximately 10-6.5 m/s, with vertically isotropic conditions and large quantities of interbasin flow entering the basin. Probabilistic isochrones (capture zone boundaries) are then presented, and as predicted, the GLUE-derived capture zones are significantly smaller in area than those from the standard Monte Carlo approach.

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

Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting

PubMed Central

Zhao, Bo; Setsompop, Kawin; Ye, Huihui; Cauley, Stephen; Wald, Lawrence L.

2017-01-01

This paper introduces a statistical estimation framework for magnetic resonance (MR) fingerprinting, a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood (ML) formalism to estimate multiple parameter maps directly from highly undersampled, noisy k-space data. A novel algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is developed to solve the resulting optimization problem. Representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation, compared to the conventional MR fingerprinting reconstruction. Moreover, the proposed framework provides new theoretical insights into the conventional approach. We show analytically that the conventional approach is an approximation to the ML reconstruction; more precisely, it is exactly equivalent to the first iteration of the proposed algorithm for the ML reconstruction, provided that a gridding reconstruction is used as an initialization. PMID:26915119

Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting.

PubMed

Zhao, Bo; Setsompop, Kawin; Ye, Huihui; Cauley, Stephen F; Wald, Lawrence L

2016-08-01

This paper introduces a statistical estimation framework for magnetic resonance (MR) fingerprinting, a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood (ML) formalism to estimate multiple MR tissue parameter maps directly from highly undersampled, noisy k-space data. A novel algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is developed to solve the resulting optimization problem. Representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation, compared to the conventional MR fingerprinting reconstruction. Moreover, the proposed framework provides new theoretical insights into the conventional approach. We show analytically that the conventional approach is an approximation to the ML reconstruction; more precisely, it is exactly equivalent to the first iteration of the proposed algorithm for the ML reconstruction, provided that a gridding reconstruction is used as an initialization.

Estimation in SEM: A Concrete Example

ERIC Educational Resources Information Center

Ferron, John M.; Hess, Melinda R.

2007-01-01

A concrete example is used to illustrate maximum likelihood estimation of a structural equation model with two unknown parameters. The fitting function is found for the example, as are the vector of first-order partial derivatives, the matrix of second-order partial derivatives, and the estimates obtained from each iteration of the Newton-Raphson…

A new method of differential structural analysis of gamma-family basic parameters

NASA Technical Reports Server (NTRS)

Melkumian, L. G.; Ter-Antonian, S. V.; Smorodin, Y. A.

1985-01-01

The maximum likelihood method is used for the first time to restore parameters of electron photon cascades registered on X-ray films. The method permits one to carry out a structural analysis of the gamma quanta family darkening spots independent of the gamma quanta overlapping degree, and to obtain maximum admissible accuracies in estimating the energies of the gamma quanta composing a family. The parameter estimation accuracy weakly depends on the value of the parameters themselves and exceeds by an order of the values obtained by integral methods.

A MATLAB toolbox for the efficient estimation of the psychometric function using the updated maximum-likelihood adaptive procedure.

PubMed

Shen, Yi; Dai, Wei; Richards, Virginia M

2015-03-01

A MATLAB toolbox for the efficient estimation of the threshold, slope, and lapse rate of the psychometric function is described. The toolbox enables the efficient implementation of the updated maximum-likelihood (UML) procedure. The toolbox uses an object-oriented architecture for organizing the experimental variables and computational algorithms, which provides experimenters with flexibility in experimental design and data management. Descriptions of the UML procedure and the UML Toolbox are provided, followed by toolbox use examples. Finally, guidelines and recommendations of parameter configurations are given.

Mixed effects versus fixed effects modelling of binary data with inter-subject variability.

PubMed

Murphy, Valda; Dunne, Adrian

2005-04-01

The question of whether or not a mixed effects model is required when modelling binary data with inter-subject variability and within subject correlation was reported in this journal by Yano et al. (J. Pharmacokin. Pharmacodyn. 28:389-412 [2001]). That report used simulation experiments to demonstrate that, under certain circumstances, the use of a fixed effects model produced more accurate estimates of the fixed effect parameters than those produced by a mixed effects model. The Laplace approximation to the likelihood was used when fitting the mixed effects model. This paper repeats one of those simulation experiments, with two binary observations recorded for every subject, and uses both the Laplace and the adaptive Gaussian quadrature approximations to the likelihood when fitting the mixed effects model. The results show that the estimates produced using the Laplace approximation include a small number of extreme outliers. This was not the case when using the adaptive Gaussian quadrature approximation. Further examination of these outliers shows that they arise in situations in which the Laplace approximation seriously overestimates the likelihood in an extreme region of the parameter space. It is also demonstrated that when the number of observations per subject is increased from two to three, the estimates based on the Laplace approximation no longer include any extreme outliers. The root mean squared error is a combination of the bias and the variability of the estimates. Increasing the sample size is known to reduce the variability of an estimator with a consequent reduction in its root mean squared error. The estimates based on the fixed effects model are inherently biased and this bias acts as a lower bound for the root mean squared error of these estimates. Consequently, it might be expected that for data sets with a greater number of subjects the estimates based on the mixed effects model would be more accurate than those based on the fixed effects model. This is borne out by the results of a further simulation experiment with an increased number of subjects in each set of data. The difference in the interpretation of the parameters of the fixed and mixed effects models is discussed. It is demonstrated that the mixed effects model and parameter estimates can be used to estimate the parameters of the fixed effects model but not vice versa.

Three methods to construct predictive models using logistic regression and likelihood ratios to facilitate adjustment for pretest probability give similar results.

PubMed

Chan, Siew Foong; Deeks, Jonathan J; Macaskill, Petra; Irwig, Les

2008-01-01

To compare three predictive models based on logistic regression to estimate adjusted likelihood ratios allowing for interdependency between diagnostic variables (tests). This study was a review of the theoretical basis, assumptions, and limitations of published models; and a statistical extension of methods and application to a case study of the diagnosis of obstructive airways disease based on history and clinical examination. Albert's method includes an offset term to estimate an adjusted likelihood ratio for combinations of tests. Spiegelhalter and Knill-Jones method uses the unadjusted likelihood ratio for each test as a predictor and computes shrinkage factors to allow for interdependence. Knottnerus' method differs from the other methods because it requires sequencing of tests, which limits its application to situations where there are few tests and substantial data. Although parameter estimates differed between the models, predicted "posttest" probabilities were generally similar. Construction of predictive models using logistic regression is preferred to the independence Bayes' approach when it is important to adjust for dependency of tests errors. Methods to estimate adjusted likelihood ratios from predictive models should be considered in preference to a standard logistic regression model to facilitate ease of interpretation and application. Albert's method provides the most straightforward approach.

Estimating ambiguity preferences and perceptions in multiple prior models: Evidence from the field

PubMed Central

Dimmock, Stephen G.; Kouwenberg, Roy; Mitchell, Olivia S.; Peijnenburg, Kim

2016-01-01

We develop a tractable method to estimate multiple prior models of decision-making under ambiguity. In a representative sample of the U.S. population, we measure ambiguity attitudes in the gain and loss domains. We find that ambiguity aversion is common for uncertain events of moderate to high likelihood involving gains, but ambiguity seeking prevails for low likelihoods and for losses. We show that choices made under ambiguity in the gain domain are best explained by the α-MaxMin model, with one parameter measuring ambiguity aversion (ambiguity preferences) and a second parameter quantifying the perceived degree of ambiguity (perceptions about ambiguity). The ambiguity aversion parameter α is constant and prior probability sets are asymmetric for low and high likelihood events. The data reject several other models, such as MaxMin and MaxMax, as well as symmetric probability intervals. Ambiguity aversion and the perceived degree of ambiguity are both higher for men and for the college-educated. Ambiguity aversion (but not perceived ambiguity) is also positively related to risk aversion. In the loss domain, we find evidence of reflection, implying that ambiguity aversion for gains tends to reverse into ambiguity seeking for losses. Our model’s estimates for preferences and perceptions about ambiguity can be used to analyze the economic and financial implications of such preferences. PMID:26924890

Calibration of two complex ecosystem models with different likelihood functions

NASA Astrophysics Data System (ADS)

Hidy, Dóra; Haszpra, László; Pintér, Krisztina; Nagy, Zoltán; Barcza, Zoltán

2014-05-01

The biosphere is a sensitive carbon reservoir. Terrestrial ecosystems were approximately carbon neutral during the past centuries, but they became net carbon sinks due to climate change induced environmental change and associated CO2 fertilization effect of the atmosphere. Model studies and measurements indicate that the biospheric carbon sink can saturate in the future due to ongoing climate change which can act as a positive feedback. Robustness of carbon cycle models is a key issue when trying to choose the appropriate model for decision support. The input parameters of the process-based models are decisive regarding the model output. At the same time there are several input parameters for which accurate values are hard to obtain directly from experiments or no local measurements are available. Due to the uncertainty associated with the unknown model parameters significant bias can be experienced if the model is used to simulate the carbon and nitrogen cycle components of different ecosystems. In order to improve model performance the unknown model parameters has to be estimated. We developed a multi-objective, two-step calibration method based on Bayesian approach in order to estimate the unknown parameters of PaSim and Biome-BGC models. Biome-BGC and PaSim are a widely used biogeochemical models that simulate the storage and flux of water, carbon, and nitrogen between the ecosystem and the atmosphere, and within the components of the terrestrial ecosystems (in this research the developed version of Biome-BGC is used which is referred as BBGC MuSo). Both models were calibrated regardless the simulated processes and type of model parameters. The calibration procedure is based on the comparison of measured data with simulated results via calculating a likelihood function (degree of goodness-of-fit between simulated and measured data). In our research different likelihood function formulations were used in order to examine the effect of the different model goodness metric on calibration. The different likelihoods are different functions of RMSE (root mean squared error) weighted by measurement uncertainty: exponential / linear / quadratic / linear normalized by correlation. As a first calibration step sensitivity analysis was performed in order to select the influential parameters which have strong effect on the output data. In the second calibration step only the sensitive parameters were calibrated (optimal values and confidence intervals were calculated). In case of PaSim more parameters were found responsible for the 95% of the output data variance than is case of BBGC MuSo. Analysis of the results of the optimized models revealed that the exponential likelihood estimation proved to be the most robust (best model simulation with optimized parameter, highest confidence interval increase). The cross-validation of the model simulations can help in constraining the highly uncertain greenhouse gas budget of grasslands.

Identification of dynamic systems, theory and formulation

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1985-01-01

The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.

Linkage analysis by genotyping of sibling populations: a genetic map for the potato cyst nematode constructed using a "pseudo-F2" mapping strategy.

PubMed

Rouppe van der Voort, J N; van Eck, H J; van Zandvoort, P M; Overmars, H; Helder, J; Bakker, J

1999-07-01

A mapping strategy is described for the construction of a linkage map of a non-inbred species in which individual offspring genotypes are not amenable to marker analysis. After one extra generation of random mating, the segregating progeny was propagated, and bulked populations of offspring were analyzed. Although the resulting population structure is different from that of commonly used mapping populations, we show that the maximum likelihood formula for a normal F2 is applicable for the estimation of recombination. This "pseudo-F2" mapping strategy, in combination with the development of an AFLP assay for single cysts, facilitated the construction of a linkage map for the potato cyst nematode Globodera rostochiensis. Using 12 pre-selected AFLP primer combinations, a total of 66 segregating markers were identified, 62 of which were mapped to nine linkage groups. These 62 AFLP markers are randomly distributed and cover about 65% of the genome. An estimate of the physical size of the Globodera genome was obtained from comparisons of the number of AFLP fragments obtained with the values for Caenorhabditis elegans. The methodology presented here resulted in the first genomic map for a cyst nematode. The low value of the kilobase/centimorgan (kb/cM) ratio for the Globodera genome will facilitate map-based cloning of genes that mediate the interaction between the nematode and its host plant.

A Variance Distribution Model of Surface EMG Signals Based on Inverse Gamma Distribution.

PubMed

Hayashi, Hideaki; Furui, Akira; Kurita, Yuichi; Tsuji, Toshio

2017-11-01

Objective: This paper describes the formulation of a surface electromyogram (EMG) model capable of representing the variance distribution of EMG signals. Methods: In the model, EMG signals are handled based on a Gaussian white noise process with a mean of zero for each variance value. EMG signal variance is taken as a random variable that follows inverse gamma distribution, allowing the representation of noise superimposed onto this variance. Variance distribution estimation based on marginal likelihood maximization is also outlined in this paper. The procedure can be approximated using rectified and smoothed EMG signals, thereby allowing the determination of distribution parameters in real time at low computational cost. Results: A simulation experiment was performed to evaluate the accuracy of distribution estimation using artificially generated EMG signals, with results demonstrating that the proposed model's accuracy is higher than that of maximum-likelihood-based estimation. Analysis of variance distribution using real EMG data also suggested a relationship between variance distribution and signal-dependent noise. Conclusion: The study reported here was conducted to examine the performance of a proposed surface EMG model capable of representing variance distribution and a related distribution parameter estimation method. Experiments using artificial and real EMG data demonstrated the validity of the model. Significance: Variance distribution estimated using the proposed model exhibits potential in the estimation of muscle force. Objective: This paper describes the formulation of a surface electromyogram (EMG) model capable of representing the variance distribution of EMG signals. Methods: In the model, EMG signals are handled based on a Gaussian white noise process with a mean of zero for each variance value. EMG signal variance is taken as a random variable that follows inverse gamma distribution, allowing the representation of noise superimposed onto this variance. Variance distribution estimation based on marginal likelihood maximization is also outlined in this paper. The procedure can be approximated using rectified and smoothed EMG signals, thereby allowing the determination of distribution parameters in real time at low computational cost. Results: A simulation experiment was performed to evaluate the accuracy of distribution estimation using artificially generated EMG signals, with results demonstrating that the proposed model's accuracy is higher than that of maximum-likelihood-based estimation. Analysis of variance distribution using real EMG data also suggested a relationship between variance distribution and signal-dependent noise. Conclusion: The study reported here was conducted to examine the performance of a proposed surface EMG model capable of representing variance distribution and a related distribution parameter estimation method. Experiments using artificial and real EMG data demonstrated the validity of the model. Significance: Variance distribution estimated using the proposed model exhibits potential in the estimation of muscle force.

Estimation of a Ramsay-Curve Item Response Theory Model by the Metropolis-Hastings Robbins-Monro Algorithm. CRESST Report 834

ERIC Educational Resources Information Center

Monroe, Scott; Cai, Li

2013-01-01

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

Estimation of a Ramsay-Curve Item Response Theory Model by the Metropolis-Hastings Robbins-Monro Algorithm

ERIC Educational Resources Information Center

Monroe, Scott; Cai, Li

2014-01-01

In Ramsay curve item response theory (RC-IRT) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's EM algorithm, which yields maximum marginal likelihood estimates. This method, however, does not produce the…

An Extension of the Partial Credit Model with an Application to the Measurement of Change.

ERIC Educational Resources Information Center

Fischer, Gerhard H.; Ponocny, Ivo

1994-01-01

An extension to the partial credit model, the linear partial credit model, is considered under the assumption of a certain linear decomposition of the item x category parameters into basic parameters. A conditional maximum likelihood algorithm for estimating basic parameters is presented and illustrated with simulation and an empirical study. (SLD)

Genealogical Working Distributions for Bayesian Model Testing with Phylogenetic Uncertainty

PubMed Central

Baele, Guy; Lemey, Philippe; Suchard, Marc A.

2016-01-01

Marginal likelihood estimates to compare models using Bayes factors frequently accompany Bayesian phylogenetic inference. Approaches to estimate marginal likelihoods have garnered increased attention over the past decade. In particular, the introduction of path sampling (PS) and stepping-stone sampling (SS) into Bayesian phylogenetics has tremendously improved the accuracy of model selection. These sampling techniques are now used to evaluate complex evolutionary and population genetic models on empirical data sets, but considerable computational demands hamper their widespread adoption. Further, when very diffuse, but proper priors are specified for model parameters, numerical issues complicate the exploration of the priors, a necessary step in marginal likelihood estimation using PS or SS. To avoid such instabilities, generalized SS (GSS) has recently been proposed, introducing the concept of “working distributions” to facilitate—or shorten—the integration process that underlies marginal likelihood estimation. However, the need to fix the tree topology currently limits GSS in a coalescent-based framework. Here, we extend GSS by relaxing the fixed underlying tree topology assumption. To this purpose, we introduce a “working” distribution on the space of genealogies, which enables estimating marginal likelihoods while accommodating phylogenetic uncertainty. We propose two different “working” distributions that help GSS to outperform PS and SS in terms of accuracy when comparing demographic and evolutionary models applied to synthetic data and real-world examples. Further, we show that the use of very diffuse priors can lead to a considerable overestimation in marginal likelihood when using PS and SS, while still retrieving the correct marginal likelihood using both GSS approaches. The methods used in this article are available in BEAST, a powerful user-friendly software package to perform Bayesian evolutionary analyses. PMID:26526428

Model-based estimation for dynamic cardiac studies using ECT

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

Chiao, P.C.; Rogers, W.L.; Clinthorne, N.H.

1994-06-01

In this paper, the authors develop a strategy for joint estimation of physiological parameters and myocardial boundaries using ECT (Emission Computed Tomography). The authors construct an observation model to relate parameters of interest to the projection data and to account for limited ECT system resolution and measurement noise. The authors then use a maximum likelihood (ML) estimator to jointly estimate all the parameters directly from the projection data without reconstruction of intermediate images. The authors also simulate myocardial perfusion studies based on a simplified heart model to evaluate the performance of the model-based joint ML estimator and compare this performancemore » to the Cramer-Rao lower bound. Finally, model assumptions and potential uses of the joint estimation strategy are discussed.« less

An empirical Bayes approach for the Poisson life distribution.

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1973-01-01

A smooth empirical Bayes estimator is derived for the intensity parameter (hazard rate) in the Poisson distribution as used in life testing. The reliability function is also estimated either by using the empirical Bayes estimate of the parameter, or by obtaining the expectation of the reliability function. The behavior of the empirical Bayes procedure is studied through Monte Carlo simulation in which estimates of mean-squared errors of the empirical Bayes estimators are compared with those of conventional estimators such as minimum variance unbiased or maximum likelihood. Results indicate a significant reduction in mean-squared error of the empirical Bayes estimators over the conventional variety.

Parameter Estimation of a Spiking Silicon Neuron

PubMed Central

Russell, Alexander; Mazurek, Kevin; Mihalaş, Stefan; Niebur, Ernst; Etienne-Cummings, Ralph

2012-01-01

Spiking neuron models are used in a multitude of tasks ranging from understanding neural behavior at its most basic level to neuroprosthetics. Parameter estimation of a single neuron model, such that the model’s output matches that of a biological neuron is an extremely important task. Hand tuning of parameters to obtain such behaviors is a difficult and time consuming process. This is further complicated when the neuron is instantiated in silicon (an attractive medium in which to implement these models) as fabrication imperfections make the task of parameter configuration more complex. In this paper we show two methods to automate the configuration of a silicon (hardware) neuron’s parameters. First, we show how a Maximum Likelihood method can be applied to a leaky integrate and fire silicon neuron with spike induced currents to fit the neuron’s output to desired spike times. We then show how a distance based method which approximates the negative log likelihood of the lognormal distribution can also be used to tune the neuron’s parameters. We conclude that the distance based method is better suited for parameter configuration of silicon neurons due to its superior optimization speed. PMID:23852978

The Extended Erlang-Truncated Exponential distribution: Properties and application to rainfall data.

PubMed

Okorie, I E; Akpanta, A C; Ohakwe, J; Chikezie, D C

2017-06-01

The Erlang-Truncated Exponential ETE distribution is modified and the new lifetime distribution is called the Extended Erlang-Truncated Exponential EETE distribution. Some statistical and reliability properties of the new distribution are given and the method of maximum likelihood estimate was proposed for estimating the model parameters. The usefulness and flexibility of the EETE distribution was illustrated with an uncensored data set and its fit was compared with that of the ETE and three other three-parameter distributions. Results based on the minimized log-likelihood ([Formula: see text]), Akaike information criterion (AIC), Bayesian information criterion (BIC) and the generalized Cramér-von Mises [Formula: see text] statistics shows that the EETE distribution provides a more reasonable fit than the one based on the other competing distributions.

Two-part models with stochastic processes for modelling longitudinal semicontinuous data: Computationally efficient inference and modelling the overall marginal mean.

PubMed

Yiu, Sean; Tom, Brian Dm

2017-01-01

Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with patient-specific random effects. However, in practice, the high dimensional integrations involved in the marginal likelihood (i.e. integrated over the stochastic processes) significantly complicates model fitting. Thus, non-standard computationally intensive procedures based on simulating the marginal likelihood have so far only been proposed. In this paper, we describe an efficient method of implementation by demonstrating how the high dimensional integrations involved in the marginal likelihood can be computed efficiently. Specifically, by using a property of the multivariate normal distribution and the standard marginal cumulative distribution function identity, we transform the marginal likelihood so that the high dimensional integrations are contained in the cumulative distribution function of a multivariate normal distribution, which can then be efficiently evaluated. Hence, maximum likelihood estimation can be used to obtain parameter estimates and asymptotic standard errors (from the observed information matrix) of model parameters. We describe our proposed efficient implementation procedure for the standard two-part model parameterisation and when it is of interest to directly model the overall marginal mean. The methodology is applied on a psoriatic arthritis data set concerning functional disability.

Semiparametric Estimation of the Impacts of Longitudinal Interventions on Adolescent Obesity using Targeted Maximum-Likelihood: Accessible Estimation with the ltmle Package

PubMed Central

Decker, Anna L.; Hubbard, Alan; Crespi, Catherine M.; Seto, Edmund Y.W.; Wang, May C.

2015-01-01

While child and adolescent obesity is a serious public health concern, few studies have utilized parameters based on the causal inference literature to examine the potential impacts of early intervention. The purpose of this analysis was to estimate the causal effects of early interventions to improve physical activity and diet during adolescence on body mass index (BMI), a measure of adiposity, using improved techniques. The most widespread statistical method in studies of child and adolescent obesity is multi-variable regression, with the parameter of interest being the coefficient on the variable of interest. This approach does not appropriately adjust for time-dependent confounding, and the modeling assumptions may not always be met. An alternative parameter to estimate is one motivated by the causal inference literature, which can be interpreted as the mean change in the outcome under interventions to set the exposure of interest. The underlying data-generating distribution, upon which the estimator is based, can be estimated via a parametric or semi-parametric approach. Using data from the National Heart, Lung, and Blood Institute Growth and Health Study, a 10-year prospective cohort study of adolescent girls, we estimated the longitudinal impact of physical activity and diet interventions on 10-year BMI z-scores via a parameter motivated by the causal inference literature, using both parametric and semi-parametric estimation approaches. The parameters of interest were estimated with a recently released R package, ltmle, for estimating means based upon general longitudinal treatment regimes. We found that early, sustained intervention on total calories had a greater impact than a physical activity intervention or non-sustained interventions. Multivariable linear regression yielded inflated effect estimates compared to estimates based on targeted maximum-likelihood estimation and data-adaptive super learning. Our analysis demonstrates that sophisticated, optimal semiparametric estimation of longitudinal treatment-specific means via ltmle provides an incredibly powerful, yet easy-to-use tool, removing impediments for putting theory into practice. PMID:26046009

Univariate and bivariate likelihood-based meta-analysis methods performed comparably when marginal sensitivity and specificity were the targets of inference.

PubMed

Dahabreh, Issa J; Trikalinos, Thomas A; Lau, Joseph; Schmid, Christopher H

2017-03-01

To compare statistical methods for meta-analysis of sensitivity and specificity of medical tests (e.g., diagnostic or screening tests). We constructed a database of PubMed-indexed meta-analyses of test performance from which 2 × 2 tables for each included study could be extracted. We reanalyzed the data using univariate and bivariate random effects models fit with inverse variance and maximum likelihood methods. Analyses were performed using both normal and binomial likelihoods to describe within-study variability. The bivariate model using the binomial likelihood was also fit using a fully Bayesian approach. We use two worked examples-thoracic computerized tomography to detect aortic injury and rapid prescreening of Papanicolaou smears to detect cytological abnormalities-to highlight that different meta-analysis approaches can produce different results. We also present results from reanalysis of 308 meta-analyses of sensitivity and specificity. Models using the normal approximation produced sensitivity and specificity estimates closer to 50% and smaller standard errors compared to models using the binomial likelihood; absolute differences of 5% or greater were observed in 12% and 5% of meta-analyses for sensitivity and specificity, respectively. Results from univariate and bivariate random effects models were similar, regardless of estimation method. Maximum likelihood and Bayesian methods produced almost identical summary estimates under the bivariate model; however, Bayesian analyses indicated greater uncertainty around those estimates. Bivariate models produced imprecise estimates of the between-study correlation of sensitivity and specificity. Differences between methods were larger with increasing proportion of studies that were small or required a continuity correction. The binomial likelihood should be used to model within-study variability. Univariate and bivariate models give similar estimates of the marginal distributions for sensitivity and specificity. Bayesian methods fully quantify uncertainty and their ability to incorporate external evidence may be useful for imprecisely estimated parameters. Copyright © 2017 Elsevier Inc. All rights reserved.

Theoretical performance analysis of doped optical fibers based on pseudo parameters

NASA Astrophysics Data System (ADS)

Karimi, Maryam; Seraji, Faramarz E.

2010-09-01

Characterization of doped optical fibers (DOFs) is an essential primary stage for design of DOF-based devices. This paper presents design of novel measurement techniques to determine DOFs parameters using mono-beam propagation in a low-loss medium by generating pseudo parameters for the DOFs. The designed techniques are able to characterize simultaneously the absorption, emission cross-sections (ACS and ECS), and dopant concentration of DOFs. In both the proposed techniques, we assume pseudo parameters for the DOFs instead of their actual values and show that the choice of these pseudo parameters values for design of DOF-based devices, such as erbium-doped fiber amplifier (EDFA), are appropriate and the resulting error is quite negligible when compared with the actual parameters values.Utilization of pseudo ACS and ECS values in design procedure of EDFAs does not require the measurement of background loss coefficient (BLC) and makes the rate equation of the DOFs simple. It is shown that by using the pseudo parameters values obtained by the proposed techniques, the error in the gain of a designed EDFA with a BLC of about 1 dB/km, are about 0.08 dB. It is further indicated that the same scenario holds good for BLC lower than 5 dB/m and higher than 12 dB/m. The proposed characterization techniques have simple procedures and are low cost that can have an advantageous use in manufacturing of the DOFs.

Optimal HRF and smoothing parameters for fMRI time series within an autoregressive modeling framework.

PubMed

Galka, Andreas; Siniatchkin, Michael; Stephani, Ulrich; Groening, Kristina; Wolff, Stephan; Bosch-Bayard, Jorge; Ozaki, Tohru

2010-12-01

The analysis of time series obtained by functional magnetic resonance imaging (fMRI) may be approached by fitting predictive parametric models, such as nearest-neighbor autoregressive models with exogeneous input (NNARX). As a part of the modeling procedure, it is possible to apply instantaneous linear transformations to the data. Spatial smoothing, a common preprocessing step, may be interpreted as such a transformation. The autoregressive parameters may be constrained, such that they provide a response behavior that corresponds to the canonical haemodynamic response function (HRF). We present an algorithm for estimating the parameters of the linear transformations and of the HRF within a rigorous maximum-likelihood framework. Using this approach, an optimal amount of both the spatial smoothing and the HRF can be estimated simultaneously for a given fMRI data set. An example from a motor-task experiment is discussed. It is found that, for this data set, weak, but non-zero, spatial smoothing is optimal. Furthermore, it is demonstrated that activated regions can be estimated within the maximum-likelihood framework.

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, Jiangjiang; Zeng, Lingzao; Chen, Cheng; Chen, Dingjiang; Wu, Laosheng

2015-01-01

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameters identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from concentration measurements in identifying unknown parameters. In this approach, the sampling locations that give the maximum expected relative entropy are selected as the optimal design. After the sampling locations are determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport equation. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. It is shown that the methods can be used to assist in both single sampling location and monitoring network design for contaminant source identifications in groundwater.

Bayesian Assessment of the Uncertainties of Estimates of a Conceptual Rainfall-Runoff Model Parameters

NASA Astrophysics Data System (ADS)

Silva, F. E. O. E.; Naghettini, M. D. C.; Fernandes, W.

2014-12-01

This paper evaluated the uncertainties associated with the estimation of the parameters of a conceptual rainfall-runoff model, through the use of Bayesian inference techniques by Monte Carlo simulation. The Pará River sub-basin, located in the upper São Francisco river basin, in southeastern Brazil, was selected for developing the studies. In this paper, we used the Rio Grande conceptual hydrologic model (EHR/UFMG, 2001) and the Markov Chain Monte Carlo simulation method named DREAM (VRUGT, 2008a). Two probabilistic models for the residues were analyzed: (i) the classic [Normal likelihood - r ≈ N (0, σ²)]; and (ii) a generalized likelihood (SCHOUPS & VRUGT, 2010), in which it is assumed that the differences between observed and simulated flows are correlated, non-stationary, and distributed as a Skew Exponential Power density. The assumptions made for both models were checked to ensure that the estimation of uncertainties in the parameters was not biased. The results showed that the Bayesian approach proved to be adequate to the proposed objectives, enabling and reinforcing the importance of assessing the uncertainties associated with hydrological modeling.

Maximum likelihood orientation estimation of 1-D patterns in Laguerre-Gauss subspaces.

