Incorporating signal-dependent noise for hyperspectral target detection

NASA Astrophysics Data System (ADS)

Morman, Christopher J.; Meola, Joseph

2015-05-01

The majority of hyperspectral target detection algorithms are developed from statistical data models employing stationary background statistics or white Gaussian noise models. Stationary background models are inaccurate as a result of two separate physical processes. First, varying background classes often exist in the imagery that possess different clutter statistics. Many algorithms can account for this variability through the use of subspaces or clustering techniques. The second physical process, which is often ignored, is a signal-dependent sensor noise term. For photon counting sensors that are often used in hyperspectral imaging systems, sensor noise increases as the measured signal level increases as a result of Poisson random processes. This work investigates the impact of this sensor noise on target detection performance. A linear noise model is developed describing sensor noise variance as a linear function of signal level. The linear noise model is then incorporated for detection of targets using data collected at Wright Patterson Air Force Base.

Composite Linear Models | Division of Cancer Prevention

Cancer.gov

By Stuart G. Baker The composite linear models software is a matrix approach to compute maximum likelihood estimates and asymptotic standard errors for models for incomplete multinomial data. It implements the method described in Baker SG. Composite linear models for incomplete multinomial data. Statistics in Medicine 1994;13:609-622. The software includes a library of thirty

Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

ERIC Educational Resources Information Center

Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

2013-01-01

In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

Nonlinear wave chaos: statistics of second harmonic fields.

PubMed

Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M

2017-10-01

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

Right-Sizing Statistical Models for Longitudinal Data

PubMed Central

Wood, Phillip K.; Steinley, Douglas; Jackson, Kristina M.

2015-01-01

Arguments are proposed that researchers using longitudinal data should consider more and less complex statistical model alternatives to their initially chosen techniques in an effort to “right-size” the model to the data at hand. Such model comparisons may alert researchers who use poorly fitting overly parsimonious models to more complex better fitting alternatives, and, alternatively, may identify more parsimonious alternatives to overly complex (and perhaps empirically under-identified and/or less powerful) statistical models. A general framework is proposed for considering (often nested) relationships between a variety of psychometric and growth curve models. A three-step approach is proposed in which models are evaluated based on the number and patterning of variance components prior to selection of better-fitting growth models that explain both mean and variation/covariation patterns. The orthogonal, free-curve slope-intercept (FCSI) growth model is considered as a general model which includes, as special cases, many models including the Factor Mean model (FM, McArdle & Epstein, 1987), McDonald's (1967) linearly constrained factor model, Hierarchical Linear Models (HLM), Repeated Measures MANOVA, and the Linear Slope Intercept (LinearSI) Growth Model. The FCSI model, in turn, is nested within the Tuckerized factor model. The approach is illustrated by comparing alternative models in a longitudinal study of children's vocabulary and by comparison of several candidate parametric growth and chronometric models in a Monte Carlo study. PMID:26237507

Right-sizing statistical models for longitudinal data.

PubMed

Wood, Phillip K; Steinley, Douglas; Jackson, Kristina M

2015-12-01

Arguments are proposed that researchers using longitudinal data should consider more and less complex statistical model alternatives to their initially chosen techniques in an effort to "right-size" the model to the data at hand. Such model comparisons may alert researchers who use poorly fitting, overly parsimonious models to more complex, better-fitting alternatives and, alternatively, may identify more parsimonious alternatives to overly complex (and perhaps empirically underidentified and/or less powerful) statistical models. A general framework is proposed for considering (often nested) relationships between a variety of psychometric and growth curve models. A 3-step approach is proposed in which models are evaluated based on the number and patterning of variance components prior to selection of better-fitting growth models that explain both mean and variation-covariation patterns. The orthogonal free curve slope intercept (FCSI) growth model is considered a general model that includes, as special cases, many models, including the factor mean (FM) model (McArdle & Epstein, 1987), McDonald's (1967) linearly constrained factor model, hierarchical linear models (HLMs), repeated-measures multivariate analysis of variance (MANOVA), and the linear slope intercept (linearSI) growth model. The FCSI model, in turn, is nested within the Tuckerized factor model. The approach is illustrated by comparing alternative models in a longitudinal study of children's vocabulary and by comparing several candidate parametric growth and chronometric models in a Monte Carlo study. (c) 2015 APA, all rights reserved).

Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices

NASA Astrophysics Data System (ADS)

Passemier, Damien; McKay, Matthew R.; Chen, Yang

2015-07-01

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked correlation), non-central Wishart with rank-one non-centrality, and a related class of non-central matrices. For a generic linear statistic, we derive simple and explicit CLT expressions as the matrix dimensions grow large. For all three ensembles under consideration, we find that the primary effect of the spike is to introduce an correction term to the asymptotic mean of the linear spectral statistic, which we characterize with simple formulas. The utility of our proposed framework is demonstrated through application to three different linear statistics problems: the classical likelihood ratio test for a population covariance, the capacity analysis of multi-antenna wireless communication systems with a line-of-sight transmission path, and a classical multiple sample significance testing problem.

Noise limitations in optical linear algebra processors.

PubMed

Batsell, S G; Jong, T L; Walkup, J F; Krile, T F

1990-05-10

A general statistical noise model is presented for optical linear algebra processors. A statistical analysis which includes device noise, the multiplication process, and the addition operation is undertaken. We focus on those processes which are architecturally independent. Finally, experimental results which verify the analytical predictions are also presented.

Statistical inference for template aging

NASA Astrophysics Data System (ADS)

Schuckers, Michael E.

2006-04-01

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

SOCR Analyses – an Instructional Java Web-based Statistical Analysis Toolkit

PubMed Central

Chu, Annie; Cui, Jenny; Dinov, Ivo D.

2011-01-01

The Statistical Online Computational Resource (SOCR) designs web-based tools for educational use in a variety of undergraduate courses (Dinov 2006). Several studies have demonstrated that these resources significantly improve students' motivation and learning experiences (Dinov et al. 2008). SOCR Analyses is a new component that concentrates on data modeling and analysis using parametric and non-parametric techniques supported with graphical model diagnostics. Currently implemented analyses include commonly used models in undergraduate statistics courses like linear models (Simple Linear Regression, Multiple Linear Regression, One-Way and Two-Way ANOVA). In addition, we implemented tests for sample comparisons, such as t-test in the parametric category; and Wilcoxon rank sum test, Kruskal-Wallis test, Friedman's test, in the non-parametric category. SOCR Analyses also include several hypothesis test models, such as Contingency tables, Friedman's test and Fisher's exact test. The code itself is open source (http://socr.googlecode.com/), hoping to contribute to the efforts of the statistical computing community. The code includes functionality for each specific analysis model and it has general utilities that can be applied in various statistical computing tasks. For example, concrete methods with API (Application Programming Interface) have been implemented in statistical summary, least square solutions of general linear models, rank calculations, etc. HTML interfaces, tutorials, source code, activities, and data are freely available via the web (www.SOCR.ucla.edu). Code examples for developers and demos for educators are provided on the SOCR Wiki website. In this article, the pedagogical utilization of the SOCR Analyses is discussed, as well as the underlying design framework. As the SOCR project is on-going and more functions and tools are being added to it, these resources are constantly improved. The reader is strongly encouraged to check the SOCR site for most updated information and newly added models. PMID:21546994

OPR-PPR, a Computer Program for Assessing Data Importance to Model Predictions Using Linear Statistics

USGS Publications Warehouse

Tonkin, Matthew J.; Tiedeman, Claire; Ely, D. Matthew; Hill, Mary C.