PubMed

Di Claudio, Elio D; Jacovitti, Giovanni; Laurenti, Alberto

2010-05-01

A method for measuring the orientation of linear (1-D) patterns, based on a local expansion with Laguerre-Gauss circular harmonic (LG-CH) functions, is presented. It lies on the property that the polar separable LG-CH functions span the same space as the 2-D Cartesian separable Hermite-Gauss (2-D HG) functions. Exploiting the simple steerability of the LG-CH functions and the peculiar block-linear relationship among the two expansion coefficients sets, maximum likelihood (ML) estimates of orientation and cross section parameters of 1-D patterns are obtained projecting them in a proper subspace of the 2-D HG family. It is shown in this paper that the conditional ML solution, derived by elimination of the cross section parameters, surprisingly yields the same asymptotic accuracy as the ML solution for known cross section parameters. The accuracy of the conditional ML estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials. A thorough proof of the key relationship between the LG-CH and the 2-D HG expansions is also provided.

Experimental Design for Parameter Estimation of Gene Regulatory Networks

PubMed Central

Timmer, Jens

2012-01-01

Systems biology aims for building quantitative models to address unresolved issues in molecular biology. In order to describe the behavior of biological cells adequately, gene regulatory networks (GRNs) are intensively investigated. As the validity of models built for GRNs depends crucially on the kinetic rates, various methods have been developed to estimate these parameters from experimental data. For this purpose, it is favorable to choose the experimental conditions yielding maximal information. However, existing experimental design principles often rely on unfulfilled mathematical assumptions or become computationally demanding with growing model complexity. To solve this problem, we combined advanced methods for parameter and uncertainty estimation with experimental design considerations. As a showcase, we optimized three simulated GRNs in one of the challenges from the Dialogue for Reverse Engineering Assessment and Methods (DREAM). This article presents our approach, which was awarded the best performing procedure at the DREAM6 Estimation of Model Parameters challenge. For fast and reliable parameter estimation, local deterministic optimization of the likelihood was applied. We analyzed identifiability and precision of the estimates by calculating the profile likelihood. Furthermore, the profiles provided a way to uncover a selection of most informative experiments, from which the optimal one was chosen using additional criteria at every step of the design process. In conclusion, we provide a strategy for optimal experimental design and show its successful application on three highly nonlinear dynamic models. Although presented in the context of the GRNs to be inferred for the DREAM6 challenge, the approach is generic and applicable to most types of quantitative models in systems biology and other disciplines. PMID:22815723

The Least-Squares Estimation of Latent Trait Variables.

ERIC Educational Resources Information Center

Tatsuoka, Kikumi

This paper presents a new method for estimating a given latent trait variable by the least-squares approach. The beta weights are obtained recursively with the help of Fourier series and expressed as functions of item parameters of response curves. The values of the latent trait variable estimated by this method and by maximum likelihood method…

Competing risk models in reliability systems, a weibull distribution model with bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, Ismed; Satria Gondokaryono, Yudi

2016-02-01

In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range between the true value and the maximum likelihood estimated value lines.

A Note on the Computation of the Second-Order Derivatives of the Elementary Symmetric Functions in the Rasch Model.

ERIC Educational Resources Information Center

Formann, Anton K.

1986-01-01

It is shown that for equal parameters explicit formulas exist, facilitating the application of the Newton-Raphson procedure to estimate the parameters in the Rasch model and related models according to the conditional maximum likelihood principle. (Author/LMO)

INFERRING THE ECCENTRICITY DISTRIBUTION

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

Hogg, David W.; Bovy, Jo; Myers, Adam D., E-mail: david.hogg@nyu.ed

2010-12-20

Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. Here, we develop and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, inferring the true eccentricity distribution, taking as input the likelihood functions for the individual star eccentricities, or samplings of the posterior probability distributions for the eccentricities (under a given, uninformative prior). The method is a simple implementationmore » of a hierarchical Bayesian model; it can also be seen as a kind of heteroscedastic deconvolution. It can be applied to any quantity measured with finite precision-other orbital parameters, or indeed any astronomical measurements of any kind, including magnitudes, distances, or photometric redshifts-so long as the measurements have been communicated as a likelihood function or a posterior sampling.« less

Methods for estimating drought streamflow probabilities for Virginia streams

USGS Publications Warehouse

Austin, Samuel H.

2014-01-01

Maximum likelihood logistic regression model equations used to estimate drought flow probabilities for Virginia streams are presented for 259 hydrologic basins in Virginia. Winter streamflows were used to estimate the likelihood of streamflows during the subsequent drought-prone summer months. The maximum likelihood logistic regression models identify probable streamflows from 5 to 8 months in advance. More than 5 million streamflow daily values collected over the period of record (January 1, 1900 through May 16, 2012) were compiled and analyzed over a minimum 10-year (maximum 112-year) period of record. The analysis yielded the 46,704 equations with statistically significant fit statistics and parameter ranges published in two tables in this report. These model equations produce summer month (July, August, and September) drought flow threshold probabilities as a function of streamflows during the previous winter months (November, December, January, and February). Example calculations are provided, demonstrating how to use the equations to estimate probable streamflows as much as 8 months in advance.

Fast automated analysis of strong gravitational lenses with convolutional neural networks

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

Hezaveh, Yashar D.; Levasseur, Laurence Perreault; Marshall, Philip J.

Quantifying image distortions caused by strong gravitational lensing—the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures—and estimating the corresponding matter distribution of these structures (the ‘gravitational lens’) has primarily been performed using maximum likelihood modelling of observations. Our procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physicalmore » processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys. We report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis of multi-filter imaging data. Our networks can recover the parameters of the ‘singular isothermal ellipsoid’ density profile, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.« less

Fast automated analysis of strong gravitational lenses with convolutional neural networks

DOE PAGES

Hezaveh, Yashar D.; Levasseur, Laurence Perreault; Marshall, Philip J.

2017-08-30

Quantifying image distortions caused by strong gravitational lensing—the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures—and estimating the corresponding matter distribution of these structures (the ‘gravitational lens’) has primarily been performed using maximum likelihood modelling of observations. Our procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physicalmore » processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys. We report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis of multi-filter imaging data. Our networks can recover the parameters of the ‘singular isothermal ellipsoid’ density profile, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.« less

Fast automated analysis of strong gravitational lenses with convolutional neural networks

NASA Astrophysics Data System (ADS)

Hezaveh, Yashar D.; Levasseur, Laurence Perreault; Marshall, Philip J.

2017-08-01

Quantifying image distortions caused by strong gravitational lensing—the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures—and estimating the corresponding matter distribution of these structures (the ‘gravitational lens’) has primarily been performed using maximum likelihood modelling of observations. This procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physical processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys. Here we report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis of multi-filter imaging data. Our networks can recover the parameters of the ‘singular isothermal ellipsoid’ density profile, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.

Probabilistic treatment of the uncertainty from the finite size of weighted Monte Carlo data

NASA Astrophysics Data System (ADS)

Glüsenkamp, Thorsten

2018-06-01

Parameter estimation in HEP experiments often involves Monte Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization schemes with a new simulation set for each parameter value. Problematically, the finite size of such Monte Carlo samples carries intrinsic uncertainty that can lead to a substantial bias in parameter estimation if it is neglected and the sample size is small. We introduce a probabilistic treatment of this problem by replacing the usual likelihood functions with novel generalized probability distributions that incorporate the finite statistics via suitable marginalization. These new PDFs are analytic, and can be used to replace the Poisson, multinomial, and sample-based unbinned likelihoods, which covers many use cases in high-energy physics. In the limit of infinite statistics, they reduce to the respective standard probability distributions. In the general case of arbitrary Monte Carlo weights, the expressions involve the fourth Lauricella function FD, for which we find a new finite-sum representation in a certain parameter setting. The result also represents an exact form for Carlson's Dirichlet average Rn with n > 0, and thereby an efficient way to calculate the probability generating function of the Dirichlet-multinomial distribution, the extended divided difference of a monomial, or arbitrary moments of univariate B-splines. We demonstrate the bias reduction of our approach with a typical toy Monte Carlo problem, estimating the normalization of a peak in a falling energy spectrum, and compare the results with previously published methods from the literature.

A new peak detection algorithm for MALDI mass spectrometry data based on a modified Asymmetric Pseudo-Voigt model.

PubMed

Wijetunge, Chalini D; Saeed, Isaam; Boughton, Berin A; Roessner, Ute; Halgamuge, Saman K

2015-01-01

Mass Spectrometry (MS) is a ubiquitous analytical tool in biological research and is used to measure the mass-to-charge ratio of bio-molecules. Peak detection is the essential first step in MS data analysis. Precise estimation of peak parameters such as peak summit location and peak area are critical to identify underlying bio-molecules and to estimate their abundances accurately. We propose a new method to detect and quantify peaks in mass spectra. It uses dual-tree complex wavelet transformation along with Stein's unbiased risk estimator for spectra smoothing. Then, a new method, based on the modified Asymmetric Pseudo-Voigt (mAPV) model and hierarchical particle swarm optimization, is used for peak parameter estimation. Using simulated data, we demonstrated the benefit of using the mAPV model over Gaussian, Lorentz and Bi-Gaussian functions for MS peak modelling. The proposed mAPV model achieved the best fitting accuracy for asymmetric peaks, with lower percentage errors in peak summit location estimation, which were 0.17% to 4.46% less than that of the other models. It also outperformed the other models in peak area estimation, delivering lower percentage errors, which were about 0.7% less than its closest competitor - the Bi-Gaussian model. In addition, using data generated from a MALDI-TOF computer model, we showed that the proposed overall algorithm outperformed the existing methods mainly in terms of sensitivity. It achieved a sensitivity of 85%, compared to 77% and 71% of the two benchmark algorithms, continuous wavelet transformation based method and Cromwell respectively. The proposed algorithm is particularly useful for peak detection and parameter estimation in MS data with overlapping peak distributions and asymmetric peaks. The algorithm is implemented using MATLAB and the source code is freely available at http://mapv.sourceforge.net.

A new peak detection algorithm for MALDI mass spectrometry data based on a modified Asymmetric Pseudo-Voigt model

PubMed Central

2015-01-01

Background Mass Spectrometry (MS) is a ubiquitous analytical tool in biological research and is used to measure the mass-to-charge ratio of bio-molecules. Peak detection is the essential first step in MS data analysis. Precise estimation of peak parameters such as peak summit location and peak area are critical to identify underlying bio-molecules and to estimate their abundances accurately. We propose a new method to detect and quantify peaks in mass spectra. It uses dual-tree complex wavelet transformation along with Stein's unbiased risk estimator for spectra smoothing. Then, a new method, based on the modified Asymmetric Pseudo-Voigt (mAPV) model and hierarchical particle swarm optimization, is used for peak parameter estimation. Results Using simulated data, we demonstrated the benefit of using the mAPV model over Gaussian, Lorentz and Bi-Gaussian functions for MS peak modelling. The proposed mAPV model achieved the best fitting accuracy for asymmetric peaks, with lower percentage errors in peak summit location estimation, which were 0.17% to 4.46% less than that of the other models. It also outperformed the other models in peak area estimation, delivering lower percentage errors, which were about 0.7% less than its closest competitor - the Bi-Gaussian model. In addition, using data generated from a MALDI-TOF computer model, we showed that the proposed overall algorithm outperformed the existing methods mainly in terms of sensitivity. It achieved a sensitivity of 85%, compared to 77% and 71% of the two benchmark algorithms, continuous wavelet transformation based method and Cromwell respectively. Conclusions The proposed algorithm is particularly useful for peak detection and parameter estimation in MS data with overlapping peak distributions and asymmetric peaks. The algorithm is implemented using MATLAB and the source code is freely available at http://mapv.sourceforge.net. PMID:26680279

Models and analysis for multivariate failure time data

NASA Astrophysics Data System (ADS)

Shih, Joanna Huang

The goal of this research is to develop and investigate models and analytic methods for multivariate failure time data. We compare models in terms of direct modeling of the margins, flexibility of dependency structure, local vs. global measures of association, and ease of implementation. In particular, we study copula models, and models produced by right neutral cumulative hazard functions and right neutral hazard functions. We examine the changes of association over time for families of bivariate distributions induced from these models by displaying their density contour plots, conditional density plots, correlation curves of Doksum et al, and local cross ratios of Oakes. We know that bivariate distributions with same margins might exhibit quite different dependency structures. In addition to modeling, we study estimation procedures. For copula models, we investigate three estimation procedures. the first procedure is full maximum likelihood. The second procedure is two-stage maximum likelihood. At stage 1, we estimate the parameters in the margins by maximizing the marginal likelihood. At stage 2, we estimate the dependency structure by fixing the margins at the estimated ones. The third procedure is two-stage partially parametric maximum likelihood. It is similar to the second procedure, but we estimate the margins by the Kaplan-Meier estimate. We derive asymptotic properties for these three estimation procedures and compare their efficiency by Monte-Carlo simulations and direct computations. For models produced by right neutral cumulative hazards and right neutral hazards, we derive the likelihood and investigate the properties of the maximum likelihood estimates. Finally, we develop goodness of fit tests for the dependency structure in the copula models. We derive a test statistic and its asymptotic properties based on the test of homogeneity of Zelterman and Chen (1988), and a graphical diagnostic procedure based on the empirical Bayes approach. We study the performance of these two methods using actual and computer generated data.

Detection and Parameter Estimation of Chirped Radar Signals.

DTIC Science & Technology

2000-01-10

Wigner - Ville distribution ( WVD ): The WVD belongs to the Cohen’s class of energy distributions ...length. 28 6. Pseudo Wigner - Ville distribution (PWVD): The PWVD introduces a time-window to the WVD definition, thereby reducing the interferences...Frequency normalized to sampling frequency 26 Figure V.2: Wigner - Ville distribution ; time normalized to the pulse length 28 Figure V.3:

Quantifying uncertainties in streamflow predictions through signature based inference of hydrological model parameters

NASA Astrophysics Data System (ADS)

Fenicia, Fabrizio; Reichert, Peter; Kavetski, Dmitri; Albert, Calro

2016-04-01

The calibration of hydrological models based on signatures (e.g. Flow Duration Curves - FDCs) is often advocated as an alternative to model calibration based on the full time series of system responses (e.g. hydrographs). Signature based calibration is motivated by various arguments. From a conceptual perspective, calibration on signatures is a way to filter out errors that are difficult to represent when calibrating on the full time series. Such errors may for example occur when observed and simulated hydrographs are shifted, either on the "time" axis (i.e. left or right), or on the "streamflow" axis (i.e. above or below). These shifts may be due to errors in the precipitation input (time or amount), and if not properly accounted in the likelihood function, may cause biased parameter estimates (e.g. estimated model parameters that do not reproduce the recession characteristics of a hydrograph). From a practical perspective, signature based calibration is seen as a possible solution for making predictions in ungauged basins. Where streamflow data are not available, it may in fact be possible to reliably estimate streamflow signatures. Previous research has for example shown how FDCs can be reliably estimated at ungauged locations based on climatic and physiographic influence factors. Typically, the goal of signature based calibration is not the prediction of the signatures themselves, but the prediction of the system responses. Ideally, the prediction of system responses should be accompanied by a reliable quantification of the associated uncertainties. Previous approaches for signature based calibration, however, do not allow reliable estimates of streamflow predictive distributions. Here, we illustrate how the Bayesian approach can be employed to obtain reliable streamflow predictive distributions based on signatures. A case study is presented, where a hydrological model is calibrated on FDCs and additional signatures. We propose an approach where the likelihood function for the signatures is derived from the likelihood for streamflow (rather than using an "ad-hoc" likelihood for the signatures as done in previous approaches). This likelihood is not easily tractable analytically and we therefore cannot apply "simple" MCMC methods. This numerical problem is solved using Approximate Bayesian Computation (ABC). Our result indicate that the proposed approach is suitable for producing reliable streamflow predictive distributions based on calibration to signature data. Moreover, our results provide indications on which signatures are more appropriate to represent the information content of the hydrograph.

Estimating the Parameters of the Beta-Binomial Distribution.

ERIC Educational Resources Information Center

Wilcox, Rand R.

1979-01-01

For some situations the beta-binomial distribution might be used to describe the marginal distribution of test scores for a particular population of examinees. Several different methods of approximating the maximum likelihood estimate were investigated, and it was found that the Newton-Raphson method should be used when it yields admissable…

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)

Estimation of the sea surface's two-scale backscatter parameters

NASA Technical Reports Server (NTRS)

Wentz, F. J.

1978-01-01

The relationship between the sea-surface normalized radar cross section and the friction velocity vector is determined using a parametric two-scale scattering model. The model parameters are found from a nonlinear maximum likelihood estimation. The estimation is based on aircraft scatterometer measurements and the sea-surface anemometer measurements collected during the JONSWAP '75 experiment. The estimates of the ten model parameters converge to realistic values that are in good agreement with the available oceanographic data. The rms discrepancy between the model and the cross section measurements is 0.7 db, which is the rms sum of a 0.3 db average measurement error and a 0.6 db modeling error.

Robust geostatistical analysis of spatial data

NASA Astrophysics Data System (ADS)

Papritz, Andreas; Künsch, Hans Rudolf; Schwierz, Cornelia; Stahel, Werner A.

2013-04-01

Most of the geostatistical software tools rely on non-robust algorithms. This is unfortunate, because outlying observations are rather the rule than the exception, in particular in environmental data sets. Outliers affect the modelling of the large-scale spatial trend, the estimation of the spatial dependence of the residual variation and the predictions by kriging. Identifying outliers manually is cumbersome and requires expertise because one needs parameter estimates to decide which observation is a potential outlier. Moreover, inference after the rejection of some observations is problematic. A better approach is to use robust algorithms that prevent automatically that outlying observations have undue influence. Former studies on robust geostatistics focused on robust estimation of the sample variogram and ordinary kriging without external drift. Furthermore, Richardson and Welsh (1995) proposed a robustified version of (restricted) maximum likelihood ([RE]ML) estimation for the variance components of a linear mixed model, which was later used by Marchant and Lark (2007) for robust REML estimation of the variogram. We propose here a novel method for robust REML estimation of the variogram of a Gaussian random field that is possibly contaminated by independent errors from a long-tailed distribution. It is based on robustification of estimating equations for the Gaussian REML estimation (Welsh and Richardson, 1997). Besides robust estimates of the parameters of the external drift and of the variogram, the method also provides standard errors for the estimated parameters, robustified kriging predictions at both sampled and non-sampled locations and kriging variances. Apart from presenting our modelling framework, we shall present selected simulation results by which we explored the properties of the new method. This will be complemented by an analysis a data set on heavy metal contamination of the soil in the vicinity of a metal smelter. Marchant, B.P. and Lark, R.M. 2007. Robust estimation of the variogram by residual maximum likelihood. Geoderma 140: 62-72. Richardson, A.M. and Welsh, A.H. 1995. Robust restricted maximum likelihood in mixed linear models. Biometrics 51: 1429-1439. Welsh, A.H. and Richardson, A.M. 1997. Approaches to the robust estimation of mixed models. In: Handbook of Statistics Vol. 15, Elsevier, pp. 343-384.

Three-dimensional whole-brain perfusion quantification using pseudo-continuous arterial spin labeling MRI at multiple post-labeling delays: accounting for both arterial transit time and impulse response function.

PubMed

Qin, Qin; Huang, Alan J; Hua, Jun; Desmond, John E; Stevens, Robert D; van Zijl, Peter C M

2014-02-01

Measurement of the cerebral blood flow (CBF) with whole-brain coverage is challenging in terms of both acquisition and quantitative analysis. In order to fit arterial spin labeling-based perfusion kinetic curves, an empirical three-parameter model which characterizes the effective impulse response function (IRF) is introduced, which allows the determination of CBF, the arterial transit time (ATT) and T(1,eff). The accuracy and precision of the proposed model were compared with those of more complicated models with four or five parameters through Monte Carlo simulations. Pseudo-continuous arterial spin labeling images were acquired on a clinical 3-T scanner in 10 normal volunteers using a three-dimensional multi-shot gradient and spin echo scheme at multiple post-labeling delays to sample the kinetic curves. Voxel-wise fitting was performed using the three-parameter model and other models that contain two, four or five unknown parameters. For the two-parameter model, T(1,eff) values close to tissue and blood were assumed separately. Standard statistical analysis was conducted to compare these fitting models in various brain regions. The fitted results indicated that: (i) the estimated CBF values using the two-parameter model show appreciable dependence on the assumed T(1,eff) values; (ii) the proposed three-parameter model achieves the optimal balance between the goodness of fit and model complexity when compared among the models with explicit IRF fitting; (iii) both the two-parameter model using fixed blood T1 values for T(1,eff) and the three-parameter model provide reasonable fitting results. Using the proposed three-parameter model, the estimated CBF (46 ± 14 mL/100 g/min) and ATT (1.4 ± 0.3 s) values averaged from different brain regions are close to the literature reports; the estimated T(1,eff) values (1.9 ± 0.4 s) are higher than the tissue T1 values, possibly reflecting a contribution from the microvascular arterial blood compartment. Copyright © 2013 John Wiley & Sons, Ltd.

Meta-analysis using Dirichlet process.

PubMed

Muthukumarana, Saman; Tiwari, Ram C

2016-02-01

This article develops a Bayesian approach for meta-analysis using the Dirichlet process. The key aspect of the Dirichlet process in meta-analysis is the ability to assess evidence of statistical heterogeneity or variation in the underlying effects across study while relaxing the distributional assumptions. We assume that the study effects are generated from a Dirichlet process. Under a Dirichlet process model, the study effects parameters have support on a discrete space and enable borrowing of information across studies while facilitating clustering among studies. We illustrate the proposed method by applying it to a dataset on the Program for International Student Assessment on 30 countries. Results from the data analysis, simulation studies, and the log pseudo-marginal likelihood model selection procedure indicate that the Dirichlet process model performs better than conventional alternative methods. © The Author(s) 2012.

A MATLAB toolbox for the efficient estimation of the psychometric function using the updated maximum-likelihood adaptive procedure

PubMed Central

Richards, V. M.; Dai, W.

2014-01-01

A MATLAB toolbox for the efficient estimation of the threshold, slope, and lapse rate of the psychometric function is described. The toolbox enables the efficient implementation of the updated maximum-likelihood (UML) procedure. The toolbox uses an object-oriented architecture for organizing the experimental variables and computational algorithms, which provides experimenters with flexibility in experimental design and data management. Descriptions of the UML procedure and the UML Toolbox are provided, followed by toolbox use examples. Finally, guidelines and recommendations of parameter configurations are given. PMID:24671826

A two-step ionospheric modeling algorithm considering the impact of GLONASS pseudo-range inter-channel biases

NASA Astrophysics Data System (ADS)

Zhang, Rui; Yao, Yi-bin; Hu, Yue-ming; Song, Wei-wei

2017-12-01

The Global Navigation Satellite System presents a plausible and cost-effective way of computing the total electron content (TEC). But TEC estimated value could be seriously affected by the differential code biases (DCB) of frequency-dependent satellites and receivers. Unlike GPS and other satellite systems, GLONASS adopts a frequency-division multiplexing access mode to distinguish different satellites. This strategy leads to different wavelengths and inter-frequency biases (IFBs) for both pseudo-range and carrier phase observations, whose impacts are rarely considered in ionospheric modeling. We obtained observations from four groups of co-stations to analyze the characteristics of the GLONASS receiver P1P2 pseudo-range IFB with a double-difference method. The results showed that the GLONASS P1P2 pseudo-range IFB remained stable for a period of time and could catch up to several meters, which cannot be absorbed by the receiver DCB during ionospheric modeling. Given the characteristics of the GLONASS P1P2 pseudo-range IFB, we proposed a two-step ionosphere modeling method with the priori IFB information. The experimental analysis showed that the new algorithm can effectively eliminate the adverse effects on ionospheric model and hardware delay parameters estimation in different space environments. During high solar activity period, compared to the traditional GPS + GLONASS modeling algorithm, the absolute average deviation of TEC decreased from 2.17 to 2.07 TECu (TEC unit); simultaneously, the average RMS of GPS satellite DCB decreased from 0.225 to 0.219 ns, and the average deviation of GLONASS satellite DCB decreased from 0.253 to 0.113 ns with a great improvement in over 55%.

Statistical Bias in Maximum Likelihood Estimators of Item Parameters.

DTIC Science & Technology

1982-04-01

34 a> E r’r~e r ,C Ie I# ne,..,.rVi rnd Id.,flfv b1 - bindk numb.r) I; ,t-i i-cd I ’ tiie bias in the maximum likelihood ,st i- i;, ’ t iIeiIrs in...NTC, IL 60088 Psychometric Laboratory University of North Carolina I ERIC Facility-Acquisitions Davie Hall 013A 4833 Rugby Avenue Chapel Hill, NC

Predicting type 2 diabetes using genetic and environmental risk factors in a multi-ethnic Malaysian cohort.

PubMed

Abdullah, N; Abdul Murad, N A; Mohd Haniff, E A; Syafruddin, S E; Attia, J; Oldmeadow, C; Kamaruddin, M A; Abd Jalal, N; Ismail, N; Ishak, M; Jamal, R; Scott, R J; Holliday, E G

2017-08-01

Malaysia has a high and rising prevalence of type 2 diabetes (T2D). While environmental (non-genetic) risk factors for the disease are well established, the role of genetic variations and gene-environment interactions remain understudied in this population. This study aimed to estimate the relative contributions of environmental and genetic risk factors to T2D in Malaysia and also to assess evidence for gene-environment interactions that may explain additional risk variation. This was a case-control study including 1604 Malays, 1654 Chinese and 1728 Indians from the Malaysian Cohort Project. The proportion of T2D risk variance explained by known genetic and environmental factors was assessed by fitting multivariable logistic regression models and evaluating McFadden's pseudo R 2 and the area under the receiver-operating characteristic curve (AUC). Models with and without the genetic risk score (GRS) were compared using the log likelihood ratio Chi-squared test and AUCs. Multiplicative interaction between genetic and environmental risk factors was assessed via logistic regression within and across ancestral groups. Interactions were assessed for the GRS and its 62 constituent variants. The models including environmental risk factors only had pseudo R 2 values of 16.5-28.3% and AUC of 0.75-0.83. Incorporating a genetic score aggregating 62 T2D-associated risk variants significantly increased the model fit (likelihood ratio P-value of 2.50 × 10 -4 -4.83 × 10 -12 ) and increased the pseudo R 2 by about 1-2% and AUC by 1-3%. None of the gene-environment interactions reached significance after multiple testing adjustment, either for the GRS or individual variants. For individual variants, 33 out of 310 tested associations showed nominal statistical significance with 0.001 < P < 0.05. This study suggests that known genetic risk variants contribute a significant but small amount to overall T2D risk variation in Malaysian population groups. If gene-environment interactions involving common genetic variants exist, they are likely of small effect, requiring substantially larger samples for detection. Copyright © 2017 The Royal Society for Public Health. All rights reserved.

On the impact of GNSS ambiguity resolution: geometry, ionosphere, time and biases

NASA Astrophysics Data System (ADS)

Khodabandeh, A.; Teunissen, P. J. G.

2018-06-01

Integer ambiguity resolution (IAR) is the key to fast and precise GNSS positioning and navigation. Next to the positioning parameters, however, there are several other types of GNSS parameters that are of importance for a range of different applications like atmospheric sounding, instrumental calibrations or time transfer. As some of these parameters may still require pseudo-range data for their estimation, their response to IAR may differ significantly. To infer the impact of ambiguity resolution on the parameters, we show how the ambiguity-resolved double-differenced phase data propagate into the GNSS parameter solutions. For that purpose, we introduce a canonical decomposition of the GNSS network model that, through its decoupled and decorrelated nature, provides direct insight into which parameters, or functions thereof, gain from IAR and which do not. Next to this qualitative analysis, we present for the GNSS estimable parameters of geometry, ionosphere, timing and instrumental biases closed-form expressions of their IAR precision gains together with supporting numerical examples.

On the impact of GNSS ambiguity resolution: geometry, ionosphere, time and biases

NASA Astrophysics Data System (ADS)

Khodabandeh, A.; Teunissen, P. J. G.

2017-11-01

Integer ambiguity resolution (IAR) is the key to fast and precise GNSS positioning and navigation. Next to the positioning parameters, however, there are several other types of GNSS parameters that are of importance for a range of different applications like atmospheric sounding, instrumental calibrations or time transfer. As some of these parameters may still require pseudo-range data for their estimation, their response to IAR may differ significantly. To infer the impact of ambiguity resolution on the parameters, we show how the ambiguity-resolved double-differenced phase data propagate into the GNSS parameter solutions. For that purpose, we introduce a canonical decomposition of the GNSS network model that, through its decoupled and decorrelated nature, provides direct insight into which parameters, or functions thereof, gain from IAR and which do not. Next to this qualitative analysis, we present for the GNSS estimable parameters of geometry, ionosphere, timing and instrumental biases closed-form expressions of their IAR precision gains together with supporting numerical examples.

Estimation of perfusion properties with MR Fingerprinting Arterial Spin Labeling.

PubMed

Wright, Katherine L; Jiang, Yun; Ma, Dan; Noll, Douglas C; Griswold, Mark A; Gulani, Vikas; Hernandez-Garcia, Luis

2018-03-12

In this study, the acquisition of ASL data and quantification of multiple hemodynamic parameters was explored using a Magnetic Resonance Fingerprinting (MRF) approach. A pseudo-continuous ASL labeling scheme was used with pseudo-randomized timings to acquire the MRF ASL data in a 2.5 min acquisition. A large dictionary of MRF ASL signals was generated by combining a wide range of physical and hemodynamic properties with the pseudo-random MRF ASL sequence and a two-compartment model. The acquired signals were matched to the dictionary to provide simultaneous quantification of cerebral blood flow, tissue time-to-peak, cerebral blood volume, arterial time-to-peak, B 1 , and T 1. A study in seven healthy volunteers resulted in the following values across the population in grey matter (mean ± standard deviation): cerebral blood flow of 69.1 ± 6.1 ml/min/100 g, arterial time-to-peak of 1.5 ± 0.1 s, tissue time-to-peak of 1.5 ± 0.1 s, T 1 of 1634 ms, cerebral blood volume of 0.0048 ± 0.0005. The CBF measurements were compared to standard pCASL CBF estimates using a one-compartment model, and a Bland-Altman analysis showed good agreement with a minor bias. Repeatability was tested in five volunteers in the same exam session, and no statistical difference was seen. In addition to this validation, the MRF ASL acquisition's sensitivity to the physical and physiological parameters of interest was studied numerically. Copyright © 2018 Elsevier Inc. All rights reserved.

A Modified Cramer-von Mises and Anderson-Darling Test for the Weibull Distribution with Unknown Location and Scale Parameters.

DTIC Science & Technology

1981-12-01

preventing the generation of 16 6 negative location estimators. Because of the invariant pro- perty of the EDF statistics, this transformation will...likelihood. If the parameter estimation method developed by Harter and Moore is used, care must be taken to prevent the location estimators from being...vs A 2 Critical Values, Level-.Ol, n-30 128 , 0 6N m m • w - APPENDIX E Computer Prgrams 129 Program to Calculate the Cramer-von Mises Critical Values

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

NASA Technical Reports Server (NTRS)

Murphy, Patrick Charles

1985-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

A Two-Stage Approach to Missing Data: Theory and Application to Auxiliary Variables

ERIC Educational Resources Information Center

Savalei, Victoria; Bentler, Peter M.

2009-01-01

A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a…

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.

Semiparametric Item Response Functions in the Context of Guessing

ERIC Educational Resources Information Center

Falk, Carl F.; Cai, Li

2016-01-01

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood-based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

Logistic regression for circular data

NASA Astrophysics Data System (ADS)

Al-Daffaie, Kadhem; Khan, Shahjahan

2017-05-01

This paper considers the relationship between a binary response and a circular predictor. It develops the logistic regression model by employing the linear-circular regression approach. The maximum likelihood method is used to estimate the parameters. The Newton-Raphson numerical method is used to find the estimated values of the parameters. A data set from weather records of Toowoomba city is analysed by the proposed methods. Moreover, a simulation study is considered. The R software is used for all computations and simulations.

Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution.

PubMed

Rigby, Robert A; Stasinopoulos, D Mikis

2004-10-15

The Box-Cox power exponential (BCPE) distribution, developed in this paper, provides a model for a dependent variable Y exhibiting both skewness and kurtosis (leptokurtosis or platykurtosis). The distribution is defined by a power transformation Y(nu) having a shifted and scaled (truncated) standard power exponential distribution with parameter tau. The distribution has four parameters and is denoted BCPE (mu,sigma,nu,tau). The parameters, mu, sigma, nu and tau, may be interpreted as relating to location (median), scale (approximate coefficient of variation), skewness (transformation to symmetry) and kurtosis (power exponential parameter), respectively. Smooth centile curves are obtained by modelling each of the four parameters of the distribution as a smooth non-parametric function of an explanatory variable. A Fisher scoring algorithm is used to fit the non-parametric model by maximizing a penalized likelihood. The first and expected second and cross derivatives of the likelihood, with respect to mu, sigma, nu and tau, required for the algorithm, are provided. The centiles of the BCPE distribution are easy to calculate, so it is highly suited to centile estimation. This application of the BCPE distribution to smooth centile estimation provides a generalization of the LMS method of the centile estimation to data exhibiting kurtosis (as well as skewness) different from that of a normal distribution and is named here the LMSP method of centile estimation. The LMSP method of centile estimation is applied to modelling the body mass index of Dutch males against age. 2004 John Wiley & Sons, Ltd.

Estimation of stochastic volatility by using Ornstein-Uhlenbeck type models

NASA Astrophysics Data System (ADS)

Mariani, Maria C.; Bhuiyan, Md Al Masum; Tweneboah, Osei K.

2018-02-01

In this study, we develop a technique for estimating the stochastic volatility (SV) of a financial time series by using Ornstein-Uhlenbeck type models. Using the daily closing prices from developed and emergent stock markets, we conclude that the incorporation of stochastic volatility into the time varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. Furthermore, our estimation algorithm is feasible with large data sets and have good convergence properties.

Empirical Bayes Gaussian likelihood estimation of exposure distributions from pooled samples in human biomonitoring.

PubMed

Li, Xiang; Kuk, Anthony Y C; Xu, Jinfeng

2014-12-10

Human biomonitoring of exposure to environmental chemicals is important. Individual monitoring is not viable because of low individual exposure level or insufficient volume of materials and the prohibitive cost of taking measurements from many subjects. Pooling of samples is an efficient and cost-effective way to collect data. Estimation is, however, complicated as individual values within each pool are not observed but are only known up to their average or weighted average. The distribution of such averages is intractable when the individual measurements are lognormally distributed, which is a common assumption. We propose to replace the intractable distribution of the pool averages by a Gaussian likelihood to obtain parameter estimates. If the pool size is large, this method produces statistically efficient estimates, but regardless of pool size, the method yields consistent estimates as the number of pools increases. An empirical Bayes (EB) Gaussian likelihood approach, as well as its Bayesian analog, is developed to pool information from various demographic groups by using a mixed-effect formulation. We also discuss methods to estimate the underlying mean-variance relationship and to select a good model for the means, which can be incorporated into the proposed EB or Bayes framework. By borrowing strength across groups, the EB estimator is more efficient than the individual group-specific estimator. Simulation results show that the EB Gaussian likelihood estimates outperform a previous method proposed for the National Health and Nutrition Examination Surveys with much smaller bias and better coverage in interval estimation, especially after correction of bias. Copyright © 2014 John Wiley & Sons, Ltd.

Expectation maximization-based likelihood inference for flexible cure rate models with Weibull lifetimes.

PubMed

Balakrishnan, Narayanaswamy; Pal, Suvra

2016-08-01

Recently, a flexible cure rate survival model has been developed by assuming the number of competing causes of the event of interest to follow the Conway-Maxwell-Poisson distribution. This model includes some of the well-known cure rate models discussed in the literature as special cases. Data obtained from cancer clinical trials are often right censored and expectation maximization algorithm can be used in this case to efficiently estimate the model parameters based on right censored data. In this paper, we consider the competing cause scenario and assuming the time-to-event to follow the Weibull distribution, we derive the necessary steps of the expectation maximization algorithm for estimating the parameters of different cure rate survival models. The standard errors of the maximum likelihood estimates are obtained by inverting the observed information matrix. The method of inference developed here is examined by means of an extensive Monte Carlo simulation study. Finally, we illustrate the proposed methodology with a real data on cancer recurrence. © The Author(s) 2013.

Programmer's manual for MMLE3, a general FORTRAN program for maximum likelihood parameter estimation

NASA Technical Reports Server (NTRS)

Maine, R. E.

1981-01-01

The MMLE3 is a maximum likelihood parameter estimation program capable of handling general bilinear dynamic equations of arbitrary order with measurement noise and/or state noise (process noise). The basic MMLE3 program is quite general and, therefore, applicable to a wide variety of problems. The basic program can interact with a set of user written problem specific routines to simplify the use of the program on specific systems. A set of user routines for the aircraft stability and control derivative estimation problem is provided with the program. The implementation of the program on specific computer systems is discussed. The structure of the program is diagrammed, and the function and operation of individual routines is described. Complete listings and reference maps of the routines are included on microfiche as a supplement. Four test cases are discussed; listings of the input cards and program output for the test cases are included on microfiche as a supplement.

A three-dimensional cohesive sediment transport model with data assimilation: Model development, sensitivity analysis and parameter estimation

NASA Astrophysics Data System (ADS)

Wang, Daosheng; Cao, Anzhou; Zhang, Jicai; Fan, Daidu; Liu, Yongzhi; Zhang, Yue

2018-06-01

Based on the theory of inverse problems, a three-dimensional sigma-coordinate cohesive sediment transport model with the adjoint data assimilation is developed. In this model, the physical processes of cohesive sediment transport, including deposition, erosion and advection-diffusion, are parameterized by corresponding model parameters. These parameters are usually poorly known and have traditionally been assigned empirically. By assimilating observations into the model, the model parameters can be estimated using the adjoint method; meanwhile, the data misfit between model results and observations can be decreased. The model developed in this work contains numerous parameters; therefore, it is necessary to investigate the parameter sensitivity of the model, which is assessed by calculating a relative sensitivity function and the gradient of the cost function with respect to each parameter. The results of parameter sensitivity analysis indicate that the model is sensitive to the initial conditions, inflow open boundary conditions, suspended sediment settling velocity and resuspension rate, while the model is insensitive to horizontal and vertical diffusivity coefficients. A detailed explanation of the pattern of sensitivity analysis is also given. In ideal twin experiments, constant parameters are estimated by assimilating 'pseudo' observations. The results show that the sensitive parameters are estimated more easily than the insensitive parameters. The conclusions of this work can provide guidance for the practical applications of this model to simulate sediment transport in the study area.

An Example of an Improvable Rao-Blackwell Improvement, Inefficient Maximum Likelihood Estimator, and Unbiased Generalized Bayes Estimator.

PubMed

Galili, Tal; Meilijson, Isaac

2016-01-02

The Rao-Blackwell theorem offers a procedure for converting a crude unbiased estimator of a parameter θ into a "better" one, in fact unique and optimal if the improvement is based on a minimal sufficient statistic that is complete. In contrast, behind every minimal sufficient statistic that is not complete, there is an improvable Rao-Blackwell improvement. This is illustrated via a simple example based on the uniform distribution, in which a rather natural Rao-Blackwell improvement is uniformly improvable. Furthermore, in this example the maximum likelihood estimator is inefficient, and an unbiased generalized Bayes estimator performs exceptionally well. Counterexamples of this sort can be useful didactic tools for explaining the true nature of a methodology and possible consequences when some of the assumptions are violated. [Received December 2014. Revised September 2015.].

New robust statistical procedures for the polytomous logistic regression models.

PubMed

Castilla, Elena; Ghosh, Abhik; Martin, Nirian; Pardo, Leandro

2018-05-17

This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies. Finally, an approach for the data-driven selection of the robustness tuning parameter is proposed with empirical justifications. © 2018, The International Biometric Society.

Robust Likelihoods for Inflationary Gravitational Waves from Maps of Cosmic Microwave Background Polarization

NASA Technical Reports Server (NTRS)

Switzer, Eric Ryan; Watts, Duncan J.

2016-01-01

The B-mode polarization of the cosmic microwave background provides a unique window into tensor perturbations from inflationary gravitational waves. Survey effects complicate the estimation and description of the power spectrum on the largest angular scales. The pixel-space likelihood yields parameter distributions without the power spectrum as an intermediate step, but it does not have the large suite of tests available to power spectral methods. Searches for primordial B-modes must rigorously reject and rule out contamination. Many forms of contamination vary or are uncorrelated across epochs, frequencies, surveys, or other data treatment subsets. The cross power and the power spectrum of the difference of subset maps provide approaches to reject and isolate excess variance. We develop an analogous joint pixel-space likelihood. Contamination not modeled in the likelihood produces parameter-dependent bias and complicates the interpretation of the difference map. We describe a null test that consistently weights the difference map. Excess variance should either be explicitly modeled in the covariance or be removed through reprocessing the data.

Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

ERIC Educational Resources Information Center

du Toit, Stephen H. C.; Cudeck, Robert

2009-01-01

A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…

Logistic Achievement Test Scaling and Equating with Fixed versus Estimated Lower Asymptotes.

ERIC Educational Resources Information Center

Phillips, S. E.

This study compared the lower asymptotes estimated by the maximum likelihood procedures of the LOGIST computer program with those obtained via application of the Norton methodology. The study also compared the equating results from the three-parameter logistic model with those obtained from the equipercentile, Rasch, and conditional…

The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables.

ERIC Educational Resources Information Center

Ethington, Corinna A.

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical manifest variables. Two types of correlation matrices were analyzed; one containing Pearson product-moment correlations and one containing tetrachoric,…

Bayesian estimation of the transmissivity spatial structure from pumping test data

NASA Astrophysics Data System (ADS)

Demir, Mehmet Taner; Copty, Nadim K.; Trinchero, Paolo; Sanchez-Vila, Xavier

2017-06-01

Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.

Study of central light concentration in nearby galaxies

NASA Astrophysics Data System (ADS)

Aswathy, S.; Ravikumar, C. D.

2018-06-01

We propose a novel technique to estimate the masses of supermassive black holes (SMBHs) residing at the centres of massive galaxies in the nearby Universe using simple photometry. Aperture photometry using SEXTRACTOR is employed to determine the central intensity ratio (CIR) at the optical centre of the galaxy image for a sample of 49 nearby galaxies with SMBH mass estimations. We find that the CIR of ellipticals and classical bulges is strongly correlated with SMBH masses whereas pseudo-bulges and ongoing mergers show significant scatter. Also, the CIR of low-luminosity AGNs in the sample shows significant connection with the 5 GHz nuclear radio emission suggesting a stronger link between the former and the SMBH evolution in these galaxies. In addition, it is seen that various structural and dynamical properties of the SMBH host galaxies are correlated with the CIR making the latter an important parameter in galaxy evolution studies. Finally, we propose the CIR to be an efficient and simple tool not only to distinguish classical bulges from pseudo-bulges but also to estimate the mass of the central SMBH.

Maximum likelihood clustering with dependent feature trees

NASA Technical Reports Server (NTRS)

Chittineni, C. B. (Principal Investigator)

1981-01-01

The decomposition of mixture density of the data into its normal component densities is considered. The densities are approximated with first order dependent feature trees using criteria of mutual information and distance measures. Expressions are presented for the criteria when the densities are Gaussian. By defining different typs of nodes in a general dependent feature tree, maximum likelihood equations are developed for the estimation of parameters using fixed point iterations. The field structure of the data is also taken into account in developing maximum likelihood equations. Experimental results from the processing of remotely sensed multispectral scanner imagery data are included.

Effects of wing modification on an aircraft's aerodynamic parameters as determined from flight data

NASA Technical Reports Server (NTRS)

Hess, R. A.

1986-01-01

A study of the effects of four wing-leading-edge modifications on a general aviation aircraft's stability and control parameters is presented. Flight data from the basic aircraft configuration and configurations with wing modifications are analyzed to determine each wing geometry's stability and control parameters. The parameter estimates and aerodynamic model forms are obtained using the stepwise regression and maximum likelihood techniques. The resulting parameter estimates and aerodynamic models are verified using vortex-lattice theory and by analysis of each model's ability to predict aircraft behavior. Comparisons of the stability and control derivative estimates from the basic wing and the four leading-edge modifications are accomplished so that the effects of each modification on aircraft stability and control derivatives can be determined.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

NASA Astrophysics Data System (ADS)

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

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

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic systemmore » leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.« less

Removal of three nitrophenols from aqueous solutions by adsorption onto char ash: equilibrium and kinetic modeling

NASA Astrophysics Data System (ADS)

Magdy, Yehia M.; Altaher, Hossam; ElQada, E.

2018-03-01

In this research, the removal of 2,4 dinitrophenol, 2 nitrophenol and 4 nitrophenol from aqueous solution using char ash from animal bones was investigated using batch technique. Three 2-parameter isotherms (Freundlich, Langmuir, and Temkin) were applied to analyze the experimental data. Both linear and nonlinear regression analyses were performed for these models to estimate the isotherm parameters. Three 3-parameter isotherms (Redlich-Peterson, Sips, Toth) were also tested. Moreover, the kinetic data were tested using pseudo-first order, pseudo-second order, Elovich, Intraparticle diffusion and Boyd methods. Langmuir adsorption isotherm provided the best fit for the experimental data indicating monolayer adsorption. The maximum adsorption capacity was 8.624, 7.55, 7.384 mg/g for 2 nitrophenol, 2,4 dinitrophenol, and 4 nitrophenol, respectively. The experimental data fitted well to pseudo-second order model suggested a chemical nature of the adsorption process. The R 2 values for this model were 0.973 up to 0.999. This result with supported by the Temkin model indicating heat of adsorption to be greater than 10 kJ/mol. The rate controlling step was intraparticle diffusion for 2 nitrophenol, and a combination of intraparticle diffusion and film diffusion for the other two phenols. The pH and temperature of solution were found to have a considerable effect, and the temperature indicated the exothermic nature of the adsorption process. The highest adsorption capacity was obtained at pH 9 and 25 °C.

Fitting a three-parameter lognormal distribution with applications to hydrogeochemical data from the National Uranium Resource Evaluation Program

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

Kane, V.E.

1979-10-01

The standard maximum likelihood and moment estimation procedures are shown to have some undesirable characteristics for estimating the parameters in a three-parameter lognormal distribution. A class of goodness-of-fit estimators is found which provides a useful alternative to the standard methods. The class of goodness-of-fit tests considered include the Shapiro-Wilk and Shapiro-Francia tests which reduce to a weighted linear combination of the order statistics that can be maximized in estimation problems. The weighted-order statistic estimators are compared to the standard procedures in Monte Carlo simulations. Bias and robustness of the procedures are examined and example data sets analyzed including geochemical datamore » from the National Uranium Resource Evaluation Program.« less

Maximum likelihood estimation for predicting the probability of obtaining variable shortleaf pine regeneration densities

Treesearch

Thomas B. Lynch; Jean Nkouka; Michael M. Huebschmann; James M. Guldin

2003-01-01

A logistic equation is the basis for a model that predicts the probability of obtaining regeneration at specified densities. The density of regeneration (trees/ha) for which an estimate of probability is desired can be specified by means of independent variables in the model. When estimating parameters, the dependent variable is set to 1 if the regeneration density (...

Essaying a Pseudo-Panel Approach: Studies on Education, Women, and Income Inequality in Thailand

ERIC Educational Resources Information Center

Warunsiri, Sasiwimon

2010-01-01

This dissertation is composed of three studies on Thai labor markets using a pseudo-panel data set: The first chapter estimates the rate of return to education in Thailand, while treating the endogeneity bias common to estimates from data on individuals. Pseudo-panel data are constructed from repeated cross sections of Labor Force Surveys…

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

Vrugt, Jasper A; Robinson, Bruce A; Ter Braak, Cajo J F

In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented usingmore » the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.« less

LS-APC v1.0: a tuning-free method for the linear inverse problem and its application to source-term determination

NASA Astrophysics Data System (ADS)

Tichý, Ondřej; Šmídl, Václav; Hofman, Radek; Stohl, Andreas

2016-11-01

Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.

A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm.

PubMed

Barrera, Antonio; Román-Román, Patricia; Torres-Ruiz, Francisco

2018-01-01

A stochastic diffusion process, whose mean function is a hyperbolastic curve of type I, is presented. The main characteristics of the process are studied and the problem of maximum likelihood estimation for the parameters of the process is considered. To this end, the firefly metaheuristic optimization algorithm is applied after bounding the parametric space by a stagewise procedure. Some examples based on simulated sample paths and real data illustrate this development. Copyright © 2017 Elsevier B.V. All rights reserved.

Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates.

PubMed

Campbell, D A; Chkrebtii, O

2013-12-01

Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.

Use of empirical likelihood to calibrate auxiliary information in partly linear monotone regression models.

PubMed

Chen, Baojiang; Qin, Jing

2014-05-10

In statistical analysis, a regression model is needed if one is interested in finding the relationship between a response variable and covariates. When the response depends on the covariate, then it may also depend on the function of this covariate. If one has no knowledge of this functional form but expect for monotonic increasing or decreasing, then the isotonic regression model is preferable. Estimation of parameters for isotonic regression models is based on the pool-adjacent-violators algorithm (PAVA), where the monotonicity constraints are built in. With missing data, people often employ the augmented estimating method to improve estimation efficiency by incorporating auxiliary information through a working regression model. However, under the framework of the isotonic regression model, the PAVA does not work as the monotonicity constraints are violated. In this paper, we develop an empirical likelihood-based method for isotonic regression model to incorporate the auxiliary information. Because the monotonicity constraints still hold, the PAVA can be used for parameter estimation. Simulation studies demonstrate that the proposed method can yield more efficient estimates, and in some situations, the efficiency improvement is substantial. We apply this method to a dementia study. Copyright © 2013 John Wiley & Sons, Ltd.

Novel scheme for rapid parallel parameter estimation of gravitational waves from compact binary coalescences

NASA Astrophysics Data System (ADS)

Pankow, C.; Brady, P.; Ochsner, E.; O'Shaughnessy, R.

2015-07-01

We introduce a highly parallelizable architecture for estimating parameters of compact binary coalescence using gravitational-wave data and waveform models. Using a spherical harmonic mode decomposition, the waveform is expressed as a sum over modes that depend on the intrinsic parameters (e.g., masses) with coefficients that depend on the observer dependent extrinsic parameters (e.g., distance, sky position). The data is then prefiltered against those modes, at fixed intrinsic parameters, enabling efficiently evaluation of the likelihood for generic source positions and orientations, independent of waveform length or generation time. We efficiently parallelize our intrinsic space calculation by integrating over all extrinsic parameters using a Monte Carlo integration strategy. Since the waveform generation and prefiltering happens only once, the cost of integration dominates the procedure. Also, we operate hierarchically, using information from existing gravitational-wave searches to identify the regions of parameter space to emphasize in our sampling. As proof of concept and verification of the result, we have implemented this algorithm using standard time-domain waveforms, processing each event in less than one hour on recent computing hardware. For most events we evaluate the marginalized likelihood (evidence) with statistical errors of ≲5 %, and even smaller in many cases. With a bounded runtime independent of the waveform model starting frequency, a nearly unchanged strategy could estimate neutron star (NS)-NS parameters in the 2018 advanced LIGO era. Our algorithm is usable with any noise curve and existing time-domain model at any mass, including some waveforms which are computationally costly to evolve.

Multifrequency InSAR height reconstruction through maximum likelihood estimation of local planes parameters.

PubMed

Pascazio, Vito; Schirinzi, Gilda

2002-01-01

In this paper, a technique that is able to reconstruct highly sloped and discontinuous terrain height profiles, starting from multifrequency wrapped phase acquired by interferometric synthetic aperture radar (SAR) systems, is presented. We propose an innovative unwrapping method, based on a maximum likelihood estimation technique, which uses multifrequency independent phase data, obtained by filtering the interferometric SAR raw data pair through nonoverlapping band-pass filters, and approximating the unknown surface by means of local planes. Since the method does not exploit the phase gradient, it assures the uniqueness of the solution, even in the case of highly sloped or piecewise continuous elevation patterns with strong discontinuities.

Maximum likelihood estimation for periodic autoregressive moving average models

USGS Publications Warehouse

Vecchia, A.V.

1985-01-01

A useful class of models for seasonal time series that cannot be filtered or standardized to achieve second-order stationarity is that of periodic autoregressive moving average (PARMA) models, which are extensions of ARMA models that allow periodic (seasonal) parameters. An approximation to the exact likelihood for Gaussian PARMA processes is developed, and a straightforward algorithm for its maximization is presented. The algorithm is tested on several periodic ARMA(1, 1) models through simulation studies and is compared to moment estimation via the seasonal Yule-Walker equations. Applicability of the technique is demonstrated through an analysis of a seasonal stream-flow series from the Rio Caroni River in Venezuela.

Optimal and Most Exact Confidence Intervals for Person Parameters in Item Response Theory Models

ERIC Educational Resources Information Center

Doebler, Anna; Doebler, Philipp; Holling, Heinz

2013-01-01

The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter [theta] is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given…

Semi-Parametric Item Response Functions in the Context of Guessing. CRESST Report 844

ERIC Educational Resources Information Center

Falk, Carl F.; Cai, Li

2015-01-01

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

Establishment of a center of excellence for applied mathematical and statistical research

NASA Technical Reports Server (NTRS)

Woodward, W. A.; Gray, H. L.

1983-01-01

The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.

M-dwarf exoplanet surface density distribution. A log-normal fit from 0.07 to 400 AU

NASA Astrophysics Data System (ADS)

Meyer, Michael R.; Amara, Adam; Reggiani, Maddalena; Quanz, Sascha P.

2018-04-01

Aims: We fit a log-normal function to the M-dwarf orbital surface density distribution of gas giant planets, over the mass range 1-10 times that of Jupiter, from 0.07 to 400 AU. Methods: We used a Markov chain Monte Carlo approach to explore the likelihoods of various parameter values consistent with point estimates of the data given our assumed functional form. Results: This fit is consistent with radial velocity, microlensing, and direct-imaging observations, is well-motivated from theoretical and phenomenological points of view, and predicts results of future surveys. We present probability distributions for each parameter and a maximum likelihood estimate solution. Conclusions: We suggest that this function makes more physical sense than other widely used functions, and we explore the implications of our results on the design of future exoplanet surveys.

Ancestral Relationships Using Metafounders: Finite Ancestral Populations and Across Population Relationships

PubMed Central

Legarra, Andres; Christensen, Ole F.; Vitezica, Zulma G.; Aguilar, Ignacio; Misztal, Ignacy

2015-01-01

Recent use of genomic (marker-based) relationships shows that relationships exist within and across base population (breeds or lines). However, current treatment of pedigree relationships is unable to consider relationships within or across base populations, although such relationships must exist due to finite size of the ancestral population and connections between populations. This complicates the conciliation of both approaches and, in particular, combining pedigree with genomic relationships. We present a coherent theoretical framework to consider base population in pedigree relationships. We suggest a conceptual framework that considers each ancestral population as a finite-sized pool of gametes. This generates across-individual relationships and contrasts with the classical view which each population is considered as an infinite, unrelated pool. Several ancestral populations may be connected and therefore related. Each ancestral population can be represented as a “metafounder,” a pseudo-individual included as founder of the pedigree and similar to an “unknown parent group.” Metafounders have self- and across relationships according to a set of parameters, which measure ancestral relationships, i.e., homozygozities within populations and relationships across populations. These parameters can be estimated from existing pedigree and marker genotypes using maximum likelihood or a method based on summary statistics, for arbitrarily complex pedigrees. Equivalences of genetic variance and variance components between the classical and this new parameterization are shown. Segregation variance on crosses of populations is modeled. Efficient algorithms for computation of relationship matrices, their inverses, and inbreeding coefficients are presented. Use of metafounders leads to compatibility of genomic and pedigree relationship matrices and to simple computing algorithms. Examples and code are given. PMID:25873631

Developing a non-point source P loss indicator in R and its parameter uncertainty assessment using GLUE: a case study in northern China.

PubMed

Su, Jingjun; Du, Xinzhong; Li, Xuyong

2018-05-16

Uncertainty analysis is an important prerequisite for model application. However, the existing phosphorus (P) loss indexes or indicators were rarely evaluated. This study applied generalized likelihood uncertainty estimation (GLUE) method to assess the uncertainty of parameters and modeling outputs of a non-point source (NPS) P indicator constructed in R language. And the influences of subjective choices of likelihood formulation and acceptability threshold of GLUE on model outputs were also detected. The results indicated the following. (1) Parameters RegR 2 , RegSDR 2 , PlossDP fer , PlossDP man , DPDR, and DPR were highly sensitive to overall TP simulation and their value ranges could be reduced by GLUE. (2) Nash efficiency likelihood (L 1 ) seemed to present better ability in accentuating high likelihood value simulations than the exponential function (L 2 ) did. (3) The combined likelihood integrating the criteria of multiple outputs acted better than single likelihood in model uncertainty assessment in terms of reducing the uncertainty band widths and assuring the fitting goodness of whole model outputs. (4) A value of 0.55 appeared to be a modest choice of threshold value to balance the interests between high modeling efficiency and high bracketing efficiency. Results of this study could provide (1) an option to conduct NPS modeling under one single computer platform, (2) important references to the parameter setting for NPS model development in similar regions, (3) useful suggestions for the application of GLUE method in studies with different emphases according to research interests, and (4) important insights into the watershed P management in similar regions.

On splice site prediction using weight array models: a comparison of smoothing techniques

NASA Astrophysics Data System (ADS)

Taher, Leila; Meinicke, Peter; Morgenstern, Burkhard

2007-11-01

In most eukaryotic genes, protein-coding exons are separated by non-coding introns which are removed from the primary transcript by a process called "splicing". The positions where introns are cut and exons are spliced together are called "splice sites". Thus, computational prediction of splice sites is crucial for gene finding in eukaryotes. Weight array models are a powerful probabilistic approach to splice site detection. Parameters for these models are usually derived from m-tuple frequencies in trusted training data and subsequently smoothed to avoid zero probabilities. In this study we compare three different ways of parameter estimation for m-tuple frequencies, namely (a) non-smoothed probability estimation, (b) standard pseudo counts and (c) a Gaussian smoothing procedure that we recently developed.

Formulation and implementation of a practical algorithm for parameter estimation with process and measurement noise

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1980-01-01

A new formulation is proposed for the problem of parameter estimation of dynamic systems with both process and measurement noise. The formulation gives estimates that are maximum likelihood asymptotically in time. The means used to overcome the difficulties encountered by previous formulations are discussed. It is then shown how the proposed formulation can be efficiently implemented in a computer program. A computer program using the proposed formulation is available in a form suitable for routine application. Examples with simulated and real data are given to illustrate that the program works well.