2007-01-01

The OPR-PPR program calculates the Observation-Prediction (OPR) and Parameter-Prediction (PPR) statistics that can be used to evaluate the relative importance of various kinds of data to simulated predictions. The data considered fall into three categories: (1) existing observations, (2) potential observations, and (3) potential information about parameters. The first two are addressed by the OPR statistic; the third is addressed by the PPR statistic. The statistics are based on linear theory and measure the leverage of the data, which depends on the location, the type, and possibly the time of the data being considered. For example, in a ground-water system the type of data might be a head measurement at a particular location and time. As a measure of leverage, the statistics do not take into account the value of the measurement. As linear measures, the OPR and PPR statistics require minimal computational effort once sensitivities have been calculated. Sensitivities need to be calculated for only one set of parameter values; commonly these are the values estimated through model calibration. OPR-PPR can calculate the OPR and PPR statistics for any mathematical model that produces the necessary OPR-PPR input files. In this report, OPR-PPR capabilities are presented in the context of using the ground-water model MODFLOW-2000 and the universal inverse program UCODE_2005. The method used to calculate the OPR and PPR statistics is based on the linear equation for prediction standard deviation. Using sensitivities and other information, OPR-PPR calculates (a) the percent increase in the prediction standard deviation that results when one or more existing observations are omitted from the calibration data set; (b) the percent decrease in the prediction standard deviation that results when one or more potential observations are added to the calibration data set; or (c) the percent decrease in the prediction standard deviation that results when potential information on one or more parameters is added.

Multivariate Strategies in Functional Magnetic Resonance Imaging

ERIC Educational Resources Information Center

Hansen, Lars Kai

2007-01-01

We discuss aspects of multivariate fMRI modeling, including the statistical evaluation of multivariate models and means for dimensional reduction. In a case study we analyze linear and non-linear dimensional reduction tools in the context of a "mind reading" predictive multivariate fMRI model.

Statistical Methodology for the Analysis of Repeated Duration Data in Behavioral Studies

ERIC Educational Resources Information Center

Letué, Frédérique; Martinez, Marie-José; Samson, Adeline; Vilain, Anne; Vilain, Coriandre

2018-01-01

Purpose: Repeated duration data are frequently used in behavioral studies. Classical linear or log-linear mixed models are often inadequate to analyze such data, because they usually consist of nonnegative and skew-distributed variables. Therefore, we recommend use of a statistical methodology specific to duration data. Method: We propose a…

Linearised and non-linearised isotherm models optimization analysis by error functions and statistical means

PubMed Central

2014-01-01

In adsorption study, to describe sorption process and evaluation of best-fitting isotherm model is a key analysis to investigate the theoretical hypothesis. Hence, numerous statistically analysis have been extensively used to estimate validity of the experimental equilibrium adsorption values with the predicted equilibrium values. Several statistical error analysis were carried out. In the present study, the following statistical analysis were carried out to evaluate the adsorption isotherm model fitness, like the Pearson correlation, the coefficient of determination and the Chi-square test, have been used. The ANOVA test was carried out for evaluating significance of various error functions and also coefficient of dispersion were evaluated for linearised and non-linearised models. The adsorption of phenol onto natural soil (Local name Kalathur soil) was carried out, in batch mode at 30 ± 20 C. For estimating the isotherm parameters, to get a holistic view of the analysis the models were compared between linear and non-linear isotherm models. The result reveled that, among above mentioned error functions and statistical functions were designed to determine the best fitting isotherm. PMID:25018878

Cost Estimation of Naval Ship Acquisition.

DTIC Science & Technology

1983-12-01

one a 9-sub- system model , the other a single total cost model . The models were developed using the linear least squares regression tech- nique with...to Linear Statistical Models , McGraw-Hill, 1961. 11. Helmer, F. T., Bibliography on Pricing Methodology and Cost Estimating, Dept. of Economics and...SUPPI.EMSaTARY NOTES IS. KWRo" (Cowaft. en tever aide of ..aesep M’ Idab~t 6 Week ONNa.) Cost estimation; Acquisition; Parametric cost estimate; linear

Some Statistics for Assessing Person-Fit Based on Continuous-Response Models

ERIC Educational Resources Information Center

Ferrando, Pere Joan

2010-01-01

This article proposes several statistics for assessing individual fit based on two unidimensional models for continuous responses: linear factor analysis and Samejima's continuous response model. Both models are approached using a common framework based on underlying response variables and are formulated at the individual level as fixed regression…

Detector noise statistics in the non-linear regime

NASA Technical Reports Server (NTRS)

Shopbell, P. L.; Bland-Hawthorn, J.