Inferring epidemiological parameters from phylogenetic information for the HIV-1 epidemic among MSM

NASA Astrophysics Data System (ADS)

Quax, Rick; van de Vijver, David A. M. C.; Frentz, Dineke; Sloot, Peter M. A.

2013-09-01

The HIV-1 epidemic in Europe is primarily sustained by a dynamic topology of sexual interactions among MSM who have individual immune systems and behavior. This epidemiological process shapes the phylogeny of the virus population. Both fields of epidemic modeling and phylogenetics have a long history, however it remains difficult to use phylogenetic data to infer epidemiological parameters such as the structure of the sexual network and the per-act infectiousness. This is because phylogenetic data is necessarily incomplete and ambiguous. Here we show that the cluster-size distribution indeed contains information about epidemiological parameters using detailed numberical experiments. We simulate the HIV epidemic among MSM many times using the Monte Carlo method with all parameter values and their ranges taken from literature. For each simulation and the corresponding set of parameter values we calculate the likelihood of reproducing an observed cluster-size distribution. The result is an estimated likelihood distribution of all parameters from the phylogenetic data, in particular the structure of the sexual network, the per-act infectiousness, and the risk behavior reduction upon diagnosis. These likelihood distributions encode the knowledge provided by the observed cluster-size distrbution, which we quantify using information theory. Our work suggests that the growing body of genetic data of patients can be exploited to understand the underlying epidemiological process.

MIXOR: a computer program for mixed-effects ordinal regression analysis.

PubMed

Hedeker, D; Gibbons, R D

1996-03-01

MIXOR provides maximum marginal likelihood estimates for mixed-effects ordinal probit, logistic, and complementary log-log regression models. These models can be used for analysis of dichotomous and ordinal outcomes from either a clustered or longitudinal design. For clustered data, the mixed-effects model assumes that data within clusters are dependent. The degree of dependency is jointly estimated with the usual model parameters, thus adjusting for dependence resulting from clustering of the data. Similarly, for longitudinal data, the mixed-effects approach can allow for individual-varying intercepts and slopes across time, and can estimate the degree to which these time-related effects vary in the population of individuals. MIXOR uses marginal maximum likelihood estimation, utilizing a Fisher-scoring solution. For the scoring solution, the Cholesky factor of the random-effects variance-covariance matrix is estimated, along with the effects of model covariates. Examples illustrating usage and features of MIXOR are provided.

Maximum Marginal Likelihood Estimation of a Monotonic Polynomial Generalized Partial Credit Model with Applications to Multiple Group Analysis.

PubMed

Falk, Carl F; Cai, Li

2016-06-01

We present a semi-parametric approach to estimating item response functions (IRF) useful when the true IRF does not strictly follow commonly used functions. Our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial. The model includes the regular generalized partial credit model at the lowest order polynomial. Our approach extends Liang's (A semi-parametric approach to estimate IRFs, Unpublished doctoral dissertation, 2007) method for dichotomous item responses to the case of polytomous data. Furthermore, item parameter estimation is implemented with maximum marginal likelihood using the Bock-Aitkin EM algorithm, thereby facilitating multiple group analyses useful in operational settings. Our approach is demonstrated on both educational and psychological data. We present simulation results comparing our approach to more standard IRF estimation approaches and other non-parametric and semi-parametric alternatives.

Do bacterial cell numbers follow a theoretical Poisson distribution? Comparison of experimentally obtained numbers of single cells with random number generation via computer simulation.

PubMed

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu

2016-12-01

We investigated a bacterial sample preparation procedure for single-cell studies. In the present study, we examined whether single bacterial cells obtained via 10-fold dilution followed a theoretical Poisson distribution. Four serotypes of Salmonella enterica, three serotypes of enterohaemorrhagic Escherichia coli and one serotype of Listeria monocytogenes were used as sample bacteria. An inoculum of each serotype was prepared via a 10-fold dilution series to obtain bacterial cell counts with mean values of one or two. To determine whether the experimentally obtained bacterial cell counts follow a theoretical Poisson distribution, a likelihood ratio test between the experimentally obtained cell counts and Poisson distribution which parameter estimated by maximum likelihood estimation (MLE) was conducted. The bacterial cell counts of each serotype sufficiently followed a Poisson distribution. Furthermore, to examine the validity of the parameters of Poisson distribution from experimentally obtained bacterial cell counts, we compared these with the parameters of a Poisson distribution that were estimated using random number generation via computer simulation. The Poisson distribution parameters experimentally obtained from bacterial cell counts were within the range of the parameters estimated using a computer simulation. These results demonstrate that the bacterial cell counts of each serotype obtained via 10-fold dilution followed a Poisson distribution. The fact that the frequency of bacterial cell counts follows a Poisson distribution at low number would be applied to some single-cell studies with a few bacterial cells. In particular, the procedure presented in this study enables us to develop an inactivation model at the single-cell level that can estimate the variability of survival bacterial numbers during the bacterial death process. Copyright © 2016 Elsevier Ltd. All rights reserved.

An Adaptive Kalman Filter using a Simple Residual Tuning Method

NASA Technical Reports Server (NTRS)

Harman, Richard R.

1999-01-01

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

Linear functional minimization for inverse modeling

DOE PAGES

Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; ...

2015-06-01

In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulicmore » head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.« less

An Empirical Comparison between Two Recursive Filters for Attitude and Rate Estimation of Spinning Spacecraft

NASA Technical Reports Server (NTRS)

Harman, Richard R.

2006-01-01

The advantages of inducing a constant spin rate on a spacecraft are well known. A variety of science missions have used this technique as a relatively low cost method for conducting science. Starting in the late 1970s, NASA focused on building spacecraft using 3-axis control as opposed to the single-axis control mentioned above. Considerable effort was expended toward sensor and control system development, as well as the development of ground systems to independently process the data. As a result, spinning spacecraft development and their resulting ground system development stagnated. In the 1990s, shrinking budgets made spinning spacecraft an attractive option for science. The attitude requirements for recent spinning spacecraft are more stringent and the ground systems must be enhanced in order to provide the necessary attitude estimation accuracy. Since spinning spacecraft (SC) typically have no gyroscopes for measuring attitude rate, any new estimator would need to rely on the spacecraft dynamics equations. One estimation technique that utilized the SC dynamics and has been used successfully in 3-axis gyro-less spacecraft ground systems is the pseudo-linear Kalman filter algorithm. Consequently, a pseudo-linear Kalman filter has been developed which directly estimates the spacecraft attitude quaternion and rate for a spinning SC. Recently, a filter using Markley variables was developed specifically for spinning spacecraft. The pseudo-linear Kalman filter has the advantage of being easier to implement but estimates the quaternion which, due to the relatively high spinning rate, changes rapidly for a spinning spacecraft. The Markley variable filter is more complicated to implement but, being based on the SC angular momentum, estimates parameters which vary slowly. This paper presents a comparison of the performance of these two filters. Monte-Carlo simulation runs will be presented which demonstrate the advantages and disadvantages of both filters.

A Maximum Likelihood Approach to Functional Mapping of Longitudinal Binary Traits

PubMed Central

Wang, Chenguang; Li, Hongying; Wang, Zhong; Wang, Yaqun; Wang, Ningtao; Wang, Zuoheng; Wu, Rongling

2013-01-01

Despite their importance in biology and biomedicine, genetic mapping of binary traits that change over time has not been well explored. In this article, we develop a statistical model for mapping quantitative trait loci (QTLs) that govern longitudinal responses of binary traits. The model is constructed within the maximum likelihood framework by which the association between binary responses is modeled in terms of conditional log odds-ratios. With this parameterization, the maximum likelihood estimates (MLEs) of marginal mean parameters are robust to the misspecification of time dependence. We implement an iterative procedures to obtain the MLEs of QTL genotype-specific parameters that define longitudinal binary responses. The usefulness of the model was validated by analyzing a real example in rice. Simulation studies were performed to investigate the statistical properties of the model, showing that the model has power to identify and map specific QTLs responsible for the temporal pattern of binary traits. PMID:23183762

Inverse Ising problem in continuous time: A latent variable approach

NASA Astrophysics Data System (ADS)

Donner, Christian; Opper, Manfred

2017-12-01

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

Modeling motor vehicle crashes using Poisson-gamma models: examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter.

PubMed

Lord, Dominique

2006-07-01

There has been considerable research conducted on the development of statistical models for predicting crashes on highway facilities. Despite numerous advancements made for improving the estimation tools of statistical models, the most common probabilistic structure used for modeling motor vehicle crashes remains the traditional Poisson and Poisson-gamma (or Negative Binomial) distribution; when crash data exhibit over-dispersion, the Poisson-gamma model is usually the model of choice most favored by transportation safety modelers. Crash data collected for safety studies often have the unusual attributes of being characterized by low sample mean values. Studies have shown that the goodness-of-fit of statistical models produced from such datasets can be significantly affected. This issue has been defined as the "low mean problem" (LMP). Despite recent developments on methods to circumvent the LMP and test the goodness-of-fit of models developed using such datasets, no work has so far examined how the LMP affects the fixed dispersion parameter of Poisson-gamma models used for modeling motor vehicle crashes. The dispersion parameter plays an important role in many types of safety studies and should, therefore, be reliably estimated. The primary objective of this research project was to verify whether the LMP affects the estimation of the dispersion parameter and, if it is, to determine the magnitude of the problem. The secondary objective consisted of determining the effects of an unreliably estimated dispersion parameter on common analyses performed in highway safety studies. To accomplish the objectives of the study, a series of Poisson-gamma distributions were simulated using different values describing the mean, the dispersion parameter, and the sample size. Three estimators commonly used by transportation safety modelers for estimating the dispersion parameter of Poisson-gamma models were evaluated: the method of moments, the weighted regression, and the maximum likelihood method. In an attempt to complement the outcome of the simulation study, Poisson-gamma models were fitted to crash data collected in Toronto, Ont. characterized by a low sample mean and small sample size. The study shows that a low sample mean combined with a small sample size can seriously affect the estimation of the dispersion parameter, no matter which estimator is used within the estimation process. The probability the dispersion parameter becomes unreliably estimated increases significantly as the sample mean and sample size decrease. Consequently, the results show that an unreliably estimated dispersion parameter can significantly undermine empirical Bayes (EB) estimates as well as the estimation of confidence intervals for the gamma mean and predicted response. The paper ends with recommendations about minimizing the likelihood of producing Poisson-gamma models with an unreliable dispersion parameter for modeling motor vehicle crashes.

Bayesian parameter estimation for the Wnt pathway: an infinite mixture models approach.

PubMed

Koutroumpas, Konstantinos; Ballarini, Paolo; Votsi, Irene; Cournède, Paul-Henry

2016-09-01

Likelihood-free methods, like Approximate Bayesian Computation (ABC), have been extensively used in model-based statistical inference with intractable likelihood functions. When combined with Sequential Monte Carlo (SMC) algorithms they constitute a powerful approach for parameter estimation and model selection of mathematical models of complex biological systems. A crucial step in the ABC-SMC algorithms, significantly affecting their performance, is the propagation of a set of parameter vectors through a sequence of intermediate distributions using Markov kernels. In this article, we employ Dirichlet process mixtures (DPMs) to design optimal transition kernels and we present an ABC-SMC algorithm with DPM kernels. We illustrate the use of the proposed methodology using real data for the canonical Wnt signaling pathway. A multi-compartment model of the pathway is developed and it is compared to an existing model. The results indicate that DPMs are more efficient in the exploration of the parameter space and can significantly improve ABC-SMC performance. In comparison to alternative sampling schemes that are commonly used, the proposed approach can bring potential benefits in the estimation of complex multimodal distributions. The method is used to estimate the parameters and the initial state of two models of the Wnt pathway and it is shown that the multi-compartment model fits better the experimental data. Python scripts for the Dirichlet Process Gaussian Mixture model and the Gibbs sampler are available at https://sites.google.com/site/kkoutroumpas/software konstantinos.koutroumpas@ecp.fr. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

A Review of System Identification Methods Applied to Aircraft

NASA Technical Reports Server (NTRS)

Klein, V.

1983-01-01

Airplane identification, equation error method, maximum likelihood method, parameter estimation in frequency domain, extended Kalman filter, aircraft equations of motion, aerodynamic model equations, criteria for the selection of a parsimonious model, and online aircraft identification are addressed.

Strain, curvature, and twist measurements in digital holographic interferometry using pseudo-Wigner-Ville distribution based method

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

Rajshekhar, G.; Gorthi, Sai Siva; Rastogi, Pramod

2009-09-15

Measurement of strain, curvature, and twist of a deformed object play an important role in deformation analysis. Strain depends on the first order displacement derivative, whereas curvature and twist are determined by second order displacement derivatives. This paper proposes a pseudo-Wigner-Ville distribution based method for measurement of strain, curvature, and twist in digital holographic interferometry where the object deformation or displacement is encoded as interference phase. In the proposed method, the phase derivative is estimated by peak detection of pseudo-Wigner-Ville distribution evaluated along each row/column of the reconstructed interference field. A complex exponential signal with unit amplitude and the phasemore » derivative estimate as the argument is then generated and the pseudo-Wigner-Ville distribution along each row/column of this signal is evaluated. The curvature is estimated by using peak tracking strategy for the new distribution. For estimation of twist, the pseudo-Wigner-Ville distribution is evaluated along each column/row (i.e., in alternate direction with respect to the previous one) for the generated complex exponential signal and the corresponding peak detection gives the twist estimate.« less

astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Jennings, E.; Madigan, M.

2017-04-01

Given the complexity of modern cosmological parameter inference where we are faced with non-Gaussian data and noise, correlated systematics and multi-probe correlated datasets,the Approximate Bayesian Computation (ABC) method is a promising alternative to traditional Markov Chain Monte Carlo approaches in the case where the Likelihood is intractable or unknown. The ABC method is called "Likelihood free" as it avoids explicit evaluation of the Likelihood by using a forward model simulation of the data which can include systematics. We introduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler for parameter estimation. A key challenge in astrophysics is the efficient use of large multi-probe datasets to constrain high dimensional, possibly correlated parameter spaces. With this in mind astroABC allows for massive parallelization using MPI, a framework that handles spawning of processes across multiple nodes. A key new feature of astroABC is the ability to create MPI groups with different communicators, one for the sampler and several others for the forward model simulation, which speeds up sampling time considerably. For smaller jobs the Python multiprocessing option is also available. Other key features of this new sampler include: a Sequential Monte Carlo sampler; a method for iteratively adapting tolerance levels; local covariance estimate using scikit-learn's KDTree; modules for specifying optimal covariance matrix for a component-wise or multivariate normal perturbation kernel and a weighted covariance metric; restart files output frequently so an interrupted sampling run can be resumed at any iteration; output and restart files are backed up at every iteration; user defined distance metric and simulation methods; a module for specifying heterogeneous parameter priors including non-standard prior PDFs; a module for specifying a constant, linear, log or exponential tolerance level; well-documented examples and sample scripts. This code is hosted online at https://github.com/EliseJ/astroABC.

Maximum likelihood estimation in calibrating a stereo camera setup.

PubMed

Muijtjens, A M; Roos, J M; Arts, T; Hasman, A

1999-02-01

Motion and deformation of the cardiac wall may be measured by following the positions of implanted radiopaque markers in three dimensions, using two x-ray cameras simultaneously. Regularly, calibration of the position measurement system is obtained by registration of the images of a calibration object, containing 10-20 radiopaque markers at known positions. Unfortunately, an accidental change of the position of a camera after calibration requires complete recalibration. Alternatively, redundant information in the measured image positions of stereo pairs can be used for calibration. Thus, a separate calibration procedure can be avoided. In the current study a model is developed that describes the geometry of the camera setup by five dimensionless parameters. Maximum Likelihood (ML) estimates of these parameters were obtained in an error analysis. It is shown that the ML estimates can be found by application of a nonlinear least squares procedure. Compared to the standard unweighted least squares procedure, the ML method resulted in more accurate estimates without noticeable bias. The accuracy of the ML method was investigated in relation to the object aperture. The reconstruction problem appeared well conditioned as long as the object aperture is larger than 0.1 rad. The angle between the two viewing directions appeared to be the parameter that was most likely to cause major inaccuracies in the reconstruction of the 3-D positions of the markers. Hence, attempts to improve the robustness of the method should primarily focus on reduction of the error in this parameter.

X-31 aerodynamic characteristics determined from flight data

NASA Technical Reports Server (NTRS)

Kokolios, Alex

1993-01-01

The lateral aerodynamic characteristics of the X-31 were determined at angles of attack ranging from 20 to 45 deg. Estimates of the lateral stability and control parameters were obtained by applying two parameter estimation techniques, linear regression, and the extended Kalman filter to flight test data. An attempt to apply maximum likelihood to extract parameters from the flight data was also made but failed for the reasons presented. An overview of the System Identification process is given. The overview includes a listing of the more important properties of all three estimation techniques that were applied to the data. A comparison is given of results obtained from flight test data and wind tunnel data for four important lateral parameters. Finally, future research to be conducted in this area is discussed.

The effects of ionic strength and organic matter on virus inactivation at low temperatures: general likelihood uncertainty estimation (GLUE) as an alternative to least-squares parameter optimization for the fitting of virus inactivation models

NASA Astrophysics Data System (ADS)

Mayotte, Jean-Marc; Grabs, Thomas; Sutliff-Johansson, Stacy; Bishop, Kevin

2017-06-01

This study examined how the inactivation of bacteriophage MS2 in water was affected by ionic strength (IS) and dissolved organic carbon (DOC) using static batch inactivation experiments at 4 °C conducted over a period of 2 months. Experimental conditions were characteristic of an operational managed aquifer recharge (MAR) scheme in Uppsala, Sweden. Experimental data were fit with constant and time-dependent inactivation models using two methods: (1) traditional linear and nonlinear least-squares techniques; and (2) a Monte-Carlo based parameter estimation technique called generalized likelihood uncertainty estimation (GLUE). The least-squares and GLUE methodologies gave very similar estimates of the model parameters and their uncertainty. This demonstrates that GLUE can be used as a viable alternative to traditional least-squares parameter estimation techniques for fitting of virus inactivation models. Results showed a slight increase in constant inactivation rates following an increase in the DOC concentrations, suggesting that the presence of organic carbon enhanced the inactivation of MS2. The experiment with a high IS and a low DOC was the only experiment which showed that MS2 inactivation may have been time-dependent. However, results from the GLUE methodology indicated that models of constant inactivation were able to describe all of the experiments. This suggested that inactivation time-series longer than 2 months were needed in order to provide concrete conclusions regarding the time-dependency of MS2 inactivation at 4 °C under these experimental conditions.

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

Estimation in a discrete tail rate family of recapture sampling models

NASA Technical Reports Server (NTRS)

Gupta, Rajan; Lee, Larry D.

1990-01-01

In the context of recapture sampling design for debugging experiments the problem of estimating the error or hitting rate of the faults remaining in a system is considered. Moment estimators are derived for a family of models in which the rate parameters are assumed proportional to the tail probabilities of a discrete distribution on the positive integers. The estimators are shown to be asymptotically normal and fully efficient. Their fixed sample properties are compared, through simulation, with those of the conditional maximum likelihood estimators.

Estimating multilevel logistic regression models when the number of clusters is low: a comparison of different statistical software procedures.

PubMed

Austin, Peter C

2010-04-22

Multilevel logistic regression models are increasingly being used to analyze clustered data in medical, public health, epidemiological, and educational research. Procedures for estimating the parameters of such models are available in many statistical software packages. There is currently little evidence on the minimum number of clusters necessary to reliably fit multilevel regression models. We conducted a Monte Carlo study to compare the performance of different statistical software procedures for estimating multilevel logistic regression models when the number of clusters was low. We examined procedures available in BUGS, HLM, R, SAS, and Stata. We found that there were qualitative differences in the performance of different software procedures for estimating multilevel logistic models when the number of clusters was low. Among the likelihood-based procedures, estimation methods based on adaptive Gauss-Hermite approximations to the likelihood (glmer in R and xtlogit in Stata) or adaptive Gaussian quadrature (Proc NLMIXED in SAS) tended to have superior performance for estimating variance components when the number of clusters was small, compared to software procedures based on penalized quasi-likelihood. However, only Bayesian estimation with BUGS allowed for accurate estimation of variance components when there were fewer than 10 clusters. For all statistical software procedures, estimation of variance components tended to be poor when there were only five subjects per cluster, regardless of the number of clusters.

Selected aspects of prior and likelihood information for a Bayesian classifier in a road safety analysis.

PubMed

Nowakowska, Marzena

2017-04-01

The development of the Bayesian logistic regression model classifying the road accident severity is discussed. The already exploited informative priors (method of moments, maximum likelihood estimation, and two-stage Bayesian updating), along with the original idea of a Boot prior proposal, are investigated when no expert opinion has been available. In addition, two possible approaches to updating the priors, in the form of unbalanced and balanced training data sets, are presented. The obtained logistic Bayesian models are assessed on the basis of a deviance information criterion (DIC), highest probability density (HPD) intervals, and coefficients of variation estimated for the model parameters. The verification of the model accuracy has been based on sensitivity, specificity and the harmonic mean of sensitivity and specificity, all calculated from a test data set. The models obtained from the balanced training data set have a better classification quality than the ones obtained from the unbalanced training data set. The two-stage Bayesian updating prior model and the Boot prior model, both identified with the use of the balanced training data set, outperform the non-informative, method of moments, and maximum likelihood estimation prior models. It is important to note that one should be careful when interpreting the parameters since different priors can lead to different models. Copyright © 2017 Elsevier Ltd. All rights reserved.

Volume effects of late term normal tissue toxicity in prostate cancer radiotherapy

NASA Astrophysics Data System (ADS)

Bonta, Dacian Viorel

Modeling of volume effects for treatment toxicity is paramount for optimization of radiation therapy. This thesis proposes a new model for calculating volume effects in gastro-intestinal and genito-urinary normal tissue complication probability (NTCP) following radiation therapy for prostate carcinoma. The radiobiological and the pathological basis for this model and its relationship to other models are detailed. A review of the radiobiological experiments and published clinical data identified salient features and specific properties a biologically adequate model has to conform to. The new model was fit to a set of actual clinical data. In order to verify the goodness of fit, two established NTCP models and a non-NTCP measure for complication risk were fitted to the same clinical data. The method of fit for the model parameters was maximum likelihood estimation. Within the framework of the maximum likelihood approach I estimated the parameter uncertainties for each complication prediction model. The quality-of-fit was determined using the Aikaike Information Criterion. Based on the model that provided the best fit, I identified the volume effects for both types of toxicities. Computer-based bootstrap resampling of the original dataset was used to estimate the bias and variance for the fitted parameter values. Computer simulation was also used to estimate the population size that generates a specific uncertainty level (3%) in the value of predicted complication probability. The same method was used to estimate the size of the patient population needed for accurate choice of the model underlying the NTCP. The results indicate that, depending on the number of parameters of a specific NTCP model, 100 (for two parameter models) and 500 patients (for three parameter models) are needed for accurate parameter fit. Correlation of complication occurrence in patients was also investigated. The results suggest that complication outcomes are correlated in a patient, although the correlation coefficient is rather small.

Image informative maps for component-wise estimating parameters of signal-dependent noise

NASA Astrophysics Data System (ADS)

Uss, Mykhail L.; Vozel, Benoit; Lukin, Vladimir V.; Chehdi, Kacem

2013-01-01

We deal with the problem of blind parameter estimation of signal-dependent noise from mono-component image data. Multispectral or color images can be processed in a component-wise manner. The main results obtained rest on the assumption that the image texture and noise parameters estimation problems are interdependent. A two-dimensional fractal Brownian motion (fBm) model is used for locally describing image texture. A polynomial model is assumed for the purpose of describing the signal-dependent noise variance dependence on image intensity. Using the maximum likelihood approach, estimates of both fBm-model and noise parameters are obtained. It is demonstrated that Fisher information (FI) on noise parameters contained in an image is distributed nonuniformly over intensity coordinates (an image intensity range). It is also shown how to find the most informative intensities and the corresponding image areas for a given noisy image. The proposed estimator benefits from these detected areas to improve the estimation accuracy of signal-dependent noise parameters. Finally, the potential estimation accuracy (Cramér-Rao Lower Bound, or CRLB) of noise parameters is derived, providing confidence intervals of these estimates for a given image. In the experiment, the proposed and existing state-of-the-art noise variance estimators are compared for a large image database using CRLB-based statistical efficiency criteria.

Probabilistic Modeling of the Renal Stone Formation Module

NASA Technical Reports Server (NTRS)

Best, Lauren M.; Myers, Jerry G.; Goodenow, Debra A.; McRae, Michael P.; Jackson, Travis C.

2013-01-01

The Integrated Medical Model (IMM) is a probabilistic tool, used in mission planning decision making and medical systems risk assessments. The IMM project maintains a database of over 80 medical conditions that could occur during a spaceflight, documenting an incidence rate and end case scenarios for each. In some cases, where observational data are insufficient to adequately define the inflight medical risk, the IMM utilizes external probabilistic modules to model and estimate the event likelihoods. One such medical event of interest is an unpassed renal stone. Due to a high salt diet and high concentrations of calcium in the blood (due to bone depletion caused by unloading in the microgravity environment) astronauts are at a considerable elevated risk for developing renal calculi (nephrolithiasis) while in space. Lack of observed incidences of nephrolithiasis has led HRP to initiate the development of the Renal Stone Formation Module (RSFM) to create a probabilistic simulator capable of estimating the likelihood of symptomatic renal stone presentation in astronauts on exploration missions. The model consists of two major parts. The first is the probabilistic component, which utilizes probability distributions to assess the range of urine electrolyte parameters and a multivariate regression to transform estimated crystal density and size distributions to the likelihood of the presentation of nephrolithiasis symptoms. The second is a deterministic physical and chemical model of renal stone growth in the kidney developed by Kassemi et al. The probabilistic component of the renal stone model couples the input probability distributions describing the urine chemistry, astronaut physiology, and system parameters with the physical and chemical outputs and inputs to the deterministic stone growth model. These two parts of the model are necessary to capture the uncertainty in the likelihood estimate. The model will be driven by Monte Carlo simulations, continuously randomly sampling the probability distributions of the electrolyte concentrations and system parameters that are inputs into the deterministic model. The total urine chemistry concentrations are used to determine the urine chemistry activity using the Joint Expert Speciation System (JESS), a biochemistry model. Information used from JESS is then fed into the deterministic growth model. Outputs from JESS and the deterministic model are passed back to the probabilistic model where a multivariate regression is used to assess the likelihood of a stone forming and the likelihood of a stone requiring clinical intervention. The parameters used to determine to quantify these risks include: relative supersaturation (RS) of calcium oxalate, citrate/calcium ratio, crystal number density, total urine volume, pH, magnesium excretion, maximum stone width, and ureteral location. Methods and Validation: The RSFM is designed to perform a Monte Carlo simulation to generate probability distributions of clinically significant renal stones, as well as provide an associated uncertainty in the estimate. Initially, early versions will be used to test integration of the components and assess component validation and verification (V&V), with later versions used to address questions regarding design reference mission scenarios. Once integrated with the deterministic component, the credibility assessment of the integrated model will follow NASA STD 7009 requirements.

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

NASA Technical Reports Server (NTRS)

Peters, C. (Principal Investigator)

1980-01-01

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

Uncertainty analysis of signal deconvolution using a measured instrument response function

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

Hartouni, E. P.; Beeman, B.; Caggiano, J. A.

2016-10-05

A common analysis procedure minimizes the ln-likelihood that a set of experimental observables matches a parameterized model of the observation. The model includes a description of the underlying physical process as well as the instrument response function (IRF). Here, we investigate the National Ignition Facility (NIF) neutron time-of-flight (nTOF) spectrometers, the IRF is constructed from measurements and models. IRF measurements have a finite precision that can make significant contributions to the uncertainty estimate of the physical model’s parameters. Finally, we apply a Bayesian analysis to properly account for IRF uncertainties in calculating the ln-likelihood function used to find the optimummore » physical parameters.« less

Rotorcraft Blade Mode Damping Identification from Random Responses Using a Recursive Maximum Likelihood Algorithm

NASA Technical Reports Server (NTRS)

Molusis, J. A.

1982-01-01

An on line technique is presented for the identification of rotor blade modal damping and frequency from rotorcraft random response test data. The identification technique is based upon a recursive maximum likelihood (RML) algorithm, which is demonstrated to have excellent convergence characteristics in the presence of random measurement noise and random excitation. The RML technique requires virtually no user interaction, provides accurate confidence bands on the parameter estimates, and can be used for continuous monitoring of modal damping during wind tunnel or flight testing. Results are presented from simulation random response data which quantify the identified parameter convergence behavior for various levels of random excitation. The data length required for acceptable parameter accuracy is shown to depend upon the amplitude of random response and the modal damping level. Random response amplitudes of 1.25 degrees to .05 degrees are investigated. The RML technique is applied to hingeless rotor test data. The inplane lag regressing mode is identified at different rotor speeds. The identification from the test data is compared with the simulation results and with other available estimates of frequency and damping.

Bivariate categorical data analysis using normal linear conditional multinomial probability model.

PubMed

Sun, Bingrui; Sutradhar, Brajendra

2015-02-10

Bivariate multinomial data such as the left and right eyes retinopathy status data are analyzed either by using a joint bivariate probability model or by exploiting certain odds ratio-based association models. However, the joint bivariate probability model yields marginal probabilities, which are complicated functions of marginal and association parameters for both variables, and the odds ratio-based association model treats the odds ratios involved in the joint probabilities as 'working' parameters, which are consequently estimated through certain arbitrary 'working' regression models. Also, this later odds ratio-based model does not provide any easy interpretations of the correlations between two categorical variables. On the basis of pre-specified marginal probabilities, in this paper, we develop a bivariate normal type linear conditional multinomial probability model to understand the correlations between two categorical variables. The parameters involved in the model are consistently estimated using the optimal likelihood and generalized quasi-likelihood approaches. The proposed model and the inferences are illustrated through an intensive simulation study as well as an analysis of the well-known Wisconsin Diabetic Retinopathy status data. Copyright © 2014 John Wiley & Sons, Ltd.

The Performance of ML, GLS, and WLS Estimation in Structural Equation Modeling under Conditions of Misspecification and Nonnormality.

ERIC Educational Resources Information Center

Olsson, Ulf Henning; Foss, Tron; Troye, Sigurd V.; Howell, Roy D.

2000-01-01

Used simulation to demonstrate how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Discusses results for maximum likelihood (ML), generalized least squares (GLS), and weighted least…

A New Lifetime Distribution with Bathtube and Unimodal Hazard Function

NASA Astrophysics Data System (ADS)

Barriga, Gladys D. C.; Louzada-Neto, Francisco; Cancho, Vicente G.

2008-11-01

In this paper we propose a new lifetime distribution which accommodate bathtub-shaped, unimodal, increasing and decreasing hazard function. Some special particular cases are derived, including the standard Weibull distribution. Maximum likelihood estimation is considered for estimate the tree parameters present in the model. The methodology is illustrated in a real data set on industrial devices on a lite test.

State-Space Modeling of Dynamic Psychological Processes via the Kalman Smoother Algorithm: Rationale, Finite Sample Properties, and Applications

ERIC Educational Resources Information Center

Song, Hairong; Ferrer, Emilio

2009-01-01

This article presents a state-space modeling (SSM) technique for fitting process factor analysis models directly to raw data. The Kalman smoother via the expectation-maximization algorithm to obtain maximum likelihood parameter estimates is used. To examine the finite sample properties of the estimates in SSM when common factors are involved, a…

Learn-as-you-go acceleration of cosmological parameter estimates

NASA Astrophysics Data System (ADS)

Aslanyan, Grigor; Easther, Richard; Price, Layne C.

2015-09-01

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitly describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of ΛCDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of 6.5 for Metropolis-Hastings and 3.5 for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.

Learn-as-you-go acceleration of cosmological parameter estimates

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

Aslanyan, Grigor; Easther, Richard; Price, Layne C., E-mail: g.aslanyan@auckland.ac.nz, E-mail: r.easther@auckland.ac.nz, E-mail: lpri691@aucklanduni.ac.nz

2015-09-01

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitlymore » describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of ΛCDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of 6.5 for Metropolis-Hastings and 3.5 for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.« less

A Statistician's View of Upcoming Grand Challenges

NASA Astrophysics Data System (ADS)

Meng, Xiao Li

2010-01-01

In this session we have seen some snapshots of the broad spectrum of challenges, in this age of huge, complex, computer-intensive models, data, instruments,and questions. These challenges bridge astronomy at many wavelengths; basic physics; machine learning; -- and statistics. At one end of our spectrum, we think of 'compressing' the data with non-parametric methods. This raises the question of creating 'pseudo-replicas' of the data for uncertainty estimates. What would be involved in, e.g. boot-strap and related methods? Somewhere in the middle are these non-parametric methods for encapsulating the uncertainty information. At the far end, we find more model-based approaches, with the physics model embedded in the likelihood and analysis. The other distinctive problem is really the 'black-box' problem, where one has a complicated e.g. fundamental physics-based computer code, or 'black box', and one needs to know how changing the parameters at input -- due to uncertainties of any kind -- will map to changing the output. All of these connect to challenges in complexity of data and computation speed. Dr. Meng will highlight ways to 'cut corners' with advanced computational techniques, such as Parallel Tempering and Equal Energy methods. As well, there are cautionary tales of running automated analysis with real data -- where "30 sigma" outliers due to data artifacts can be more common than the astrophysical event of interest.

Case-Deletion Diagnostics for Nonlinear Structural Equation Models

ERIC Educational Resources Information Center

Lee, Sik-Yum; Lu, Bin

2003-01-01

In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the…

Objectively combining AR5 instrumental period and paleoclimate climate sensitivity evidence

NASA Astrophysics Data System (ADS)

Lewis, Nicholas; Grünwald, Peter

2018-03-01

Combining instrumental period evidence regarding equilibrium climate sensitivity with largely independent paleoclimate proxy evidence should enable a more constrained sensitivity estimate to be obtained. Previous, subjective Bayesian approaches involved selection of a prior probability distribution reflecting the investigators' beliefs about climate sensitivity. Here a recently developed approach employing two different statistical methods—objective Bayesian and frequentist likelihood-ratio—is used to combine instrumental period and paleoclimate evidence based on data presented and assessments made in the IPCC Fifth Assessment Report. Probabilistic estimates from each source of evidence are represented by posterior probability density functions (PDFs) of physically-appropriate form that can be uniquely factored into a likelihood function and a noninformative prior distribution. The three-parameter form is shown accurately to fit a wide range of estimated climate sensitivity PDFs. The likelihood functions relating to the probabilistic estimates from the two sources are multiplicatively combined and a prior is derived that is noninformative for inference from the combined evidence. A posterior PDF that incorporates the evidence from both sources is produced using a single-step approach, which avoids the order-dependency that would arise if Bayesian updating were used. Results are compared with an alternative approach using the frequentist signed root likelihood ratio method. Results from these two methods are effectively identical, and provide a 5-95% range for climate sensitivity of 1.1-4.05 K (median 1.87 K).

Estimation of submarine mass failure probability from a sequence of deposits with age dates

USGS Publications Warehouse

Geist, Eric L.; Chaytor, Jason D.; Parsons, Thomas E.; ten Brink, Uri S.

2013-01-01

The empirical probability of submarine mass failure is quantified from a sequence of dated mass-transport deposits. Several different techniques are described to estimate the parameters for a suite of candidate probability models. The techniques, previously developed for analyzing paleoseismic data, include maximum likelihood and Type II (Bayesian) maximum likelihood methods derived from renewal process theory and Monte Carlo methods. The estimated mean return time from these methods, unlike estimates from a simple arithmetic mean of the center age dates and standard likelihood methods, includes the effects of age-dating uncertainty and of open time intervals before the first and after the last event. The likelihood techniques are evaluated using Akaike’s Information Criterion (AIC) and Akaike’s Bayesian Information Criterion (ABIC) to select the optimal model. The techniques are applied to mass transport deposits recorded in two Integrated Ocean Drilling Program (IODP) drill sites located in the Ursa Basin, northern Gulf of Mexico. Dates of the deposits were constrained by regional bio- and magnetostratigraphy from a previous study. Results of the analysis indicate that submarine mass failures in this location occur primarily according to a Poisson process in which failures are independent and return times follow an exponential distribution. However, some of the model results suggest that submarine mass failures may occur quasiperiodically at one of the sites (U1324). The suite of techniques described in this study provides quantitative probability estimates of submarine mass failure occurrence, for any number of deposits and age uncertainty distributions.

An Adaptive Kalman Filter Using a Simple Residual Tuning Method

NASA Technical Reports Server (NTRS)

Harman, Richard R.

1999-01-01

One difficulty in using Kalman filters in real world situations is the selection of the correct process noise, measurement noise, and initial state estimate and covariance. These parameters are commonly referred to as tuning parameters. Multiple methods have been developed to estimate these parameters. Most of those methods such as maximum likelihood, subspace, and observer Kalman Identification require extensive offline processing and are not suitable for real time processing. One technique, which is suitable for real time processing, is the residual tuning method. Any mismodeling of the filter tuning parameters will result in a non-white sequence for the filter measurement residuals. The residual tuning technique uses this information to estimate corrections to those tuning parameters. The actual implementation results in a set of sequential equations that run in parallel with the Kalman filter. A. H. Jazwinski developed a specialized version of this technique for estimation of process noise. Equations for the estimation of the measurement noise have also been developed. These algorithms are used to estimate the process noise and measurement noise for the Wide Field Infrared Explorer star tracker and gyro.

Multilevel modeling of single-case data: A comparison of maximum likelihood and Bayesian estimation.

PubMed

Moeyaert, Mariola; Rindskopf, David; Onghena, Patrick; Van den Noortgate, Wim

2017-12-01

The focus of this article is to describe Bayesian estimation, including construction of prior distributions, and to compare parameter recovery under the Bayesian framework (using weakly informative priors) and the maximum likelihood (ML) framework in the context of multilevel modeling of single-case experimental data. Bayesian estimation results were found similar to ML estimation results in terms of the treatment effect estimates, regardless of the functional form and degree of information included in the prior specification in the Bayesian framework. In terms of the variance component estimates, both the ML and Bayesian estimation procedures result in biased and less precise variance estimates when the number of participants is small (i.e., 3). By increasing the number of participants to 5 or 7, the relative bias is close to 5% and more precise estimates are obtained for all approaches, except for the inverse-Wishart prior using the identity matrix. When a more informative prior was added, more precise estimates for the fixed effects and random effects were obtained, even when only 3 participants were included. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

LFlGRB: Luminosity function of long gamma-ray bursts

NASA Astrophysics Data System (ADS)

Paul, Debdutta

2018-04-01

LFlGRB models the luminosity function (LF) of long Gamma Ray Bursts (lGRBs) by using a sample of Swift and Fermi lGRBs to re-derive the parameters of the Yonetoku correlation and self-consistently estimate pseudo-redshifts of all the bursts with unknown redshifts. The GRB formation rate is modeled as the product of the cosmic star formation rate and a GRB formation efficiency for a given stellar mass.

The use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

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

Rupšys, P.

A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.

Robust Methods for Moderation Analysis with a Two-Level Regression Model.

PubMed

Yang, Miao; Yuan, Ke-Hai

2016-01-01

Moderation analysis has many applications in social sciences. Most widely used estimation methods for moderation analysis assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the results from a classical moderation analysis can be misleading. For more reliable moderation analysis, this article proposes two robust methods with a two-level regression model when the predictors do not contain measurement error. One method is based on maximum likelihood with Student's t distribution and the other is based on M-estimators with Huber-type weights. An algorithm for obtaining the robust estimators is developed. Consistent estimates of standard errors of the robust estimators are provided. The robust approaches are compared against normal-distribution-based maximum likelihood (NML) with respect to power and accuracy of parameter estimates through a simulation study. Results show that the robust approaches outperform NML under various distributional conditions. Application of the robust methods is illustrated through a real data example. An R program is developed and documented to facilitate the application of the robust methods.

A comparison of minimum distance and maximum likelihood techniques for proportion estimation

NASA Technical Reports Server (NTRS)

Woodward, W. A.; Schucany, W. R.; Lindsey, H.; Gray, H. L.

1982-01-01

The estimation of mixing proportions P sub 1, P sub 2,...P sub m in the mixture density f(x) = the sum of the series P sub i F sub i(X) with i = 1 to M is often encountered in agricultural remote sensing problems in which case the p sub i's usually represent crop proportions. In these remote sensing applications, component densities f sub i(x) have typically been assumed to be normally distributed, and parameter estimation has been accomplished using maximum likelihood (ML) techniques. Minimum distance (MD) estimation is examined as an alternative to ML where, in this investigation, both procedures are based upon normal components. Results indicate that ML techniques are superior to MD when component distributions actually are normal, while MD estimation provides better estimates than ML under symmetric departures from normality. When component distributions are not symmetric, however, it is seen that neither of these normal based techniques provides satisfactory results.

Maximum likelihood estimation for semiparametric transformation models with interval-censored data

PubMed Central

Mao, Lu; Lin, D. Y.

2016-01-01

Abstract Interval censoring arises frequently in clinical, epidemiological, financial and sociological studies, where the event or failure of interest is known only to occur within an interval induced by periodic monitoring. We formulate the effects of potentially time-dependent covariates on the interval-censored failure time through a broad class of semiparametric transformation models that encompasses proportional hazards and proportional odds models. We consider nonparametric maximum likelihood estimation for this class of models with an arbitrary number of monitoring times for each subject. We devise an EM-type algorithm that converges stably, even in the presence of time-dependent covariates, and show that the estimators for the regression parameters are consistent, asymptotically normal, and asymptotically efficient with an easily estimated covariance matrix. Finally, we demonstrate the performance of our procedures through simulation studies and application to an HIV/AIDS study conducted in Thailand. PMID:27279656

Score Estimating Equations from Embedded Likelihood Functions under Accelerated Failure Time Model

PubMed Central

NING, JING; QIN, JING; SHEN, YU

2014-01-01

SUMMARY The semiparametric accelerated failure time (AFT) model is one of the most popular models for analyzing time-to-event outcomes. One appealing feature of the AFT model is that the observed failure time data can be transformed to identically independent distributed random variables without covariate effects. We describe a class of estimating equations based on the score functions for the transformed data, which are derived from the full likelihood function under commonly used semiparametric models such as the proportional hazards or proportional odds model. The methods of estimating regression parameters under the AFT model can be applied to traditional right-censored survival data as well as more complex time-to-event data subject to length-biased sampling. We establish the asymptotic properties and evaluate the small sample performance of the proposed estimators. We illustrate the proposed methods through applications in two examples. PMID:25663727

Rational selection of experimental readout and intervention sites for reducing uncertainties in computational model predictions.

PubMed

Flassig, Robert J; Migal, Iryna; der Zalm, Esther van; Rihko-Struckmann, Liisa; Sundmacher, Kai

2015-01-16

Understanding the dynamics of biological processes can substantially be supported by computational models in the form of nonlinear ordinary differential equations (ODE). Typically, this model class contains many unknown parameters, which are estimated from inadequate and noisy data. Depending on the ODE structure, predictions based on unmeasured states and associated parameters are highly uncertain, even undetermined. For given data, profile likelihood analysis has been proven to be one of the most practically relevant approaches for analyzing the identifiability of an ODE structure, and thus model predictions. In case of highly uncertain or non-identifiable parameters, rational experimental design based on various approaches has shown to significantly reduce parameter uncertainties with minimal amount of effort. In this work we illustrate how to use profile likelihood samples for quantifying the individual contribution of parameter uncertainty to prediction uncertainty. For the uncertainty quantification we introduce the profile likelihood sensitivity (PLS) index. Additionally, for the case of several uncertain parameters, we introduce the PLS entropy to quantify individual contributions to the overall prediction uncertainty. We show how to use these two criteria as an experimental design objective for selecting new, informative readouts in combination with intervention site identification. The characteristics of the proposed multi-criterion objective are illustrated with an in silico example. We further illustrate how an existing practically non-identifiable model for the chlorophyll fluorescence induction in a photosynthetic organism, D. salina, can be rendered identifiable by additional experiments with new readouts. Having data and profile likelihood samples at hand, the here proposed uncertainty quantification based on prediction samples from the profile likelihood provides a simple way for determining individual contributions of parameter uncertainties to uncertainties in model predictions. The uncertainty quantification of specific model predictions allows identifying regions, where model predictions have to be considered with care. Such uncertain regions can be used for a rational experimental design to render initially highly uncertain model predictions into certainty. Finally, our uncertainty quantification directly accounts for parameter interdependencies and parameter sensitivities of the specific prediction.

Pseudo-spectral methodology for a quantitative assessment of the cover of in-stream vegetation in small streams

NASA Astrophysics Data System (ADS)

Hershkovitz, Yaron; Anker, Yaakov; Ben-Dor, Eyal; Schwartz, Guy; Gasith, Avital

2010-05-01

In-stream vegetation is a key ecosystem component in many fluvial ecosystems, having cascading effects on stream conditions and biotic structure. Traditionally, ground-level surveys (e.g. grid and transect analyses) are commonly used for estimating cover of aquatic macrophytes. Nonetheless, this methodological approach is highly time consuming and usually yields information which is practically limited to habitat and sub-reach scales. In contrast, remote-sensing techniques (e.g. satellite imagery and airborne photography), enable collection of large datasets over section, stream and basin scales, in relatively short time and reasonable cost. However, the commonly used spatial high resolution (1m) is often inadequate for examining aquatic vegetation on habitat or sub-reach scales. We examined the utility of a pseudo-spectral methodology, using RGB digital photography for estimating the cover of in-stream vegetation in a small Mediterranean-climate stream. We compared this methodology with that obtained by traditional ground-level grid methodology and with an airborne hyper-spectral remote sensing survey (AISA-ES). The study was conducted along a 2 km section of an intermittent stream (Taninim stream, Israel). When studied, the stream was dominated by patches of watercress (Nasturtium officinale) and mats of filamentous algae (Cladophora glomerata). The extent of vegetation cover at the habitat and section scales (100 and 104 m, respectively) were estimated by the pseudo-spectral methodology, using an airborne Roli camera with a Phase-One P 45 (39 MP) CCD image acquisition unit. The swaths were taken in elevation of about 460 m having a spatial resolution of about 4 cm (NADIR). For measuring vegetation cover at the section scale (104 m) we also used a 'push-broom' AISA-ES hyper-spectral swath having a sensor configuration of 182 bands (350-2500 nm) at elevation of ca. 1,200 m (i.e. spatial resolution of ca. 1 m). Simultaneously, with every swath we used an Analytical Spectral Device (ASD) to measure hyper-spectral signatures (2150 bands configuration; 350-2500 nm) of selected ground-level targets (located by GPS) of soil, water; vegetation (common reed, watercress, filamentous algae) and standard EVA foam colored sheets (red, green, blue, black and white). Processing and analysis of the data were performed over an ITT ENVI platform. The hyper-spectral image underwent radiometric calibration according to the flight and sensor calibration parameters on CALIGEO platform and the raw DN scale was converted into radiance scale. Ground level visual survey of vegetation cover and height was applied at the habitat scale (100 m) by placing a 1m2 netted grids (10x10cm cells) along 'bank-to-bank' transect (in triplicates). Estimates of plant cover obtained by the pseudo-spectral methodology at the habitat scale were 35-61% for the watercress, 0.4-25% for the filamentous algae and 27-51% for plant-free patches. The respective estimates by ground level visual survey were 26-50, 14-43% and 36-50%. The pseudo-spectral methodology also yielded estimates for the section scale (104 m) of ca. 39% for the watercress, ca. 32% for the filamentous algae and 6% for plant-free patches. The respective estimates obtained by hyper-spectral swath were 38, 26 and 8%. Validation against ground-level measurements proved that pseudo-spectral methodology gives reasonably good estimates of in-stream plant cover. Therefore, this methodology can serve as a substitute for ground level estimates at small stream scales and for the low resolution hyper-spectral methodology at larger scales.

Application of parameter estimation to highly unstable aircraft

NASA Technical Reports Server (NTRS)

Maine, R. E.; Murray, J. E.

1986-01-01

This paper discusses the application of parameter estimation to highly unstable aircraft. It includes a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

Application of parameter estimation to highly unstable aircraft

NASA Technical Reports Server (NTRS)

Maine, R. E.; Murray, J. E.

1986-01-01

The application of parameter estimation to highly unstable aircraft is discussed. Included are a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

Adjusting for overdispersion in piecewise exponential regression models to estimate excess mortality rate in population-based research.

PubMed

Luque-Fernandez, Miguel Angel; Belot, Aurélien; Quaresma, Manuela; Maringe, Camille; Coleman, Michel P; Rachet, Bernard

2016-10-01

In population-based cancer research, piecewise exponential regression models are used to derive adjusted estimates of excess mortality due to cancer using the Poisson generalized linear modelling framework. However, the assumption that the conditional mean and variance of the rate parameter given the set of covariates x i are equal is strong and may fail to account for overdispersion given the variability of the rate parameter (the variance exceeds the mean). Using an empirical example, we aimed to describe simple methods to test and correct for overdispersion. We used a regression-based score test for overdispersion under the relative survival framework and proposed different approaches to correct for overdispersion including a quasi-likelihood, robust standard errors estimation, negative binomial regression and flexible piecewise modelling. All piecewise exponential regression models showed the presence of significant inherent overdispersion (p-value <0.001). However, the flexible piecewise exponential model showed the smallest overdispersion parameter (3.2 versus 21.3) for non-flexible piecewise exponential models. We showed that there were no major differences between methods. However, using a flexible piecewise regression modelling, with either a quasi-likelihood or robust standard errors, was the best approach as it deals with both, overdispersion due to model misspecification and true or inherent overdispersion.

Sensor management in RADAR/IRST track fusion

NASA Astrophysics Data System (ADS)

Hu, Shi-qiang; Jing, Zhong-liang

2004-07-01

In this paper, a novel radar management strategy technique suitable for RADAR/IRST track fusion, which is based on Fisher Information Matrix (FIM) and fuzzy stochastic decision approach, is put forward. Firstly, optimal radar measurements' scheduling is obtained by the method of maximizing determinant of the Fisher information matrix of radar and IRST measurements, which is managed by the expert system. Then, suggested a "pseudo sensor" to predict the possible target position using the polynomial method based on the radar and IRST measurements, using "pseudo sensor" model to estimate the target position even if the radar is turned off. At last, based on the tracking performance and the state of target maneuver, fuzzy stochastic decision is used to adjust the optimal radar scheduling and retrieve the module parameter of "pseudo sensor". The experiment result indicates that the algorithm can not only limit Radar activity effectively but also keep the tracking accuracy of active/passive system well. And this algorithm eliminates the drawback of traditional Radar management methods that the Radar activity is fixed and not easy to control and protect.

The relative pose estimation of aircraft based on contour model

NASA Astrophysics Data System (ADS)

Fu, Tai; Sun, Xiangyi

2017-02-01

This paper proposes a relative pose estimation approach based on object contour model. The first step is to obtain a two-dimensional (2D) projection of three-dimensional (3D)-model-based target, which will be divided into 40 forms by clustering and LDA analysis. Then we proceed by extracting the target contour in each image and computing their Pseudo-Zernike Moments (PZM), thus a model library is constructed in an offline mode. Next, we spot a projection contour that resembles the target silhouette most in the present image from the model library with reference of PZM; then similarity transformation parameters are generated as the shape context is applied to match the silhouette sampling location, from which the identification parameters of target can be further derived. Identification parameters are converted to relative pose parameters, in the premise that these values are the initial result calculated via iterative refinement algorithm, as the relative pose parameter is in the neighborhood of actual ones. At last, Distance Image Iterative Least Squares (DI-ILS) is employed to acquire the ultimate relative pose parameters.

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.

dPIRPLE: a joint estimation framework for deformable registration and penalized-likelihood CT image reconstruction using prior images

NASA Astrophysics Data System (ADS)

Dang, H.; Wang, A. S.; Sussman, Marc S.; Siewerdsen, J. H.; Stayman, J. W.

2014-09-01

Sequential imaging studies are conducted in many clinical scenarios. Prior images from previous studies contain a great deal of patient-specific anatomical information and can be used in conjunction with subsequent imaging acquisitions to maintain image quality while enabling radiation dose reduction (e.g., through sparse angular sampling, reduction in fluence, etc). However, patient motion between images in such sequences results in misregistration between the prior image and current anatomy. Existing prior-image-based approaches often include only a simple rigid registration step that can be insufficient for capturing complex anatomical motion, introducing detrimental effects in subsequent image reconstruction. In this work, we propose a joint framework that estimates the 3D deformation between an unregistered prior image and the current anatomy (based on a subsequent data acquisition) and reconstructs the current anatomical image using a model-based reconstruction approach that includes regularization based on the deformed prior image. This framework is referred to as deformable prior image registration, penalized-likelihood estimation (dPIRPLE). Central to this framework is the inclusion of a 3D B-spline-based free-form-deformation model into the joint registration-reconstruction objective function. The proposed framework is solved using a maximization strategy whereby alternating updates to the registration parameters and image estimates are applied allowing for improvements in both the registration and reconstruction throughout the optimization process. Cadaver experiments were conducted on a cone-beam CT testbench emulating a lung nodule surveillance scenario. Superior reconstruction accuracy and image quality were demonstrated using the dPIRPLE algorithm as compared to more traditional reconstruction methods including filtered backprojection, penalized-likelihood estimation (PLE), prior image penalized-likelihood estimation (PIPLE) without registration, and prior image penalized-likelihood estimation with rigid registration of a prior image (PIRPLE) over a wide range of sampling sparsity and exposure levels.

NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model

NASA Technical Reports Server (NTRS)

1979-01-01

A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.

Methods and Tools for Evaluating Uncertainty in Ecological Models: A Survey

EPA Science Inventory

Poster presented at the Ecological Society of America Meeting. Ecologists are familiar with a variety of uncertainty techniques, particularly in the intersection of maximum likelihood parameter estimation and Monte Carlo analysis techniques, as well as a recent increase in Baye...

On Correlated-noise Analyses Applied to Exoplanet Light Curves

NASA Astrophysics Data System (ADS)

Cubillos, Patricio; Harrington, Joseph; Loredo, Thomas J.; Lust, Nate B.; Blecic, Jasmina; Stemm, Madison

2017-01-01

Time-correlated noise is a significant source of uncertainty when modeling exoplanet light-curve data. A correct assessment of correlated noise is fundamental to determine the true statistical significance of our findings. Here, we review three of the most widely used correlated-noise estimators in the exoplanet field, the time-averaging, residual-permutation, and wavelet-likelihood methods. We argue that the residual-permutation method is unsound in estimating the uncertainty of parameter estimates. We thus recommend to refrain from this method altogether. We characterize the behavior of the time averaging’s rms-versus-bin-size curves at bin sizes similar to the total observation duration, which may lead to underestimated uncertainties. For the wavelet-likelihood method, we note errors in the published equations and provide a list of corrections. We further assess the performance of these techniques by injecting and retrieving eclipse signals into synthetic and real Spitzer light curves, analyzing the results in terms of the relative-accuracy and coverage-fraction statistics. Both the time-averaging and wavelet-likelihood methods significantly improve the estimate of the eclipse depth over a white-noise analysis (a Markov-chain Monte Carlo exploration assuming uncorrelated noise). However, the corrections are not perfect when retrieving the eclipse depth from Spitzer data sets, these methods covered the true (injected) depth within the 68% credible region in only ˜45%-65% of the trials. Lastly, we present our open-source model-fitting tool, Multi-Core Markov-Chain Monte Carlo (MC3). This package uses Bayesian statistics to estimate the best-fitting values and the credible regions for the parameters for a (user-provided) model. MC3 is a Python/C code, available at https://github.com/pcubillos/MCcubed.

On the use of Bayesian Monte-Carlo in evaluation of nuclear data

NASA Astrophysics Data System (ADS)

De Saint Jean, Cyrille; Archier, Pascal; Privas, Edwin; Noguere, Gilles

2017-09-01

As model parameters, necessary ingredients of theoretical models, are not always predicted by theory, a formal mathematical framework associated to the evaluation work is needed to obtain the best set of parameters (resonance parameters, optical models, fission barrier, average width, multigroup cross sections) with Bayesian statistical inference by comparing theory to experiment. The formal rule related to this methodology is to estimate the posterior density probability function of a set of parameters by solving an equation of the following type: pdf(posterior) ˜ pdf(prior) × a likelihood function. A fitting procedure can be seen as an estimation of the posterior density probability of a set of parameters (referred as x→?) knowing a prior information on these parameters and a likelihood which gives the probability density function of observing a data set knowing x→?. To solve this problem, two major paths could be taken: add approximations and hypothesis and obtain an equation to be solved numerically (minimum of a cost function or Generalized least Square method, referred as GLS) or use Monte-Carlo sampling of all prior distributions and estimate the final posterior distribution. Monte Carlo methods are natural solution for Bayesian inference problems. They avoid approximations (existing in traditional adjustment procedure based on chi-square minimization) and propose alternative in the choice of probability density distribution for priors and likelihoods. This paper will propose the use of what we are calling Bayesian Monte Carlo (referred as BMC in the rest of the manuscript) in the whole energy range from thermal, resonance and continuum range for all nuclear reaction models at these energies. Algorithms will be presented based on Monte-Carlo sampling and Markov chain. The objectives of BMC are to propose a reference calculation for validating the GLS calculations and approximations, to test probability density distributions effects and to provide the framework of finding global minimum if several local minimums exist. Application to resolved resonance, unresolved resonance and continuum evaluation as well as multigroup cross section data assimilation will be presented.

R programming for parameters estimation of geographically weighted ordinal logistic regression (GWOLR) model based on Newton Raphson

NASA Astrophysics Data System (ADS)

Zuhdi, Shaifudin; Saputro, Dewi Retno Sari

2017-03-01

GWOLR model used for represent relationship between dependent variable has categories and scale of category is ordinal with independent variable influenced the geographical location of the observation site. Parameters estimation of GWOLR model use maximum likelihood provide system of nonlinear equations and hard to be found the result in analytic resolution. By finishing it, it means determine the maximum completion, this thing associated with optimizing problem. The completion nonlinear system of equations optimize use numerical approximation, which one is Newton Raphson method. The purpose of this research is to make iteration algorithm Newton Raphson and program using R software to estimate GWOLR model. Based on the research obtained that program in R can be used to estimate the parameters of GWOLR model by forming a syntax program with command "while".

Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Cheong, R. Y.; Gabda, D.

2017-09-01

Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.

Cross-validation to select Bayesian hierarchical models in phylogenetics.