1992-01-01

The statistical behavior of an idealized linear detector in the presence of threshold and saturation levels is examined. It is assumed that the noise is governed by the statistical fluctuations in the number of photons emitted by the source during an exposure. Since physical detectors cannot have infinite dynamic range, our model illustrates that all devices have non-linear regimes, particularly at high count rates. The primary effect is a decrease in the statistical variance about the mean signal due to a portion of the expected noise distribution being removed via clipping. Higher order statistical moments are also examined, in particular, skewness and kurtosis. In principle, the expected distortion in the detector noise characteristics can be calibrated using flatfield observations with count rates matched to the observations. For this purpose, some basic statistical methods that utilize Fourier analysis techniques are described.

INTRODUCTION TO A COMBINED MULTIPLE LINEAR REGRESSION AND ARMA MODELING APPROACH FOR BEACH BACTERIA PREDICTION

EPA Science Inventory

Due to the complexity of the processes contributing to beach bacteria concentrations, many researchers rely on statistical modeling, among which multiple linear regression (MLR) modeling is most widely used. Despite its ease of use and interpretation, there may be time dependence...

An Investigation of the Fit of Linear Regression Models to Data from an SAT[R] Validity Study. Research Report 2011-3

ERIC Educational Resources Information Center

Kobrin, Jennifer L.; Sinharay, Sandip; Haberman, Shelby J.; Chajewski, Michael

2011-01-01

This study examined the adequacy of a multiple linear regression model for predicting first-year college grade point average (FYGPA) using SAT[R] scores and high school grade point average (HSGPA). A variety of techniques, both graphical and statistical, were used to examine if it is possible to improve on the linear regression model. The results…

Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

NASA Astrophysics Data System (ADS)

Qi, D.; Majda, A.

2017-12-01

A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures.

Identifiability of PBPK Models with Applications to ...

EPA Pesticide Factsheets

Any statistical model should be identifiable in order for estimates and tests using it to be meaningful. We consider statistical analysis of physiologically-based pharmacokinetic (PBPK) models in which parameters cannot be estimated precisely from available data, and discuss different types of identifiability that occur in PBPK models and give reasons why they occur. We particularly focus on how the mathematical structure of a PBPK model and lack of appropriate data can lead to statistical models in which it is impossible to estimate at least some parameters precisely. Methods are reviewed which can determine whether a purely linear PBPK model is globally identifiable. We propose a theorem which determines when identifiability at a set of finite and specific values of the mathematical PBPK model (global discrete identifiability) implies identifiability of the statistical model. However, we are unable to establish conditions that imply global discrete identifiability, and conclude that the only safe approach to analysis of PBPK models involves Bayesian analysis with truncated priors. Finally, computational issues regarding posterior simulations of PBPK models are discussed. The methodology is very general and can be applied to numerous PBPK models which can be expressed as linear time-invariant systems. A real data set of a PBPK model for exposure to dimethyl arsinic acid (DMA(V)) is presented to illustrate the proposed methodology. We consider statistical analy

A multiphase non-linear mixed effects model: An application to spirometry after lung transplantation.

PubMed

Rajeswaran, Jeevanantham; Blackstone, Eugene H

2017-02-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients.

Differential gene expression detection and sample classification using penalized linear regression models.