PubMed

Duchêne, Sebastián; Duchêne, David A; Di Giallonardo, Francesca; Eden, John-Sebastian; Geoghegan, Jemma L; Holt, Kathryn E; Ho, Simon Y W; Holmes, Edward C

2016-05-26

Recent developments in Bayesian phylogenetic models have increased the range of inferences that can be drawn from molecular sequence data. Accordingly, model selection has become an important component of phylogenetic analysis. Methods of model selection generally consider the likelihood of the data under the model in question. In the context of Bayesian phylogenetics, the most common approach involves estimating the marginal likelihood, which is typically done by integrating the likelihood across model parameters, weighted by the prior. Although this method is accurate, it is sensitive to the presence of improper priors. We explored an alternative approach based on cross-validation that is widely used in evolutionary analysis. This involves comparing models according to their predictive performance. We analysed simulated data and a range of viral and bacterial data sets using a cross-validation approach to compare a variety of molecular clock and demographic models. Our results show that cross-validation can be effective in distinguishing between strict- and relaxed-clock models and in identifying demographic models that allow growth in population size over time. In most of our empirical data analyses, the model selected using cross-validation was able to match that selected using marginal-likelihood estimation. The accuracy of cross-validation appears to improve with longer sequence data, particularly when distinguishing between relaxed-clock models. Cross-validation is a useful method for Bayesian phylogenetic model selection. This method can be readily implemented even when considering complex models where selecting an appropriate prior for all parameters may be difficult.

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: towards a computationally efficient analysis without informative priors

NASA Astrophysics Data System (ADS)

Pellejero-Ibanez, Marcos; Chuang, Chia-Hsun; Rubiño-Martín, J. A.; Cuesta, Antonio J.; Wang, Yuting; Zhao, Gongbo; Ross, Ashley J.; Rodríguez-Torres, Sergio; Prada, Francisco; Slosar, Anže; Vazquez, Jose A.; Alam, Shadab; Beutler, Florian; Eisenstein, Daniel J.; Gil-Marín, Héctor; Grieb, Jan Niklas; Ho, Shirley; Kitaura, Francisco-Shu; Percival, Will J.; Rossi, Graziano; Salazar-Albornoz, Salvador; Samushia, Lado; Sánchez, Ariel G.; Satpathy, Siddharth; Seo, Hee-Jong; Tinker, Jeremy L.; Tojeiro, Rita; Vargas-Magaña, Mariana; Brownstein, Joel R.; Nichol, Robert C.; Olmstead, Matthew D.

2017-07-01

We develop a new computationally efficient methodology called double-probe analysis with the aim of minimizing informative priors (those coming from extra probes) in the estimation of cosmological parameters. Using our new methodology, we extract the dark energy model-independent cosmological constraints from the joint data sets of the Baryon Oscillation Spectroscopic Survey (BOSS) galaxy sample and Planck cosmic microwave background (CMB) measurements. We measure the mean values and covariance matrix of {R, la, Ωbh2, ns, log(As), Ωk, H(z), DA(z), f(z)σ8(z)}, which give an efficient summary of the Planck data and two-point statistics from the BOSS galaxy sample. The CMB shift parameters are R=√{Ω _m H_0^2} r(z_*) and la = πr(z*)/rs(z*), where z* is the redshift at the last scattering surface, and r(z*) and rs(z*) denote our comoving distance to the z* and sound horizon at z*, respectively; Ωb is the baryon fraction at z = 0. This approximate methodology guarantees that we will not need to put informative priors on the cosmological parameters that galaxy clustering is unable to constrain, I.e. Ωbh2 and ns. The main advantage is that the computational time required for extracting these parameters is decreased by a factor of 60 with respect to exact full-likelihood analyses. The results obtained show no tension with the flat Λ cold dark matter (ΛCDM) cosmological paradigm. By comparing with the full-likelihood exact analysis with fixed dark energy models, on one hand we demonstrate that the double-probe method provides robust cosmological parameter constraints that can be conveniently used to study dark energy models, and on the other hand we provide a reliable set of measurements assuming dark energy models to be used, for example, in distance estimations. We extend our study to measure the sum of the neutrino mass using different methodologies, including double-probe analysis (introduced in this study), full-likelihood analysis and single-probe analysis. From full-likelihood analysis, we obtain Σmν < 0.12 (68 per cent), assuming ΛCDM and Σmν < 0.20 (68 per cent) assuming owCDM. We also find that there is degeneracy between observational systematics and neutrino masses, which suggests that one should take great care when estimating these parameters in the case of not having control over the systematics of a given sample.

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.

2013-12-01

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameter identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from indirect concentration measurements in identifying unknown source parameters such as the release time, strength and location. In this approach, the sampling location that gives the maximum relative entropy is selected as the optimal one. Once the sampling location is determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown source parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. Compared with the traditional optimal design, which is based on the Gaussian linear assumption, the method developed in this study can cope with arbitrary nonlinearity. It can be used to assist in groundwater monitor network design and identification of unknown contaminant sources. Contours of the expected information gain. The optimal observing location corresponds to the maximum value. Posterior marginal probability densities of unknown parameters, the thick solid black lines are for the designed location. For comparison, other 7 lines are for randomly chosen locations. The true values are denoted by vertical lines. It is obvious that the unknown parameters are estimated better with the desinged location.

Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET

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

Gopich, Irina V.

2015-01-21

Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when themore » FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a “chevron” shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated.« less

Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET

PubMed Central

Gopich, Irina V.

2015-01-01

Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when the FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a “chevron” shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated. PMID:25612692

Spatial hydrological drought characteristics in Karkheh River basin, southwest Iran using copulas

NASA Astrophysics Data System (ADS)

Dodangeh, Esmaeel; Shahedi, Kaka; Shiau, Jenq-Tzong; MirAkbari, Maryam

2017-08-01

Investigation on drought characteristics such as severity, duration, and frequency is crucial for water resources planning and management in a river basin. While the methodology for multivariate drought frequency analysis is well established by applying the copulas, the estimation on the associated parameters by various parameter estimation methods and the effects on the obtained results have not yet been investigated. This research aims at conducting a comparative analysis between the maximum likelihood parametric and non-parametric method of the Kendall τ estimation method for copulas parameter estimation. The methods were employed to study joint severity-duration probability and recurrence intervals in Karkheh River basin (southwest Iran) which is facing severe water-deficit problems. Daily streamflow data at three hydrological gauging stations (Tang Sazbon, Huleilan and Polchehr) near the Karkheh dam were used to draw flow duration curves (FDC) of these three stations. The Q_{75} index extracted from the FDC were set as threshold level to abstract drought characteristics such as drought duration and severity on the basis of the run theory. Drought duration and severity were separately modeled using the univariate probabilistic distributions and gamma-GEV, LN2-exponential, and LN2-gamma were selected as the best paired drought severity-duration inputs for copulas according to the Akaike Information Criteria (AIC), Kolmogorov-Smirnov and chi-square tests. Archimedean Clayton, Frank, and extreme value Gumbel copulas were employed to construct joint cumulative distribution functions (JCDF) of droughts for each station. Frank copula at Tang Sazbon and Gumbel at Huleilan and Polchehr stations were identified as the best copulas based on the performance evaluation criteria including AIC, BIC, log-likelihood and root mean square error (RMSE) values. Based on the RMSE values, nonparametric Kendall-τ is preferred to the parametric maximum likelihood estimation method. The results showed greater drought return periods by the parametric ML method in comparison to the nonparametric Kendall τ estimation method. The results also showed that stations located in tributaries (Huleilan and Polchehr) have close return periods, while the station along the main river (Tang Sazbon) has the smaller return periods for the drought events with identical drought duration and severity.

Make the most of your samples: Bayes factor estimators for high-dimensional models of sequence evolution.

PubMed

Baele, Guy; Lemey, Philippe; Vansteelandt, Stijn

2013-03-06

Accurate model comparison requires extensive computation times, especially for parameter-rich models of sequence evolution. In the Bayesian framework, model selection is typically performed through the evaluation of a Bayes factor, the ratio of two marginal likelihoods (one for each model). Recently introduced techniques to estimate (log) marginal likelihoods, such as path sampling and stepping-stone sampling, offer increased accuracy over the traditional harmonic mean estimator at an increased computational cost. Most often, each model's marginal likelihood will be estimated individually, which leads the resulting Bayes factor to suffer from errors associated with each of these independent estimation processes. We here assess the original 'model-switch' path sampling approach for direct Bayes factor estimation in phylogenetics, as well as an extension that uses more samples, to construct a direct path between two competing models, thereby eliminating the need to calculate each model's marginal likelihood independently. Further, we provide a competing Bayes factor estimator using an adaptation of the recently introduced stepping-stone sampling algorithm and set out to determine appropriate settings for accurately calculating such Bayes factors, with context-dependent evolutionary models as an example. While we show that modest efforts are required to roughly identify the increase in model fit, only drastically increased computation times ensure the accuracy needed to detect more subtle details of the evolutionary process. We show that our adaptation of stepping-stone sampling for direct Bayes factor calculation outperforms the original path sampling approach as well as an extension that exploits more samples. Our proposed approach for Bayes factor estimation also has preferable statistical properties over the use of individual marginal likelihood estimates for both models under comparison. Assuming a sigmoid function to determine the path between two competing models, we provide evidence that a single well-chosen sigmoid shape value requires less computational efforts in order to approximate the true value of the (log) Bayes factor compared to the original approach. We show that the (log) Bayes factors calculated using path sampling and stepping-stone sampling differ drastically from those estimated using either of the harmonic mean estimators, supporting earlier claims that the latter systematically overestimate the performance of high-dimensional models, which we show can lead to erroneous conclusions. Based on our results, we argue that highly accurate estimation of differences in model fit for high-dimensional models requires much more computational effort than suggested in recent studies on marginal likelihood estimation.

Make the most of your samples: Bayes factor estimators for high-dimensional models of sequence evolution

PubMed Central

2013-01-01

Background Accurate model comparison requires extensive computation times, especially for parameter-rich models of sequence evolution. In the Bayesian framework, model selection is typically performed through the evaluation of a Bayes factor, the ratio of two marginal likelihoods (one for each model). Recently introduced techniques to estimate (log) marginal likelihoods, such as path sampling and stepping-stone sampling, offer increased accuracy over the traditional harmonic mean estimator at an increased computational cost. Most often, each model’s marginal likelihood will be estimated individually, which leads the resulting Bayes factor to suffer from errors associated with each of these independent estimation processes. Results We here assess the original ‘model-switch’ path sampling approach for direct Bayes factor estimation in phylogenetics, as well as an extension that uses more samples, to construct a direct path between two competing models, thereby eliminating the need to calculate each model’s marginal likelihood independently. Further, we provide a competing Bayes factor estimator using an adaptation of the recently introduced stepping-stone sampling algorithm and set out to determine appropriate settings for accurately calculating such Bayes factors, with context-dependent evolutionary models as an example. While we show that modest efforts are required to roughly identify the increase in model fit, only drastically increased computation times ensure the accuracy needed to detect more subtle details of the evolutionary process. Conclusions We show that our adaptation of stepping-stone sampling for direct Bayes factor calculation outperforms the original path sampling approach as well as an extension that exploits more samples. Our proposed approach for Bayes factor estimation also has preferable statistical properties over the use of individual marginal likelihood estimates for both models under comparison. Assuming a sigmoid function to determine the path between two competing models, we provide evidence that a single well-chosen sigmoid shape value requires less computational efforts in order to approximate the true value of the (log) Bayes factor compared to the original approach. We show that the (log) Bayes factors calculated using path sampling and stepping-stone sampling differ drastically from those estimated using either of the harmonic mean estimators, supporting earlier claims that the latter systematically overestimate the performance of high-dimensional models, which we show can lead to erroneous conclusions. Based on our results, we argue that highly accurate estimation of differences in model fit for high-dimensional models requires much more computational effort than suggested in recent studies on marginal likelihood estimation. PMID:23497171

An Efficient Acoustic Density Estimation Method with Human Detectors Applied to Gibbons in Cambodia.

PubMed

Kidney, Darren; Rawson, Benjamin M; Borchers, David L; Stevenson, Ben C; Marques, Tiago A; Thomas, Len

2016-01-01

Some animal species are hard to see but easy to hear. Standard visual methods for estimating population density for such species are often ineffective or inefficient, but methods based on passive acoustics show more promise. We develop spatially explicit capture-recapture (SECR) methods for territorial vocalising species, in which humans act as an acoustic detector array. We use SECR and estimated bearing data from a single-occasion acoustic survey of a gibbon population in northeastern Cambodia to estimate the density of calling groups. The properties of the estimator are assessed using a simulation study, in which a variety of survey designs are also investigated. We then present a new form of the SECR likelihood for multi-occasion data which accounts for the stochastic availability of animals. In the context of gibbon surveys this allows model-based estimation of the proportion of groups that produce territorial vocalisations on a given day, thereby enabling the density of groups, instead of the density of calling groups, to be estimated. We illustrate the performance of this new estimator by simulation. We show that it is possible to estimate density reliably from human acoustic detections of visually cryptic species using SECR methods. For gibbon surveys we also show that incorporating observers' estimates of bearings to detected groups substantially improves estimator performance. Using the new form of the SECR likelihood we demonstrate that estimates of availability, in addition to population density and detection function parameters, can be obtained from multi-occasion data, and that the detection function parameters are not confounded with the availability parameter. This acoustic SECR method provides a means of obtaining reliable density estimates for territorial vocalising species. It is also efficient in terms of data requirements since since it only requires routine survey data. We anticipate that the low-tech field requirements will make this method an attractive option in many situations where populations can be surveyed acoustically by humans.

Diversity and toxicity of the diatom Pseudo-nitzschia Peragallo in the Gulf of Maine, Northwestern Atlantic Ocean

PubMed Central

Fernandes, Luciano F.; Hubbard, Katherine A.; Richlen, Mindy L.; Smith, Juliette; Bates, Stephen S.; Ehrman, James; Léger, Claude; Mafra, Luiz L.; Kulis, David; Quilliam, Michael; Libera, Katie; McCauley, Linda; Anderson, Donald M.

2014-01-01

Multiple species in the toxic marine diatom genus Pseudo-nitzschia have been identified in the Northwestern Atlantic region encompassing the Gulf of Maine (GOM), including the Bay of Fundy (BOF). To gain further knowledge of the taxonomic composition and toxicity of species in this region, Pseudo-nitzschia isolates (n=146) were isolated from samples collected during research cruises that provided broad spatial coverage across the GOM and the southern New England shelf, herein referred to as the GOM region, during 2007-2008. Isolates, and cells in field material collected at 38 stations, were identified using electron microscopy (EM). Eight species (P. americana, P. fraudulenta, P. subpacifica, P. heimii, P. pungens, P. seriata, P. delicatissima and P. turgidula), and a novel form, Pseudo-nitzschia sp. GOM, were identified. Species identity was confirmed by sequencing the large subunit of the ribosomal rDNA (28S) and the internal transcribed spacer 2 (ITS2) for six species (36 isolates). Phylogenetic analyses (including neighbor joining, maximum parsimony, and maximum likelihood estimates and ITS2 secondary structure analysis) and morphometric data supported the placement of P. sp. GOM in a novel clade that includes morphologically and genetically similar isolates from Australia and Spain and is genetically most similar to P. pseudodelicatissima and P. cuspidata. Seven species (46 isolates) were grown in nutrient-replete batch culture and aliquots consisting of cells and growth medium were screened by Biosense ASP ELISA to measure total domoic acid (DA) produced (intracellular + extracellular); P. americana and P. heimii were excluded from all toxin analyses as they did not persist in culture long enough for testing. All 46 isolates screened produced DA in culture and total DA varied among species (e.g., 0.04 to 320 ng ml-1 for P. pungens and P. sp. GOM isolates, respectively) and among isolates of the same species (e.g., 0.24 – 320 ng ml-1 for P. sp. GOM). The 15 most toxic isolates corresponded to P. seriata, P. sp. GOM and P. pungens, and fg DA cell-1 was determined for whole cultures (cells and medium) using ELISA and liquid chromatography (LC) with fluorescence detection (FLD); for seven isolates, toxin levels were also estimated using LC - with mass spectrometry and ultraviolet absorbance detection. Pseudo-nitzschia seriata was the most toxic species (up to 3,500 fg cell-1) and was observed in the GOM region during all cruises (i.e., during the months of April, May, June and October). Pseudo-nitzschia sp. GOM, observed only during September and October 2007, was less toxic (19 – 380 fg cell-1) than P. seriata but more toxic than P. pungens var. pungens (0. 4 fg cell-1). Quantitation of DA indicated that concentrations measured by LC and ELISA were positively and significantly correlated; the lower detection limit of the ELISA permitted quantification of toxicity in isolates that were found to be nontoxic with LC methods. The confirmation of at least seven toxic species and the broad spatial and temporal distribution of toxic Pseudo-nitzschia spp. have significant implications for the regional management of nearshore and offshore shellfisheries resources. PMID:25143669

A new model to predict weak-lensing peak counts. II. Parameter constraint strategies

NASA Astrophysics Data System (ADS)

Lin, Chieh-An; Kilbinger, Martin

2015-11-01

Context. Peak counts have been shown to be an excellent tool for extracting the non-Gaussian part of the weak lensing signal. Recently, we developed a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analysis. Aims: In this work, we explore and compare various strategies for constraining a parameter using our model, focusing on the matter density Ωm and the density fluctuation amplitude σ8. Methods: First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analysis with the copula likelihood, a technique that makes a weaker assumption than does the Gaussian likelihood. Third, direct, non-analytic parameter estimations are applied using the full information of the distribution. Fourth, we obtain constraints with approximate Bayesian computation (ABC), an efficient, robust, and likelihood-free algorithm based on accept-reject sampling. Results: We find that neglecting the CDC effect enlarges parameter contours by 22% and that the covariance-varying copula likelihood is a very good approximation to the true likelihood. The direct techniques work well in spite of noisier contours. Concerning ABC, the iterative process converges quickly to a posterior distribution that is in excellent agreement with results from our other analyses. The time cost for ABC is reduced by two orders of magnitude. Conclusions: The stochastic nature of our weak-lensing peak count model allows us to use various techniques that approach the true underlying probability distribution of observables, without making simplifying assumptions. Our work can be generalized to other observables where forward simulations provide samples of the underlying distribution.

Phase History Decomposition for efficient Scatterer Classification in SAR Imagery

DTIC Science & Technology

2011-09-15

frequency. Professor Rick Martin provided key advice on frequency parameter estimation and the relationship between likelihood ratio testing and the least...132 6.1.1 Imaging Error Due to Interpolation . . . . . . . . . . . . . . . . . . . . . . . . 135 6.2 Subwindow Design and Weighting... test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 MF matched filter

a Threshold-Free Filtering Algorithm for Airborne LIDAR Point Clouds Based on Expectation-Maximization

NASA Astrophysics Data System (ADS)

Hui, Z.; Cheng, P.; Ziggah, Y. Y.; Nie, Y.

2018-04-01

Filtering is a key step for most applications of airborne LiDAR point clouds. Although lots of filtering algorithms have been put forward in recent years, most of them suffer from parameters setting or thresholds adjusting, which will be time-consuming and reduce the degree of automation of the algorithm. To overcome this problem, this paper proposed a threshold-free filtering algorithm based on expectation-maximization. The proposed algorithm is developed based on an assumption that point clouds are seen as a mixture of Gaussian models. The separation of ground points and non-ground points from point clouds can be replaced as a separation of a mixed Gaussian model. Expectation-maximization (EM) is applied for realizing the separation. EM is used to calculate maximum likelihood estimates of the mixture parameters. Using the estimated parameters, the likelihoods of each point belonging to ground or object can be computed. After several iterations, point clouds can be labelled as the component with a larger likelihood. Furthermore, intensity information was also utilized to optimize the filtering results acquired using the EM method. The proposed algorithm was tested using two different datasets used in practice. Experimental results showed that the proposed method can filter non-ground points effectively. To quantitatively evaluate the proposed method, this paper adopted the dataset provided by the ISPRS for the test. The proposed algorithm can obtain a 4.48 % total error which is much lower than most of the eight classical filtering algorithms reported by the ISPRS.

Terrain Classification Using Multi-Wavelength Lidar Data

DTIC Science & Technology

2015-09-01

Figure 9. Pseudo- NDVI of three layers within the vertical structure of the forest. (Top) First return from the LiDAR instrument, including the ground...in NDVI throughout the vertical canopy. ........................................................17 Figure 10. Optech Titan operating wavelengths...and Ranging LMS LiDAR Mapping Suite ML Maximum Likelihood NIR Near Infrared N-D VIS n-Dimensional Visualizer NDVI Normalized Difference

Assessing Interval Estimation Methods for Hill Model ...

EPA Pesticide Factsheets

The Hill model of concentration-response is ubiquitous in toxicology, perhaps because its parameters directly relate to biologically significant metrics of toxicity such as efficacy and potency. Point estimates of these parameters obtained through least squares regression or maximum likelihood are commonly used in high-throughput risk assessment, but such estimates typically fail to include reliable information concerning confidence in (or precision of) the estimates. To address this issue, we examined methods for assessing uncertainty in Hill model parameter estimates derived from concentration-response data. In particular, using a sample of ToxCast concentration-response data sets, we applied four methods for obtaining interval estimates that are based on asymptotic theory, bootstrapping (two varieties), and Bayesian parameter estimation, and then compared the results. These interval estimation methods generally did not agree, so we devised a simulation study to assess their relative performance. We generated simulated data by constructing four statistical error models capable of producing concentration-response data sets comparable to those observed in ToxCast. We then applied the four interval estimation methods to the simulated data and compared the actual coverage of the interval estimates to the nominal coverage (e.g., 95%) in order to quantify performance of each of the methods in a variety of cases (i.e., different values of the true Hill model paramet

Fast maximum likelihood estimation using continuous-time neural point process models.

PubMed

Lepage, Kyle Q; MacDonald, Christopher J

2015-06-01

A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np(2)) to O(qp(2)). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.

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.

Probabilistic estimation of splitting coefficients of normal modes of the Earth, and their uncertainties, using an autoregressive technique

NASA Astrophysics Data System (ADS)

Pachhai, S.; Masters, G.; Laske, G.

2017-12-01

Earth's normal-mode spectra are crucial to studying the long wavelength structure of the Earth. Such observations have been used extensively to estimate "splitting coefficients" which, in turn, can be used to determine the three-dimensional velocity and density structure. Most past studies apply a non-linear iterative inversion to estimate the splitting coefficients which requires that the earthquake source is known. However, it is challenging to know the source details, particularly for big events as used in normal-mode analyses. Additionally, the final solution of the non-linear inversion can depend on the choice of damping parameter and starting model. To circumvent the need to know the source, a two-step linear inversion has been developed and successfully applied to many mantle and core sensitive modes. The first step takes combinations of the data from a single event to produce spectra known as "receiver strips". The autoregressive nature of the receiver strips can then be used to estimate the structure coefficients without the need to know the source. Based on this approach, we recently employed a neighborhood algorithm to measure the splitting coefficients for an isolated inner-core sensitive mode (13S2). This approach explores the parameter space efficiently without any need of regularization and finds the structure coefficients which best fit the observed strips. Here, we implement a Bayesian approach to data collected for earthquakes from early 2000 and more recent. This approach combines the data (through likelihood) and prior information to provide rigorous parameter values and their uncertainties for both isolated and coupled modes. The likelihood function is derived from the inferred errors of the receiver strips which allows us to retrieve proper uncertainties. Finally, we apply model selection criteria that balance the trade-offs between fit (likelihood) and model complexity to investigate the degree and type of structure (elastic and anelastic) required to explain the data.

Cosmological Parameters and Hyper-Parameters: The Hubble Constant from Boomerang and Maxima

NASA Astrophysics Data System (ADS)

Lahav, Ofer

Recently several studies have jointly analysed data from different cosmological probes with the motivation of estimating cosmological parameters. Here we generalise this procedure to allow freedom in the relative weights of various probes. This is done by including in the joint likelihood function a set of `Hyper-Parameters', which are dealt with using Bayesian considerations. The resulting algorithm, which assumes uniform priors on the log of the Hyper-Parameters, is very simple to implement. We illustrate the method by estimating the Hubble constant H0 from different sets of recent CMB experiments (including Saskatoon, Python V, MSAM1, TOCO, Boomerang and Maxima). The approach can be generalised for a combination of cosmic probes, and for other priors on the Hyper-Parameters. Reference: Lahav, Bridle, Hobson, Lasenby & Sodre, 2000, MNRAS, in press (astro-ph/9912105)

Ancestral Relationships Using Metafounders: Finite Ancestral Populations and Across Population Relationships.

PubMed

Legarra, Andres; Christensen, Ole F; Vitezica, Zulma G; Aguilar, Ignacio; Misztal, Ignacy

2015-06-01

Recent use of genomic (marker-based) relationships shows that relationships exist within and across base population (breeds or lines). However, current treatment of pedigree relationships is unable to consider relationships within or across base populations, although such relationships must exist due to finite size of the ancestral population and connections between populations. This complicates the conciliation of both approaches and, in particular, combining pedigree with genomic relationships. We present a coherent theoretical framework to consider base population in pedigree relationships. We suggest a conceptual framework that considers each ancestral population as a finite-sized pool of gametes. This generates across-individual relationships and contrasts with the classical view which each population is considered as an infinite, unrelated pool. Several ancestral populations may be connected and therefore related. Each ancestral population can be represented as a "metafounder," a pseudo-individual included as founder of the pedigree and similar to an "unknown parent group." Metafounders have self- and across relationships according to a set of parameters, which measure ancestral relationships, i.e., homozygozities within populations and relationships across populations. These parameters can be estimated from existing pedigree and marker genotypes using maximum likelihood or a method based on summary statistics, for arbitrarily complex pedigrees. Equivalences of genetic variance and variance components between the classical and this new parameterization are shown. Segregation variance on crosses of populations is modeled. Efficient algorithms for computation of relationship matrices, their inverses, and inbreeding coefficients are presented. Use of metafounders leads to compatibility of genomic and pedigree relationship matrices and to simple computing algorithms. Examples and code are given. Copyright © 2015 by the Genetics Society of America.

Model parameter estimation approach based on incremental analysis for lithium-ion batteries without using open circuit voltage

NASA Astrophysics Data System (ADS)

Wu, Hongjie; Yuan, Shifei; Zhang, Xi; Yin, Chengliang; Ma, Xuerui

2015-08-01

To improve the suitability of lithium-ion battery model under varying scenarios, such as fluctuating temperature and SoC variation, dynamic model with parameters updated realtime should be developed. In this paper, an incremental analysis-based auto regressive exogenous (I-ARX) modeling method is proposed to eliminate the modeling error caused by the OCV effect and improve the accuracy of parameter estimation. Then, its numerical stability, modeling error, and parametric sensitivity are analyzed at different sampling rates (0.02, 0.1, 0.5 and 1 s). To identify the model parameters recursively, a bias-correction recursive least squares (CRLS) algorithm is applied. Finally, the pseudo random binary sequence (PRBS) and urban dynamic driving sequences (UDDSs) profiles are performed to verify the realtime performance and robustness of the newly proposed model and algorithm. Different sampling rates (1 Hz and 10 Hz) and multiple temperature points (5, 25, and 45 °C) are covered in our experiments. The experimental and simulation results indicate that the proposed I-ARX model can present high accuracy and suitability for parameter identification without using open circuit voltage.

Hybrid pairwise likelihood analysis of animal behavior experiments.

PubMed

Cattelan, Manuela; Varin, Cristiano

2013-12-01

The study of the determinants of fights between animals is an important issue in understanding animal behavior. For this purpose, tournament experiments among a set of animals are often used by zoologists. The results of these tournament experiments are naturally analyzed by paired comparison models. Proper statistical analysis of these models is complicated by the presence of dependence between the outcomes of fights because the same animal is involved in different contests. This paper discusses two different model specifications to account for between-fights dependence. Models are fitted through the hybrid pairwise likelihood method that iterates between optimal estimating equations for the regression parameters and pairwise likelihood inference for the association parameters. This approach requires the specification of means and covariances only. For this reason, the method can be applied also when the computation of the joint distribution is difficult or inconvenient. The proposed methodology is investigated by simulation studies and applied to real data about adult male Cape Dwarf Chameleons. © 2013, The International Biometric Society.

COSMOABC: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Ishida, E. E. O.; Vitenti, S. D. P.; Penna-Lima, M.; Cisewski, J.; de Souza, R. S.; Trindade, A. M. M.; Cameron, E.; Busti, V. C.; COIN Collaboration

2015-11-01

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogues. Here we present COSMOABC, a Python ABC sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code is very flexible and can be easily coupled to an external simulator, while allowing to incorporate arbitrary distance and prior functions. As an example of practical application, we coupled COSMOABC with the NUMCOSMO library and demonstrate how it can be used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function. COSMOABC is published under the GPLv3 license on PyPI and GitHub and documentation is available at http://goo.gl/SmB8EX.

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

La Russa, D

Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference. Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributionsmore » found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates. Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10{sup 7} cm−{sup 3}. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates. Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.« less

Joint coverage probability in a simulation study on Continuous-Time Markov Chain parameter estimation.

PubMed

Benoit, Julia S; Chan, Wenyaw; Doody, Rachelle S

2015-01-01

Parameter dependency within data sets in simulation studies is common, especially in models such as Continuous-Time Markov Chains (CTMC). Additionally, the literature lacks a comprehensive examination of estimation performance for the likelihood-based general multi-state CTMC. Among studies attempting to assess the estimation, none have accounted for dependency among parameter estimates. The purpose of this research is twofold: 1) to develop a multivariate approach for assessing accuracy and precision for simulation studies 2) to add to the literature a comprehensive examination of the estimation of a general 3-state CTMC model. Simulation studies are conducted to analyze longitudinal data with a trinomial outcome using a CTMC with and without covariates. Measures of performance including bias, component-wise coverage probabilities, and joint coverage probabilities are calculated. An application is presented using Alzheimer's disease caregiver stress levels. Comparisons of joint and component-wise parameter estimates yield conflicting inferential results in simulations from models with and without covariates. In conclusion, caution should be taken when conducting simulation studies aiming to assess performance and choice of inference should properly reflect the purpose of the simulation.

Fisher Scoring Method for Parameter Estimation of Geographically Weighted Ordinal Logistic Regression (GWOLR) Model

NASA Astrophysics Data System (ADS)

Widyaningsih, Purnami; Retno Sari Saputro, Dewi; Nugrahani Putri, Aulia

2017-06-01

GWOLR model combines geographically weighted regression (GWR) and (ordinal logistic reression) OLR models. Its parameter estimation employs maximum likelihood estimation. Such parameter estimation, however, yields difficult-to-solve system of nonlinear equations, and therefore numerical approximation approach is required. The iterative approximation approach, in general, uses Newton-Raphson (NR) method. The NR method has a disadvantage—its Hessian matrix is always the second derivatives of each iteration so it does not always produce converging results. With regard to this matter, NR model is modified by substituting its Hessian matrix into Fisher information matrix, which is termed Fisher scoring (FS). The present research seeks to determine GWOLR model parameter estimation using Fisher scoring method and apply the estimation on data of the level of vulnerability to Dengue Hemorrhagic Fever (DHF) in Semarang. The research concludes that health facilities give the greatest contribution to the probability of the number of DHF sufferers in both villages. Based on the number of the sufferers, IR category of DHF in both villages can be determined.

Multidimensional stochastic approximation using locally contractive functions

NASA Technical Reports Server (NTRS)

Lawton, W. M.

1975-01-01

A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.

PSYCHOACOUSTICS: a comprehensive MATLAB toolbox for auditory testing.

PubMed

Soranzo, Alessandro; Grassi, Massimo

2014-01-01

PSYCHOACOUSTICS is a new MATLAB toolbox which implements three classic adaptive procedures for auditory threshold estimation. The first includes those of the Staircase family (method of limits, simple up-down and transformed up-down); the second is the Parameter Estimation by Sequential Testing (PEST); and the third is the Maximum Likelihood Procedure (MLP). The toolbox comes with more than twenty built-in experiments each provided with the recommended (default) parameters. However, if desired, these parameters can be modified through an intuitive and user friendly graphical interface and stored for future use (no programming skills are required). Finally, PSYCHOACOUSTICS is very flexible as it comes with several signal generators and can be easily extended for any experiment.

Static shape control for flexible structures

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1986-01-01

An integrated methodology is described for defining static shape control laws for large flexible structures. The techniques include modeling, identifying and estimating the control laws of distributed systems characterized in terms of infinite dimensional state and parameter spaces. The models are expressed as interconnected elliptic partial differential equations governing a range of static loads, with the capability of analyzing electromagnetic fields around antenna systems. A second-order analysis is carried out for statistical errors, and model parameters are determined by maximizing an appropriate defined likelihood functional which adjusts the model to observational data. The parameter estimates are derived from the conditional mean of the observational data, resulting in a least squares superposition of shape functions obtained from the structural model.

PSYCHOACOUSTICS: a comprehensive MATLAB toolbox for auditory testing

PubMed Central

Soranzo, Alessandro; Grassi, Massimo

2014-01-01

PSYCHOACOUSTICS is a new MATLAB toolbox which implements three classic adaptive procedures for auditory threshold estimation. The first includes those of the Staircase family (method of limits, simple up-down and transformed up-down); the second is the Parameter Estimation by Sequential Testing (PEST); and the third is the Maximum Likelihood Procedure (MLP). The toolbox comes with more than twenty built-in experiments each provided with the recommended (default) parameters. However, if desired, these parameters can be modified through an intuitive and user friendly graphical interface and stored for future use (no programming skills are required). Finally, PSYCHOACOUSTICS is very flexible as it comes with several signal generators and can be easily extended for any experiment. PMID:25101013

Aerodynamic parameter estimation via Fourier modulating function techniques

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1995-01-01

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Estimating Arrhenius parameters using temperature programmed molecular dynamics.

PubMed

Imandi, Venkataramana; Chatterjee, Abhijit

2016-07-21

Kinetic rates at different temperatures and the associated Arrhenius parameters, whenever Arrhenius law is obeyed, are efficiently estimated by applying maximum likelihood analysis to waiting times collected using the temperature programmed molecular dynamics method. When transitions involving many activated pathways are available in the dataset, their rates may be calculated using the same collection of waiting times. Arrhenius behaviour is ascertained by comparing rates at the sampled temperatures with ones from the Arrhenius expression. Three prototype systems with corrugated energy landscapes, namely, solvated alanine dipeptide, diffusion at the metal-solvent interphase, and lithium diffusion in silicon, are studied to highlight various aspects of the method. The method becomes particularly appealing when the Arrhenius parameters can be used to find rates at low temperatures where transitions are rare. Systematic coarse-graining of states can further extend the time scales accessible to the method. Good estimates for the rate parameters are obtained with 500-1000 waiting times.

A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior

DOE PAGES

Ye, Xin; Garikapati, Venu M.; You, Daehyun; ...

2017-11-08

Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basismore » of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components of utility functions in both the multinomial logit (MNL) model and multiple discrete-continuous extreme value (MDCEV) model. Based on a semi-nonparametric approach, a closed-form likelihood function that nests the MNL or MDCEV model being tested is derived. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed test yields acceptable Type-I and Type-II error probabilities at commonly available sample sizes. The test is then applied to three real-world discrete and discrete-continuous choice models. For all three models, the proposed test rejects the validity of the standard Gumbel distribution in most utility functions, calling for the development of robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.« less

A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior

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

Ye, Xin; Garikapati, Venu M.; You, Daehyun

Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basismore » of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components of utility functions in both the multinomial logit (MNL) model and multiple discrete-continuous extreme value (MDCEV) model. Based on a semi-nonparametric approach, a closed-form likelihood function that nests the MNL or MDCEV model being tested is derived. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed test yields acceptable Type-I and Type-II error probabilities at commonly available sample sizes. The test is then applied to three real-world discrete and discrete-continuous choice models. For all three models, the proposed test rejects the validity of the standard Gumbel distribution in most utility functions, calling for the development of robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.« less

MC3: Multi-core Markov-chain Monte Carlo code

NASA Astrophysics Data System (ADS)

Cubillos, Patricio; Harrington, Joseph; Lust, Nate; Foster, AJ; Stemm, Madison; Loredo, Tom; Stevenson, Kevin; Campo, Chris; Hardin, Matt; Hardy, Ryan

2016-10-01

MC3 (Multi-core Markov-chain Monte Carlo) is a Bayesian statistics tool that can be executed from the shell prompt or interactively through the Python interpreter with single- or multiple-CPU parallel computing. It offers Markov-chain Monte Carlo (MCMC) posterior-distribution sampling for several algorithms, Levenberg-Marquardt least-squares optimization, and uniform non-informative, Jeffreys non-informative, or Gaussian-informative priors. MC3 can share the same value among multiple parameters and fix the value of parameters to constant values, and offers Gelman-Rubin convergence testing and correlated-noise estimation with time-averaging or wavelet-based likelihood estimation methods.

Local neighborhood transition probability estimation and its use in contextual classification

NASA Technical Reports Server (NTRS)

Chittineni, C. B.

1979-01-01

The problem of incorporating spatial or contextual information into classifications is considered. A simple model that describes the spatial dependencies between the neighboring pixels with a single parameter, Theta, is presented. Expressions are derived for updating the posteriori probabilities of the states of nature of the pattern under consideration using information from the neighboring patterns, both for spatially uniform context and for Markov dependencies in terms of Theta. Techniques for obtaining the optimal value of the parameter Theta as a maximum likelihood estimate from the local neighborhood of the pattern under consideration are developed.

Computational Software for Fitting Seismic Data to Epidemic-Type Aftershock Sequence Models

NASA Astrophysics Data System (ADS)

Chu, A.

2014-12-01

Modern earthquake catalogs are often analyzed using spatial-temporal point process models such as the epidemic-type aftershock sequence (ETAS) models of Ogata (1998). My work introduces software to implement two of ETAS models described in Ogata (1998). To find the Maximum-Likelihood Estimates (MLEs), my software provides estimates of the homogeneous background rate parameter and the temporal and spatial parameters that govern triggering effects by applying the Expectation-Maximization (EM) algorithm introduced in Veen and Schoenberg (2008). Despite other computer programs exist for similar data modeling purpose, using EM-algorithm has the benefits of stability and robustness (Veen and Schoenberg, 2008). Spatial shapes that are very long and narrow cause difficulties in optimization convergence and problems with flat or multi-modal log-likelihood functions encounter similar issues. My program uses a robust method to preset a parameter to overcome the non-convergence computational issue. In addition to model fitting, the software is equipped with useful tools for examining modeling fitting results, for example, visualization of estimated conditional intensity, and estimation of expected number of triggered aftershocks. A simulation generator is also given with flexible spatial shapes that may be defined by the user. This open-source software has a very simple user interface. The user may execute it on a local computer, and the program also has potential to be hosted online. Java language is used for the software's core computing part and an optional interface to the statistical package R is provided.

Maximum likelihood estimation of protein kinetic parameters under weak assumptions from unfolding force spectroscopy experiments

NASA Astrophysics Data System (ADS)

Aioanei, Daniel; Samorì, Bruno; Brucale, Marco

2009-12-01

Single molecule force spectroscopy (SMFS) is extensively used to characterize the mechanical unfolding behavior of individual protein domains under applied force by pulling chimeric polyproteins consisting of identical tandem repeats. Constant velocity unfolding SMFS data can be employed to reconstruct the protein unfolding energy landscape and kinetics. The methods applied so far require the specification of a single stretching force increase function, either theoretically derived or experimentally inferred, which must then be assumed to accurately describe the entirety of the experimental data. The very existence of a suitable optimal force model, even in the context of a single experimental data set, is still questioned. Herein, we propose a maximum likelihood (ML) framework for the estimation of protein kinetic parameters which can accommodate all the established theoretical force increase models. Our framework does not presuppose the existence of a single force characteristic function. Rather, it can be used with a heterogeneous set of functions, each describing the protein behavior in the stretching time range leading to one rupture event. We propose a simple way of constructing such a set of functions via piecewise linear approximation of the SMFS force vs time data and we prove the suitability of the approach both with synthetic data and experimentally. Additionally, when the spontaneous unfolding rate is the only unknown parameter, we find a correction factor that eliminates the bias of the ML estimator while also reducing its variance. Finally, we investigate which of several time-constrained experiment designs leads to better estimators.

Parameter expansion for estimation of reduced rank covariance matrices (Open Access publication)

PubMed Central

Meyer, Karin

2008-01-01

Parameter expanded and standard expectation maximisation algorithms are described for reduced rank estimation of covariance matrices by restricted maximum likelihood, fitting the leading principal components only. Convergence behaviour of these algorithms is examined for several examples and contrasted to that of the average information algorithm, and implications for practical analyses are discussed. It is shown that expectation maximisation type algorithms are readily adapted to reduced rank estimation and converge reliably. However, as is well known for the full rank case, the convergence is linear and thus slow. Hence, these algorithms are most useful in combination with the quadratically convergent average information algorithm, in particular in the initial stages of an iterative solution scheme. PMID:18096112

Parameter Estimation for a Model of Space-Time Rainfall

NASA Astrophysics Data System (ADS)

Smith, James A.; Karr, Alan F.

1985-08-01

In this paper, parameter estimation procedures, based on data from a network of rainfall gages, are developed for a class of space-time rainfall models. The models, which are designed to represent the spatial distribution of daily rainfall, have three components, one that governs the temporal occurrence of storms, a second that distributes rain cells spatially for a given storm, and a third that determines the rainfall pattern within a rain cell. Maximum likelihood and method of moments procedures are developed. We illustrate that limitations on model structure are imposed by restricting data sources to rain gage networks. The estimation procedures are applied to a 240-mi2 (621 km2) catchment in the Potomac River basin.

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our method to others in the literature as well as the aforementioned TRW estimator.

Empirical likelihood method for non-ignorable missing data problems.

PubMed

Guan, Zhong; Qin, Jing

2017-01-01

Missing response problem is ubiquitous in survey sampling, medical, social science and epidemiology studies. It is well known that non-ignorable missing is the most difficult missing data problem where the missing of a response depends on its own value. In statistical literature, unlike the ignorable missing data problem, not many papers on non-ignorable missing data are available except for the full parametric model based approach. In this paper we study a semiparametric model for non-ignorable missing data in which the missing probability is known up to some parameters, but the underlying distributions are not specified. By employing Owen (1988)'s empirical likelihood method we can obtain the constrained maximum empirical likelihood estimators of the parameters in the missing probability and the mean response which are shown to be asymptotically normal. Moreover the likelihood ratio statistic can be used to test whether the missing of the responses is non-ignorable or completely at random. The theoretical results are confirmed by a simulation study. As an illustration, the analysis of a real AIDS trial data shows that the missing of CD4 counts around two years are non-ignorable and the sample mean based on observed data only is biased.

Detection and Estimation of Multi-Pulse LFMCW Radar Signals

DTIC Science & Technology

2010-01-01

the Hough transform (HT) of the Wigner - Ville distribution ( WVD ), has been shown to be equivalent to the generalized likelihood ratio test (GLRT...virginia.edu Abstract— The Wigner - Ville Hough transform (WVHT) has been applied to detect and estimate the parameters of linear frequency-modulated...well studied in the literature. One of the most prominent techniques is the Wigner - Ville Hough Transform [8], [9]. The Wigner - Ville Hough transform (WVHT

Constrained inference in mixed-effects models for longitudinal data with application to hearing loss.

PubMed

Davidov, Ori; Rosen, Sophia

2011-04-01

In medical studies, endpoints are often measured for each patient longitudinally. The mixed-effects model has been a useful tool for the analysis of such data. There are situations in which the parameters of the model are subject to some restrictions or constraints. For example, in hearing loss studies, we expect hearing to deteriorate with time. This means that hearing thresholds which reflect hearing acuity will, on average, increase over time. Therefore, the regression coefficients associated with the mean effect of time on hearing ability will be constrained. Such constraints should be accounted for in the analysis. We propose maximum likelihood estimation procedures, based on the expectation-conditional maximization either algorithm, to estimate the parameters of the model while accounting for the constraints on them. The proposed methods improve, in terms of mean square error, on the unconstrained estimators. In some settings, the improvement may be substantial. Hypotheses testing procedures that incorporate the constraints are developed. Specifically, likelihood ratio, Wald, and score tests are proposed and investigated. Their empirical significance levels and power are studied using simulations. It is shown that incorporating the constraints improves the mean squared error of the estimates and the power of the tests. These improvements may be substantial. The methodology is used to analyze a hearing loss study.

On equivalent parameter learning in simplified feature space based on Bayesian asymptotic analysis.

PubMed

Yamazaki, Keisuke

2012-07-01

Parametric models for sequential data, such as hidden Markov models, stochastic context-free grammars, and linear dynamical systems, are widely used in time-series analysis and structural data analysis. Computation of the likelihood function is one of primary considerations in many learning methods. Iterative calculation of the likelihood such as the model selection is still time-consuming though there are effective algorithms based on dynamic programming. The present paper studies parameter learning in a simplified feature space to reduce the computational cost. Simplifying data is a common technique seen in feature selection and dimension reduction though an oversimplified space causes adverse learning results. Therefore, we mathematically investigate a condition of the feature map to have an asymptotically equivalent convergence point of estimated parameters, referred to as the vicarious map. As a demonstration to find vicarious maps, we consider the feature space, which limits the length of data, and derive a necessary length for parameter learning in hidden Markov models. Copyright © 2012 Elsevier Ltd. All rights reserved.

Development and system identification of a light unmanned aircraft for flying qualities research

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

Peters, M.E.; Andrisani, D. II

This paper describes the design, construction, flight testing and system identification of a light weight remotely piloted aircraft and its use in studying flying qualities in the longitudinal axis. The short period approximation to the longitudinal dynamics of the aircraft was used. Parameters in this model were determined a priori using various empirical estimators. These parameters were then estimated from flight data using a maximum likelihood parameter identification method. A comparison of the parameter values revealed that the stability derivatives obtained from the empirical estimators were reasonably close to the flight test results. However, the control derivatives determined by themore » empirical estimators were too large by a factor of two. The aircraft was also flown to determine how the longitudinal flying qualities of light weight remotely piloted aircraft compared to full size manned aircraft. It was shown that light weight remotely piloted aircraft require much faster short period dynamics to achieve level I flying qualities in an up-and-away flight task.« less

Stochastic differential equation (SDE) model of opening gold share price of bursa saham malaysia

NASA Astrophysics Data System (ADS)

Hussin, F. N.; Rahman, H. A.; Bahar, A.

2017-09-01

Black and Scholes option pricing model is one of the most recognized stochastic differential equation model in mathematical finance. Two parameter estimation methods have been utilized for the Geometric Brownian model (GBM); historical and discrete method. The historical method is a statistical method which uses the property of independence and normality logarithmic return, giving out the simplest parameter estimation. Meanwhile, discrete method considers the function of density of transition from the process of diffusion normal log which has been derived from maximum likelihood method. These two methods are used to find the parameter estimates samples of Malaysians Gold Share Price data such as: Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas, and Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas Shariah. Modelling of gold share price is essential since fluctuation of gold affects worldwide economy nowadays, including Malaysia. It is found that discrete method gives the best parameter estimates than historical method due to the smallest Root Mean Square Error (RMSE) value.

Bayesian Estimation of Reliability Burr Type XII Under Al-Bayyatis’ Suggest Loss Function with Numerical Solution

NASA Astrophysics Data System (ADS)

Mohammed, Amal A.; Abraheem, Sudad K.; Fezaa Al-Obedy, Nadia J.

2018-05-01

In this paper is considered with Burr type XII distribution. The maximum likelihood, Bayes methods of estimation are used for estimating the unknown scale parameter (α). Al-Bayyatis’ loss function and suggest loss function are used to find the reliability with the least loss. So the reliability function is expanded in terms of a set of power function. For this performance, the Matlab (ver.9) is used in computations and some examples are given.

Lateral stability and control derivatives extracted from five early flights of the space shuttle Columbia

NASA Technical Reports Server (NTRS)

Schiess, J. R.

1986-01-01

Flight data taken from the first five flights (STS-2, 3, 4, 5 and 9) of the Space Transportation System Shuttle Columbia during entry are analyzed to determine the Shuttle lateral aerodynamic characteristics. Maximum likelihood estimation is applied to data derived from accelerometer and rate gyro measurements and trajectory, meteorological and control surface data to estimate lateral-directional stability and control derivatives. The estimated parameters are compared across the five flights and to preflight predicted values.

The impact of cigarette excise taxes on smoking cessation rates from 1994 to 2010 in Poland, Russia, and Ukraine.

PubMed

Ross, Hana; Kostova, Deliana; Stoklosa, Michal; Leon, Maria

2014-01-01

We studied the impact of cigarette excise taxes on the rates of smoking cessation with data from 3 neighboring Eastern European countries (Russia, Poland, and Ukraine) during the post-transitional period of the 1990s and 2000s. Using Global Adult Tobacco Survey data from 11,106 former and current smokers, we estimated the impact of cigarette taxes on the smokers' likelihood of quitting over time. We first transformed the survey's cross-sectional data into a pseudo-longitudinal format in which the average observation period for individual subjects was 12 years and then employed duration analysis. We estimated that a 10% increase in cigarette taxes during the observation period increased the probability of smoking cessation among smokers in these countries by 1.6% to 2.3%. Cigarette tax increases have played a significant role in driving smoking cessation in Poland, Russia, and Ukraine. Further increases in cigarette excise taxes are likely to encourage further cessation and thus impact the prevalence of smoking in the region.

The geography of hospital admission in a national health service with patient choice.

PubMed

Fabbri, Daniele; Robone, Silvana

2010-09-01

Each year about 20% of the 10 million hospital inpatients in Italy get admitted to hospitals outside the Local Health Authority of residence. In this paper we carefully explore this phenomenon and estimate gravity equations for 'trade' in hospital care using a Poisson pseudo-maximum likelihood method. Consistency of the PPML estimator is guaranteed under the null of independence provided that the conditional mean is correctly specified. In our case we find that patients' flows are affected by network autocorrelation. We correct for it by relying upon spatial filtering. Our results suggest that the gravity model is a good framework for explaining patient mobility in most of the examined diagnostic groups. We find that the ability to restrain patients' outflows increases with the size of the pool of enrollees. Moreover, the ability to attract patients' inflows is reduced by the size of pool of enrollees for all LHAs except for the very big LHAs. For LHAs in the top quintile of size of enrollees, the ability to attract inflows increases with the size of the pool. Copyright (c) 2010 John Wiley & Sons, Ltd.

Joint state and parameter estimation of the hemodynamic model by particle smoother expectation maximization method

NASA Astrophysics Data System (ADS)

Aslan, Serdar; Taylan Cemgil, Ali; Akın, Ata

2016-08-01

Objective. In this paper, we aimed for the robust estimation of the parameters and states of the hemodynamic model by using blood oxygen level dependent signal. Approach. In the fMRI literature, there are only a few successful methods that are able to make a joint estimation of the states and parameters of the hemodynamic model. In this paper, we implemented a maximum likelihood based method called the particle smoother expectation maximization (PSEM) algorithm for the joint state and parameter estimation. Main results. Former sequential Monte Carlo methods were only reliable in the hemodynamic state estimates. They were claimed to outperform the local linearization (LL) filter and the extended Kalman filter (EKF). The PSEM algorithm is compared with the most successful method called square-root cubature Kalman smoother (SCKS) for both state and parameter estimation. SCKS was found to be better than the dynamic expectation maximization (DEM) algorithm, which was shown to be a better estimator than EKF, LL and particle filters. Significance. PSEM was more accurate than SCKS for both the state and the parameter estimation. Hence, PSEM seems to be the most accurate method for the system identification and state estimation for the hemodynamic model inversion literature. This paper do not compare its results with Tikhonov-regularized Newton—CKF (TNF-CKF), a recent robust method which works in filtering sense.

Statistics of some atmospheric turbulence records relevant to aircraft response calculations

NASA Technical Reports Server (NTRS)

Mark, W. D.; Fischer, R. W.

1981-01-01

Methods for characterizing atmospheric turbulence are described. The methods illustrated include maximum likelihood estimation of the integral scale and intensity of records obeying the von Karman transverse power spectral form, constrained least-squares estimation of the parameters of a parametric representation of autocorrelation functions, estimation of the power spectra density of the instantaneous variance of a record with temporally fluctuating variance, and estimation of the probability density functions of various turbulence components. Descriptions of the computer programs used in the computations are given, and a full listing of these programs is included.

Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models.

PubMed

Mulder, Han A; Rönnegård, Lars; Fikse, W Freddy; Veerkamp, Roel F; Strandberg, Erling

2013-07-04

Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike's information criterion using h-likelihood to select the best fitting model. We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike's information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters. Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike's information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed. The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.

Elimination of trait blocks from multiple trait mixed model equations with singular (Co)variance parameter matrices

USDA-ARS?s Scientific Manuscript database

Transformations to multiple trait mixed model equations (MME) which are intended to improve computational efficiency in best linear unbiased prediction (BLUP) and restricted maximum likelihood (REML) are described. It is shown that traits that are expected or estimated to have zero residual variance...

Maximum Likelihood and Minimum Distance Applied to Univariate Mixture Distributions.

ERIC Educational Resources Information Center

Wang, Yuh-Yin Wu; Schafer, William D.

This Monte-Carlo study compared modified Newton (NW), expectation-maximization algorithm (EM), and minimum Cramer-von Mises distance (MD), used to estimate parameters of univariate mixtures of two components. Data sets were fixed at size 160 and manipulated by mean separation, variance ratio, component proportion, and non-normality. Results…

Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions.

ERIC Educational Resources Information Center

Holland, Paul W.; Thayer, Dorothy T.

2000-01-01

Applied the theory of exponential families of distributions to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. Considers efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and computationally efficient…

Measurement and Structural Model Class Separation in Mixture CFA: ML/EM versus MCMC

ERIC Educational Resources Information Center

Depaoli, Sarah

2012-01-01

Parameter recovery was assessed within mixture confirmatory factor analysis across multiple estimator conditions under different simulated levels of mixture class separation. Mixture class separation was defined in the measurement model (through factor loadings) and the structural model (through factor variances). Maximum likelihood (ML) via the…

Local Influence and Robust Procedures for Mediation Analysis

ERIC Educational Resources Information Center

Zu, Jiyun; Yuan, Ke-Hai

2010-01-01

Existing studies of mediation models have been limited to normal-theory maximum likelihood (ML). Because real data in the social and behavioral sciences are seldom normally distributed and often contain outliers, classical methods generally lead to inefficient or biased parameter estimates. Consequently, the conclusions from a mediation analysis…

Determinants of Standard Errors of MLEs in Confirmatory Factor Analysis

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Cheng, Ying; Zhang, Wei

2010-01-01

This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found.…

Maximum likelihood methods for investigating reporting rates of rings on hunter-shot birds

USGS Publications Warehouse

Conroy, M.J.; Morgan, B.J.T.; North, P.M.

1985-01-01

It is well known that hunters do not report 100% of the rings that they find on shot birds. Reward studies can be used to estimate what this reporting rate is, by comparison of recoveries of rings offering a monetary reward, to ordinary rings. A reward study of American Black Ducks (Anas rubripes) is used to illustrate the design, and to motivate the development of statistical models for estimation and for testing hypotheses of temporal and geographic variation in reporting rates. The method involves indexing the data (recoveries) and parameters (reporting, harvest, and solicitation rates) by geographic and temporal strata. Estimates are obtained under unconstrained (e.g., allowing temporal variability in reporting rates) and constrained (e.g., constant reporting rates) models, and hypotheses are tested by likelihood ratio. A FORTRAN program, available from the author, is used to perform the computations.

Hyperspectral image reconstruction for x-ray fluorescence tomography

DOE PAGES

Gürsoy, Doǧa; Biçer, Tekin; Lanzirotti, Antonio; ...

2015-01-01

A penalized maximum-likelihood estimation is proposed to perform hyperspectral (spatio-spectral) image reconstruction for X-ray fluorescence tomography. The approach minimizes a Poisson-based negative log-likelihood of the observed photon counts, and uses a penalty term that has the effect of encouraging local continuity of model parameter estimates in both spatial and spectral dimensions simultaneously. The performance of the reconstruction method is demonstrated with experimental data acquired from a seed of arabidopsis thaliana collected at the 13-ID-E microprobe beamline at the Advanced Photon Source. The resulting element distribution estimates with the proposed approach show significantly better reconstruction quality than the conventional analytical inversionmore » approaches, and allows for a high data compression factor which can reduce data acquisition times remarkably. In particular, this technique provides the capability to tomographically reconstruct full energy dispersive spectra without compromising reconstruction artifacts that impact the interpretation of results.« less

Modelling of extreme rainfall events in Peninsular Malaysia based on annual maximum and partial duration series

NASA Astrophysics Data System (ADS)

Zin, Wan Zawiah Wan; Shinyie, Wendy Ling; Jemain, Abdul Aziz

2015-02-01

In this study, two series of data for extreme rainfall events are generated based on Annual Maximum and Partial Duration Methods, derived from 102 rain-gauge stations in Peninsular from 1982-2012. To determine the optimal threshold for each station, several requirements must be satisfied and Adapted Hill estimator is employed for this purpose. A semi-parametric bootstrap is then used to estimate the mean square error (MSE) of the estimator at each threshold and the optimal threshold is selected based on the smallest MSE. The mean annual frequency is also checked to ensure that it lies in the range of one to five and the resulting data is also de-clustered to ensure independence. The two data series are then fitted to Generalized Extreme Value and Generalized Pareto distributions for annual maximum and partial duration series, respectively. The parameter estimation methods used are the Maximum Likelihood and the L-moment methods. Two goodness of fit tests are then used to evaluate the best-fitted distribution. The results showed that the Partial Duration series with Generalized Pareto distribution and Maximum Likelihood parameter estimation provides the best representation for extreme rainfall events in Peninsular Malaysia for majority of the stations studied. Based on these findings, several return values are also derived and spatial mapping are constructed to identify the distribution characteristic of extreme rainfall in Peninsular Malaysia.

Unsupervised Deep Hashing With Pseudo Labels for Scalable Image Retrieval.

PubMed

Zhang, Haofeng; Liu, Li; Long, Yang; Shao, Ling

2018-04-01

In order to achieve efficient similarity searching, hash functions are designed to encode images into low-dimensional binary codes with the constraint that similar features will have a short distance in the projected Hamming space. Recently, deep learning-based methods have become more popular, and outperform traditional non-deep methods. However, without label information, most state-of-the-art unsupervised deep hashing (DH) algorithms suffer from severe performance degradation for unsupervised scenarios. One of the main reasons is that the ad-hoc encoding process cannot properly capture the visual feature distribution. In this paper, we propose a novel unsupervised framework that has two main contributions: 1) we convert the unsupervised DH model into supervised by discovering pseudo labels; 2) the framework unifies likelihood maximization, mutual information maximization, and quantization error minimization so that the pseudo labels can maximumly preserve the distribution of visual features. Extensive experiments on three popular data sets demonstrate the advantages of the proposed method, which leads to significant performance improvement over the state-of-the-art unsupervised hashing algorithms.