PubMed

Wu, Baolin

2006-02-15

Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p > n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-differentially expressed genes that can classify the samples very well. The idea of shrinkage is to regularize the model parameters to reduce the effects of noise and produce reliable inferences. Shrinkage has been successfully applied in the microarray data analysis. The SAM statistics proposed by Tusher et al. and the 'nearest shrunken centroid' proposed by Tibshirani et al. are ad hoc shrinkage methods. Both methods are simple, intuitive and prove to be useful in empirical studies. Recently Wu proposed the penalized t/F-statistics with shrinkage by formally using the (1) penalized linear regression models for two-class microarray data, showing good performance. In this paper we systematically discussed the use of penalized regression models for analyzing microarray data. We generalize the two-class penalized t/F-statistics proposed by Wu to multi-class microarray data. We formally derive the ad hoc shrunken centroid used by Tibshirani et al. using the (1) penalized regression models. And we show that the penalized linear regression models provide a rigorous and unified statistical framework for sample classification and differential gene expression detection.

Estimating Traffic Accidents in Turkey Using Differential Evolution Algorithm

NASA Astrophysics Data System (ADS)

Akgüngör, Ali Payıdar; Korkmaz, Ersin

2017-06-01

Estimating traffic accidents play a vital role to apply road safety procedures. This study proposes Differential Evolution Algorithm (DEA) models to estimate the number of accidents in Turkey. In the model development, population (P) and the number of vehicles (N) are selected as model parameters. Three model forms, linear, exponential and semi-quadratic models, are developed using DEA with the data covering from 2000 to 2014. Developed models are statistically compared to select the best fit model. The results of the DE models show that the linear model form is suitable to estimate the number of accidents. The statistics of this form is better than other forms in terms of performance criteria which are the Mean Absolute Percentage Errors (MAPE) and the Root Mean Square Errors (RMSE). To investigate the performance of linear DE model for future estimations, a ten-year period from 2015 to 2024 is considered. The results obtained from future estimations reveal the suitability of DE method for road safety applications.

Comparing Regression Coefficients between Nested Linear Models for Clustered Data with Generalized Estimating Equations

ERIC Educational Resources Information Center

Yan, Jun; Aseltine, Robert H., Jr.; Harel, Ofer

2013-01-01

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…

Comparison Between Linear and Non-parametric Regression Models for Genome-Enabled Prediction in Wheat

PubMed Central

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-01-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models. PMID:23275882

Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat.

PubMed

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-12-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.

SOME STATISTICAL ISSUES RELATED TO MULTIPLE LINEAR REGRESSION MODELING OF BEACH BACTERIA CONCENTRATIONS

EPA Science Inventory

As a fast and effective technique, the multiple linear regression (MLR) method has been widely used in modeling and prediction of beach bacteria concentrations. Among previous works on this subject, however, several issues were insufficiently or inconsistently addressed. Those is...

On the Stability of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs

NASA Technical Reports Server (NTRS)

Patilkulkarni, Sudarshan; Herencia-Zapana, Heber; Gray, W. Steven; Gonzalez, Oscar R.

2004-01-01

This paper presents two mean-square stability tests for a jump-linear system driven by a finite-state machine with a first-order Markovian input process. The first test is based on conventional Markov jump-linear theory and avoids the use of any higher-order statistics. The second test is developed directly using the higher-order statistics of the machine s output process. The two approaches are illustrated with a simple model for a recoverable computer control system.

Boosting Bayesian parameter inference of stochastic differential equation models with methods from statistical physics

NASA Astrophysics Data System (ADS)