Pseudo CT estimation from MRI using patch-based random forest

NASA Astrophysics Data System (ADS)

Yang, Xiaofeng; Lei, Yang; Shu, Hui-Kuo; Rossi, Peter; Mao, Hui; Shim, Hyunsuk; Curran, Walter J.; Liu, Tian

2017-02-01

Recently, MR simulators gain popularity because of unnecessary radiation exposure of CT simulators being used in radiation therapy planning. We propose a method for pseudo CT estimation from MR images based on a patch-based random forest. Patient-specific anatomical features are extracted from the aligned training images and adopted as signatures for each voxel. The most robust and informative features are identified using feature selection to train the random forest. The well-trained random forest is used to predict the pseudo CT of a new patient. This prediction technique was tested with human brain images and the prediction accuracy was assessed using the original CT images. Peak signal-to-noise ratio (PSNR) and feature similarity (FSIM) indexes were used to quantify the differences between the pseudo and original CT images. The experimental results showed the proposed method could accurately generate pseudo CT images from MR images. In summary, we have developed a new pseudo CT prediction method based on patch-based random forest, demonstrated its clinical feasibility, and validated its prediction accuracy. This pseudo CT prediction technique could be a useful tool for MRI-based radiation treatment planning and attenuation correction in a PET/MRI scanner.

Scanning linear estimation: improvements over region of interest (ROI) methods

NASA Astrophysics Data System (ADS)

Kupinski, Meredith K.; Clarkson, Eric W.; Barrett, Harrison H.

2013-03-01

In tomographic medical imaging, a signal activity is typically estimated by summing voxels from a reconstructed image. We introduce an alternative estimation scheme that operates on the raw projection data and offers a substantial improvement, as measured by the ensemble mean-square error (EMSE), when compared to using voxel values from a maximum-likelihood expectation-maximization (MLEM) reconstruction. The scanning-linear (SL) estimator operates on the raw projection data and is derived as a special case of maximum-likelihood estimation with a series of approximations to make the calculation tractable. The approximated likelihood accounts for background randomness, measurement noise and variability in the parameters to be estimated. When signal size and location are known, the SL estimate of signal activity is unbiased, i.e. the average estimate equals the true value. By contrast, unpredictable bias arising from the null functions of the imaging system affect standard algorithms that operate on reconstructed data. The SL method is demonstrated for two different tasks: (1) simultaneously estimating a signal’s size, location and activity; (2) for a fixed signal size and location, estimating activity. Noisy projection data are realistically simulated using measured calibration data from the multi-module multi-resolution small-animal SPECT imaging system. For both tasks, the same set of images is reconstructed using the MLEM algorithm (80 iterations), and the average and maximum values within the region of interest (ROI) are calculated for comparison. This comparison shows dramatic improvements in EMSE for the SL estimates. To show that the bias in ROI estimates affects not only absolute values but also relative differences, such as those used to monitor the response to therapy, the activity estimation task is repeated for three different signal sizes.

Parameter identifiability and regional calibration for reservoir inflow prediction

NASA Astrophysics Data System (ADS)

Kolberg, Sjur; Engeland, Kolbjørn; Tøfte, Lena S.; Bruland, Oddbjørn

2013-04-01

The large hydropower producer Statkraft is currently testing regional, distributed models for operational reservoir inflow prediction. The need for simultaneous forecasts and consistent updating in a large number of catchments supports the shift from catchment-oriented to regional models. Low-quality naturalized inflow series in the reservoir catchments further encourages the use of donor catchments and regional simulation for calibration purposes. MCMC based parameter estimation (the Dream algorithm; Vrugt et al, 2009) is adapted to regional parameter estimation, and implemented within the open source ENKI framework. The likelihood is based on the concept of effectively independent number of observations, spatially as well as in time. Marginal and conditional (around an optimum) parameter distributions for each catchment may be extracted, even though the MCMC algorithm itself is guided only by the regional likelihood surface. Early results indicate that the average performance loss associated with regional calibration (difference in Nash-Sutcliffe R2 between regionally and locally optimal parameters) is in the range of 0.06. The importance of the seasonal snow storage and melt in Norwegian mountain catchments probably contributes to the high degree of similarity among catchments. The evaluation continues for several regions, focusing on posterior parameter uncertainty and identifiability. Vrugt, J. A., C. J. F. ter Braak, C. G. H. Diks, B. A. Robinson, J. M. Hyman and D. Higdon: Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling. Int. J. of nonlinear sciences and numerical simulation 10, 3, 273-290, 2009.

Distribution of rain height over subtropical region: Durban, South Africa for satellite communication systems

NASA Astrophysics Data System (ADS)

Olurotimi, E. O.; Sokoya, O.; Ojo, J. S.; Owolawi, P. A.

2018-03-01

Rain height is one of the significant parameters for prediction of rain attenuation for Earth-space telecommunication links, especially those operating at frequencies above 10 GHz. This study examines Three-parameter Dagum distribution of the rain height over Durban, South Africa. 5-year data were used to study the monthly, seasonal, and annual variations using the parameters estimated by the maximum likelihood of the distribution. The performance estimation of the distribution was determined using the statistical goodness of fit. Three-parameter Dagum distribution shows an appropriate distribution for the modeling of rain height over Durban with the Root Mean Square Error of 0.26. Also, the shape and scale parameters for the distribution show a wide variation. The probability exceedance of time for 0.01% indicates the high probability of rain attenuation at higher frequencies.

Robust generative asymmetric GMM for brain MR image segmentation.

PubMed

Ji, Zexuan; Xia, Yong; Zheng, Yuhui

2017-11-01

Accurate segmentation of brain tissues from magnetic resonance (MR) images based on the unsupervised statistical models such as Gaussian mixture model (GMM) has been widely studied during last decades. However, most GMM based segmentation methods suffer from limited accuracy due to the influences of noise and intensity inhomogeneity in brain MR images. To further improve the accuracy for brain MR image segmentation, this paper presents a Robust Generative Asymmetric GMM (RGAGMM) for simultaneous brain MR image segmentation and intensity inhomogeneity correction. First, we develop an asymmetric distribution to fit the data shapes, and thus construct a spatial constrained asymmetric model. Then, we incorporate two pseudo-likelihood quantities and bias field estimation into the model's log-likelihood, aiming to exploit the neighboring priors of within-cluster and between-cluster and to alleviate the impact of intensity inhomogeneity, respectively. Finally, an expectation maximization algorithm is derived to iteratively maximize the approximation of the data log-likelihood function to overcome the intensity inhomogeneity in the image and segment the brain MR images simultaneously. To demonstrate the performances of the proposed algorithm, we first applied the proposed algorithm to a synthetic brain MR image to show the intermediate illustrations and the estimated distribution of the proposed algorithm. The next group of experiments is carried out in clinical 3T-weighted brain MR images which contain quite serious intensity inhomogeneity and noise. Then we quantitatively compare our algorithm to state-of-the-art segmentation approaches by using Dice coefficient (DC) on benchmark images obtained from IBSR and BrainWeb with different level of noise and intensity inhomogeneity. The comparison results on various brain MR images demonstrate the superior performances of the proposed algorithm in dealing with the noise and intensity inhomogeneity. In this paper, the RGAGMM algorithm is proposed which can simply and efficiently incorporate spatial constraints into an EM framework to simultaneously segment brain MR images and estimate the intensity inhomogeneity. The proposed algorithm is flexible to fit the data shapes, and can simultaneously overcome the influence of noise and intensity inhomogeneity, and hence is capable of improving over 5% segmentation accuracy comparing with several state-of-the-art algorithms. Copyright © 2017 Elsevier B.V. All rights reserved.

CosmoSIS: A system for MC parameter estimation

DOE PAGES

Bridle, S.; Dodelson, S.; Jennings, E.; ...

2015-12-23

CosmoSIS is a modular system for cosmological parameter estimation, based on Markov Chain Monte Carlo and related techniques. It provides a series of samplers, which drive the exploration of the parameter space, and a series of modules, which calculate the likelihood of the observed data for a given physical model, determined by the location of a sample in the parameter space. While CosmoSIS ships with a set of modules that calculate quantities of interest to cosmologists, there is nothing about the framework itself, nor in the Markov Chain Monte Carlo technique, that is specific to cosmology. Thus CosmoSIS could bemore » used for parameter estimation problems in other fields, including HEP. This paper describes the features of CosmoSIS and show an example of its use outside of cosmology. Furthermore, it also discusses how collaborative development strategies differ between two different communities: that of HEP physicists, accustomed to working in large collaborations, and that of cosmologists, who have traditionally not worked in large groups.« less

Polar bears in the Beaufort Sea: A 30-year mark-recapture case history

USGS Publications Warehouse

Amstrup, Steven C.; McDonald, T.L.; Stirling, I.

2001-01-01

Knowledge of population size and trend is necessary to manage anthropogenic risks to polar bears (Ursus maritimus). Despite capturing over 1,025 females between 1967 and 1998, previously calculated estimates of the size of the southern Beaufort Sea (SBS) population have been unreliable. We improved estimates of numbers of polar bears by modeling heterogeneity in capture probability with covariates. Important covariates referred to the year of the study, age of the bear, capture effort, and geographic location. Our choice of best approximating model was based on the inverse relationship between variance in parameter estimates and likelihood of the fit and suggested a growth from ≈ 500 to over 1,000 females during this study. The mean coefficient of variation on estimates for the last decade of the study was 0.16—the smallest yet derived. A similar model selection approach is recommended for other projects where a best model is not identified by likelihood criteria alone.

Monaural room acoustic parameters from music and speech.

PubMed

Kendrick, Paul; Cox, Trevor J; Li, Francis F; Zhang, Yonggang; Chambers, Jonathon A

2008-07-01

This paper compares two methods for extracting room acoustic parameters from reverberated speech and music. An approach which uses statistical machine learning, previously developed for speech, is extended to work with music. For speech, reverberation time estimations are within a perceptual difference limen of the true value. For music, virtually all early decay time estimations are within a difference limen of the true value. The estimation accuracy is not good enough in other cases due to differences between the simulated data set used to develop the empirical model and real rooms. The second method carries out a maximum likelihood estimation on decay phases at the end of notes or speech utterances. This paper extends the method to estimate parameters relating to the balance of early and late energies in the impulse response. For reverberation time and speech, the method provides estimations which are within the perceptual difference limen of the true value. For other parameters such as clarity, the estimations are not sufficiently accurate due to the natural reverberance of the excitation signals. Speech is a better test signal than music because of the greater periods of silence in the signal, although music is needed for low frequency measurement.

Normal Theory Two-Stage ML Estimator When Data Are Missing at the Item Level

PubMed Central

Savalei, Victoria; Rhemtulla, Mijke

2017-01-01

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately handle missing data at the item level. Item-level multiple imputation (MI), however, can handle such missing data straightforwardly. In this article, we develop an analytic approach for dealing with item-level missing data—that is, one that obtains a unique set of parameter estimates directly from the incomplete data set and does not require imputations. The proposed approach is a variant of the two-stage maximum likelihood (TSML) methodology, and it is the analytic equivalent of item-level MI. We compare the new TSML approach to three existing alternatives for handling item-level missing data: scale-level full information maximum likelihood, available-case maximum likelihood, and item-level MI. We find that the TSML approach is the best analytic approach, and its performance is similar to item-level MI. We recommend its implementation in popular software and its further study. PMID:29276371

Normal Theory Two-Stage ML Estimator When Data Are Missing at the Item Level.

PubMed

Savalei, Victoria; Rhemtulla, Mijke

2017-08-01

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately handle missing data at the item level. Item-level multiple imputation (MI), however, can handle such missing data straightforwardly. In this article, we develop an analytic approach for dealing with item-level missing data-that is, one that obtains a unique set of parameter estimates directly from the incomplete data set and does not require imputations. The proposed approach is a variant of the two-stage maximum likelihood (TSML) methodology, and it is the analytic equivalent of item-level MI. We compare the new TSML approach to three existing alternatives for handling item-level missing data: scale-level full information maximum likelihood, available-case maximum likelihood, and item-level MI. We find that the TSML approach is the best analytic approach, and its performance is similar to item-level MI. We recommend its implementation in popular software and its further study.

Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models

PubMed Central

Schwab, Joshua; Gruber, Susan; Blaser, Nello; Schomaker, Michael; van der Laan, Mark

2015-01-01

This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart. PMID:25909047

Aerodynamics of the pseudo-glottis.

PubMed

Kotby, M N; Hegazi, M A; Kamal, I; Gamal El Dien, N; Nassar, J

2009-01-01

The aim of this work is to study the hitherto unclear aerodynamic parameters of the pseudo-glottis following total laryngectomy. These parameters include airflow rate, sub-pseudo-glottic pressure (SubPsG), efficiency and resistance, as well as sound pressure level (SPL). Eighteen male patients who have undergone total laryngectomy, with an age range from 54 to 72 years, were investigated in this study. All tested patients were fluent esophageal 'voice' speakers utilizing tracheo-esophageal prosthesis. The airflow rate, SubPsG and SPL were measured. The results showed that the mean value of the airflow rate was 53 ml/s, the SubPsG pressure was 13 cm H(2)O, while the SPL was 66 dB. The normative data obtained from the true glottis in healthy age-matched subjects are 89 ml/s, 7.9 cm H(2)O and 70 dB, respectively. Other aerodynamic indices were calculated and compared to the data obtained from the true glottis. Such a comparison of the pseudo-glottic aerodynamic data to the data of the true glottis gives an insight into the mechanism of action of the pseudo-glottis. The data obtained suggests possible clinical applications in pseudo-voice training. Copyright 2009 S. Karger AG, Basel.

Challenges in Species Tree Estimation Under the Multispecies Coalescent Model

PubMed Central

Xu, Bo; Yang, Ziheng

2016-01-01

The multispecies coalescent (MSC) model has emerged as a powerful framework for inferring species phylogenies while accounting for ancestral polymorphism and gene tree-species tree conflict. A number of methods have been developed in the past few years to estimate the species tree under the MSC. The full likelihood methods (including maximum likelihood and Bayesian inference) average over the unknown gene trees and accommodate their uncertainties properly but involve intensive computation. The approximate or summary coalescent methods are computationally fast and are applicable to genomic datasets with thousands of loci, but do not make an efficient use of information in the multilocus data. Most of them take the two-step approach of reconstructing the gene trees for multiple loci by phylogenetic methods and then treating the estimated gene trees as observed data, without accounting for their uncertainties appropriately. In this article we review the statistical nature of the species tree estimation problem under the MSC, and explore the conceptual issues and challenges of species tree estimation by focusing mainly on simple cases of three or four closely related species. We use mathematical analysis and computer simulation to demonstrate that large differences in statistical performance may exist between the two classes of methods. We illustrate that several counterintuitive behaviors may occur with the summary methods but they are due to inefficient use of information in the data by summary methods and vanish when the data are analyzed using full-likelihood methods. These include (i) unidentifiability of parameters in the model, (ii) inconsistency in the so-called anomaly zone, (iii) singularity on the likelihood surface, and (iv) deterioration of performance upon addition of more data. We discuss the challenges and strategies of species tree inference for distantly related species when the molecular clock is violated, and highlight the need for improving the computational efficiency and model realism of the likelihood methods as well as the statistical efficiency of the summary methods. PMID:27927902

Wireless Intrusion Detection

DTIC Science & Technology

2007-03-01

32 4.4 Algorithm Pseudo - Code ...................................................................................34 4.5 WIND Interface With a...difference estimates of xc temporal derivatives, or by using a polynomial fit to the previous values of xc. 34 4.4 ALGORITHM PSEUDO - CODE Pseudo ...Phase Shift Keying DQPSK Differential Quadrature Phase Shift Keying EVM Error Vector Magnitude FFT Fast Fourier Transform FPGA Field Programmable

Likelihood analysis of spatial capture-recapture models for stratified or class structured populations

USGS Publications Warehouse

Royle, J. Andrew; Sutherland, Christopher S.; Fuller, Angela K.; Sun, Catherine C.

2015-01-01

We develop a likelihood analysis framework for fitting spatial capture-recapture (SCR) models to data collected on class structured or stratified populations. Our interest is motivated by the necessity of accommodating the problem of missing observations of individual class membership. This is particularly problematic in SCR data arising from DNA analysis of scat, hair or other material, which frequently yields individual identity but fails to identify the sex. Moreover, this can represent a large fraction of the data and, given the typically small sample sizes of many capture-recapture studies based on DNA information, utilization of the data with missing sex information is necessary. We develop the class structured likelihood for the case of missing covariate values, and then we address the scaling of the likelihood so that models with and without class structured parameters can be formally compared regardless of missing values. We apply our class structured model to black bear data collected in New York in which sex could be determined for only 62 of 169 uniquely identified individuals. The models containing sex-specificity of both the intercept of the SCR encounter probability model and the distance coefficient, and including a behavioral response are strongly favored by log-likelihood. Estimated population sex ratio is strongly influenced by sex structure in model parameters illustrating the importance of rigorous modeling of sex differences in capture-recapture models.

Parameter Estimation of Multiple Frequency-Hopping Signals with Two Sensors

PubMed Central

Pan, Jin; Ma, Boyuan

2018-01-01

This paper essentially focuses on parameter estimation of multiple wideband emitting sources with time-varying frequencies, such as two-dimensional (2-D) direction of arrival (DOA) and signal sorting, with a low-cost circular synthetic array (CSA) consisting of only two rotating sensors. Our basic idea is to decompose the received data, which is a superimposition of phase measurements from multiple sources into separated groups and separately estimate the DOA associated with each source. Motivated by joint parameter estimation, we propose to adopt the expectation maximization (EM) algorithm in this paper; our method involves two steps, namely, the expectation-step (E-step) and the maximization (M-step). In the E-step, the correspondence of each signal with its emitting source is found. Then, in the M-step, the maximum-likelihood (ML) estimates of the DOA parameters are obtained. These two steps are iteratively and alternatively executed to jointly determine the DOAs and sort multiple signals. Closed-form DOA estimation formulae are developed by ML estimation based on phase data, which also realize an optimal estimation. Directional ambiguity is also addressed by another ML estimation method based on received complex responses. The Cramer-Rao lower bound is derived for understanding the estimation accuracy and performance comparison. The verification of the proposed method is demonstrated with simulations. PMID:29617323

Dynamically heterogenous partitions and phylogenetic inference: an evaluation of analytical strategies with cytochrome b and ND6 gene sequences in cranes.

PubMed

Krajewski, C; Fain, M G; Buckley, L; King, D G

1999-11-01

ki ctes over whether molecular sequence data should be partitioned for phylogenetic analysis often confound two types of heterogeneity among partitions. We distinguish historical heterogeneity (i.e., different partitions have different evolutionary relationships) from dynamic heterogeneity (i.e., different partitions show different patterns of sequence evolution) and explore the impact of the latter on phylogenetic accuracy and precision with a two-gene, mitochondrial data set for cranes. The well-established phylogeny of cranes allows us to contrast tree-based estimates of relevant parameter values with estimates based on pairwise comparisons and to ascertain the effects of incorporating different amounts of process information into phylogenetic estimates. We show that codon positions in the cytochrome b and NADH dehydrogenase subunit 6 genes are dynamically heterogenous under both Poisson and invariable-sites + gamma-rates versions of the F84 model and that heterogeneity includes variation in base composition and transition bias as well as substitution rate. Estimates of transition-bias and relative-rate parameters from pairwise sequence comparisons were comparable to those obtained as tree-based maximum likelihood estimates. Neither rate-category nor mixed-model partitioning strategies resulted in a loss of phylogenetic precision relative to unpartitioned analyses. We suggest that weighted-average distances provide a computationally feasible alternative to direct maximum likelihood estimates of phylogeny for mixed-model analyses of large, dynamically heterogenous data sets. Copyright 1999 Academic Press.

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

Howell, L. W., Jr.

2003-01-01

A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.

A consistent NPMLE of the joint distribution function with competing risks data under the dependent masking and right-censoring model.

PubMed

Li, Jiahui; Yu, Qiqing

2016-01-01

Dinse (Biometrics, 38:417-431, 1982) provides a special type of right-censored and masked competing risks data and proposes a non-parametric maximum likelihood estimator (NPMLE) and a pseudo MLE of the joint distribution function [Formula: see text] with such data. However, their asymptotic properties have not been studied so far. Under the extention of either the conditional masking probability (CMP) model or the random partition masking (RPM) model (Yu and Li, J Nonparametr Stat 24:753-764, 2012), we show that (1) Dinse's estimators are consistent if [Formula: see text] takes on finitely many values and each point in the support set of [Formula: see text] can be observed; (2) if the failure time is continuous, the NPMLE is not uniquely determined, and the standard approach (which puts weights only on one element in each observed set) leads to an inconsistent NPMLE; (3) in general, Dinse's estimators are not consistent even under the discrete assumption; (4) we construct a consistent NPMLE. The consistency is given under a new model called dependent masking and right-censoring model. The CMP model and the RPM model are indeed special cases of the new model. We compare our estimator to Dinse's estimators through simulation and real data. Simulation study indicates that the consistent NPMLE is a good approximation to the underlying distribution for moderate sample sizes.

Zero-inflated Poisson model based likelihood ratio test for drug safety signal detection.

PubMed

Huang, Lan; Zheng, Dan; Zalkikar, Jyoti; Tiwari, Ram

2017-02-01

In recent decades, numerous methods have been developed for data mining of large drug safety databases, such as Food and Drug Administration's (FDA's) Adverse Event Reporting System, where data matrices are formed by drugs such as columns and adverse events as rows. Often, a large number of cells in these data matrices have zero cell counts and some of them are "true zeros" indicating that the drug-adverse event pairs cannot occur, and these zero counts are distinguished from the other zero counts that are modeled zero counts and simply indicate that the drug-adverse event pairs have not occurred yet or have not been reported yet. In this paper, a zero-inflated Poisson model based likelihood ratio test method is proposed to identify drug-adverse event pairs that have disproportionately high reporting rates, which are also called signals. The maximum likelihood estimates of the model parameters of zero-inflated Poisson model based likelihood ratio test are obtained using the expectation and maximization algorithm. The zero-inflated Poisson model based likelihood ratio test is also modified to handle the stratified analyses for binary and categorical covariates (e.g. gender and age) in the data. The proposed zero-inflated Poisson model based likelihood ratio test method is shown to asymptotically control the type I error and false discovery rate, and its finite sample performance for signal detection is evaluated through a simulation study. The simulation results show that the zero-inflated Poisson model based likelihood ratio test method performs similar to Poisson model based likelihood ratio test method when the estimated percentage of true zeros in the database is small. Both the zero-inflated Poisson model based likelihood ratio test and likelihood ratio test methods are applied to six selected drugs, from the 2006 to 2011 Adverse Event Reporting System database, with varying percentages of observed zero-count cells.

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.

Parameter sensitivity analysis of a 1-D cold region lake model for land-surface schemes

NASA Astrophysics Data System (ADS)

Guerrero, José-Luis; Pernica, Patricia; Wheater, Howard; Mackay, Murray; Spence, Chris

2017-12-01

Lakes might be sentinels of climate change, but the uncertainty in their main feedback to the atmosphere - heat-exchange fluxes - is often not considered within climate models. Additionally, these fluxes are seldom measured, hindering critical evaluation of model output. Analysis of the Canadian Small Lake Model (CSLM), a one-dimensional integral lake model, was performed to assess its ability to reproduce diurnal and seasonal variations in heat fluxes and the sensitivity of simulated fluxes to changes in model parameters, i.e., turbulent transport parameters and the light extinction coefficient (Kd). A C++ open-source software package, Problem Solving environment for Uncertainty Analysis and Design Exploration (PSUADE), was used to perform sensitivity analysis (SA) and identify the parameters that dominate model behavior. The generalized likelihood uncertainty estimation (GLUE) was applied to quantify the fluxes' uncertainty, comparing daily-averaged eddy-covariance observations to the output of CSLM. Seven qualitative and two quantitative SA methods were tested, and the posterior likelihoods of the modeled parameters, obtained from the GLUE analysis, were used to determine the dominant parameters and the uncertainty in the modeled fluxes. Despite the ubiquity of the equifinality issue - different parameter-value combinations yielding equivalent results - the answer to the question was unequivocal: Kd, a measure of how much light penetrates the lake, dominates sensible and latent heat fluxes, and the uncertainty in their estimates is strongly related to the accuracy with which Kd is determined. This is important since accurate and continuous measurements of Kd could reduce modeling uncertainty.

Estimation of primordial spectrum with post-WMAP 3-year data

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

Shafieloo, Arman; Souradeep, Tarun

2008-07-15

In this paper we implement an improved (error-sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the Wilkinson Microwave Anisotropy Probe (WMAP) 3 year data to determine the primordial power spectrum assuming different points in the cosmological parameter space for a flat {lambda}CDM cosmological model. We also present the preliminary results of the cosmological parameter estimation by assuming a free form of the primordial spectrum, for a reasonably large volume of the parameter space. The recovered spectrum for a considerably large number of the points in the cosmological parameter space has a likelihood far better than a 'bestmore » fit' power law spectrum up to {delta}{chi}{sub eff}{sup 2}{approx_equal}-30. We use discrete wavelet transform (DWT) for smoothing the raw recovered spectrum from the binned data. The results obtained here reconfirm and sharpen the conclusion drawn from our previous analysis of the WMAP 1st year data. A sharp cut off around the horizon scale and a bump after the horizon scale seem to be a common feature for all of these reconstructed primordial spectra. We have shown that although the WMAP 3 year data prefers a lower value of matter density for a power law form of the primordial spectrum, for a free form of the spectrum, we can get a very good likelihood to the data for higher values of matter density. We have also shown that even a flat cold dark matter model, allowing a free form of the primordial spectrum, can give a very high likelihood fit to the data. Theoretical interpretation of the results is open to the cosmology community. However, this work provides strong evidence that the data retains discriminatory power in the cosmological parameter space even when there is full freedom in choosing the primordial spectrum.« less

On the validity of cosmological Fisher matrix forecasts

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

Wolz, Laura; Kilbinger, Martin; Weller, Jochen

2012-09-01

We present a comparison of Fisher matrix forecasts for cosmological probes with Monte Carlo Markov Chain (MCMC) posterior likelihood estimation methods. We analyse the performance of future Dark Energy Task Force (DETF) stage-III and stage-IV dark-energy surveys using supernovae, baryon acoustic oscillations and weak lensing as probes. We concentrate in particular on the dark-energy equation of state parameters w{sub 0} and w{sub a}. For purely geometrical probes, and especially when marginalising over w{sub a}, we find considerable disagreement between the two methods, since in this case the Fisher matrix can not reproduce the highly non-elliptical shape of the likelihood function.more » More quantitatively, the Fisher method underestimates the marginalized errors for purely geometrical probes between 30%-70%. For cases including structure formation such as weak lensing, we find that the posterior probability contours from the Fisher matrix estimation are in good agreement with the MCMC contours and the forecasted errors only changing on the 5% level. We then explore non-linear transformations resulting in physically-motivated parameters and investigate whether these parameterisations exhibit a Gaussian behaviour. We conclude that for the purely geometrical probes and, more generally, in cases where it is not known whether the likelihood is close to Gaussian, the Fisher matrix is not the appropriate tool to produce reliable forecasts.« less

Predicting phase behavior of mixtures of reservoir fluids with carbon dioxide

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

Grigg, R.B.; Lingane, P.J.

1983-10-01

The use of an equation of state to predict phase behavior during carbon dioxide flooding is well established. There is consensus that the characterization of the C fraction, the grouping of this fraction into ''pseudo components'', and the selection of interaction parameters are the most important variables. However, the literature is vague as to how to best select the pseudo components, especially when aiming for a few-component representation as for a field scale compositional simulation. Single-contact phase behavior is presented for mixtures of Ford Geraldine (Delaware), Maljamar (Grayburg), West Sussex (Shannon), and Reservoir D reservoir fluids, and of a syntheticmore » oil C/C/C, with carbon dioxide. One can reproduce the phase behavior of these mixtures using 3-5 pseudo components and common interaction parameters. The critical properties of the pseudo components are calculated from detailed oil characterizations. Because the parameters are not further adjusted, this approach reduces the empiricism in fitting phase data and may result in a more accurate representation of the system as the composition of the oil changes during the approach to miscibility.« less

Estimation of the ARNO model baseflow parameters using daily streamflow data

NASA Astrophysics Data System (ADS)

Abdulla, F. A.; Lettenmaier, D. P.; Liang, Xu

1999-09-01

An approach is described for estimation of baseflow parameters of the ARNO model, using historical baseflow recession sequences extracted from daily streamflow records. This approach allows four of the model parameters to be estimated without rainfall data, and effectively facilitates partitioning of the parameter estimation procedure so that parsimonious search procedures can be used to estimate the remaining storm response parameters separately. Three methods of optimization are evaluated for estimation of four baseflow parameters. These methods are the downhill Simplex (S), Simulated Annealing combined with the Simplex method (SA) and Shuffled Complex Evolution (SCE). These estimation procedures are explored in conjunction with four objective functions: (1) ordinary least squares; (2) ordinary least squares with Box-Cox transformation; (3) ordinary least squares on prewhitened residuals; (4) ordinary least squares applied to prewhitened with Box-Cox transformation of residuals. The effects of changing the seed random generator for both SA and SCE methods are also explored, as are the effects of the bounds of the parameters. Although all schemes converge to the same values of the objective function, SCE method was found to be less sensitive to these issues than both the SA and the Simplex schemes. Parameter uncertainty and interactions are investigated through estimation of the variance-covariance matrix and confidence intervals. As expected the parameters were found to be correlated and the covariance matrix was found to be not diagonal. Furthermore, the linearized confidence interval theory failed for about one-fourth of the catchments while the maximum likelihood theory did not fail for any of the catchments.