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Measured time-series of both precipitation and runoff are known to exhibit highly non-trivial statistical properties. For making reliable probabilistic predictions in hydrology, it is therefore desirable to have stochastic models with output distributions that share these properties. When parameters of such models have to be inferred from data, we also need to quantify the associated parametric uncertainty. For non-trivial stochastic models, however, this latter step is typically very demanding, both conceptually and numerically, and always never done in hydrology. Here, we demonstrate that methods developed in statistical physics make a large class of stochastic differential equation (SDE) models amenable to a full-fledged Bayesian parameter inference. For concreteness we demonstrate these methods by means of a simple yet non-trivial toy SDE model. We consider a natural catchment that can be described by a linear reservoir, at the scale of observation. All the neglected processes are assumed to happen at much shorter time-scales and are therefore modeled with a Gaussian white noise term, the standard deviation of which is assumed to scale linearly with the system state (water volume in the catchment). Even for constant input, the outputs of this simple non-linear SDE model show a wealth of desirable statistical properties, such as fat-tailed distributions and long-range correlations. Standard algorithms for Bayesian inference fail, for models of this kind, because their likelihood functions are extremely high-dimensional intractable integrals over all possible model realizations. The use of Kalman filters is illegitimate due to the non-linearity of the model. Particle filters could be used but become increasingly inefficient with growing number of data points. Hamiltonian Monte Carlo algorithms allow us to translate this inference problem to the problem of simulating the dynamics of a statistical mechanics system and give us access to most sophisticated methods that have been developed in the statistical physics community over the last few decades. We demonstrate that such methods, along with automated differentiation algorithms, allow us to perform a full-fledged Bayesian inference, for a large class of SDE models, in a highly efficient and largely automatized manner. Furthermore, our algorithm is highly parallelizable. For our toy model, discretized with a few hundred points, a full Bayesian inference can be performed in a matter of seconds on a standard PC.

Solar granulation and statistical crystallography: A modeling approach using size-shape relations

NASA Technical Reports Server (NTRS)

Noever, D. A.

1994-01-01

The irregular polygonal pattern of solar granulation is analyzed for size-shape relations using statistical crystallography. In contrast to previous work which has assumed perfectly hexagonal patterns for granulation, more realistic accounting of cell (granule) shapes reveals a broader basis for quantitative analysis. Several features emerge as noteworthy: (1) a linear correlation between number of cell-sides and neighboring shapes (called Aboav-Weaire's law); (2) a linear correlation between both average cell area and perimeter and the number of cell-sides (called Lewis's law and a perimeter law, respectively) and (3) a linear correlation between cell area and squared perimeter (called convolution index). This statistical picture of granulation is consistent with a finding of no correlation in cell shapes beyond nearest neighbors. A comparative calculation between existing model predictions taken from luminosity data and the present analysis shows substantial agreements for cell-size distributions. A model for understanding grain lifetimes is proposed which links convective times to cell shape using crystallographic results.

Comparison of statistical models for analyzing wheat yield time series.

PubMed

Michel, Lucie; Makowski, David

2013-01-01

The world's population is predicted to exceed nine billion by 2050 and there is increasing concern about the capability of agriculture to feed such a large population. Foresight studies on food security are frequently based on crop yield trends estimated from yield time series provided by national and regional statistical agencies. Various types of statistical models have been proposed for the analysis of yield time series, but the predictive performances of these models have not yet been evaluated in detail. In this study, we present eight statistical models for analyzing yield time series and compare their ability to predict wheat yield at the national and regional scales, using data provided by the Food and Agriculture Organization of the United Nations and by the French Ministry of Agriculture. The Holt-Winters and dynamic linear models performed equally well, giving the most accurate predictions of wheat yield. However, dynamic linear models have two advantages over Holt-Winters models: they can be used to reconstruct past yield trends retrospectively and to analyze uncertainty. The results obtained with dynamic linear models indicated a stagnation of wheat yields in many countries, but the estimated rate of increase of wheat yield remained above 0.06 t ha⁻¹ year⁻¹ in several countries in Europe, Asia, Africa and America, and the estimated values were highly uncertain for several major wheat producing countries. The rate of yield increase differed considerably between French regions, suggesting that efforts to identify the main causes of yield stagnation should focus on a subnational scale.

Correlation and simple linear regression.

PubMed

Eberly, Lynn E

2007-01-01

This chapter highlights important steps in using correlation and simple linear regression to address scientific questions about the association of two continuous variables with each other. These steps include estimation and inference, assessing model fit, the connection between regression and ANOVA, and study design. Examples in microbiology are used throughout. This chapter provides a framework that is helpful in understanding more complex statistical techniques, such as multiple linear regression, linear mixed effects models, logistic regression, and proportional hazards regression.

The Impact of Model Misspecification on Parameter Estimation and Item-Fit Assessment in Log-Linear Diagnostic Classification Models

ERIC Educational Resources Information Center

Kunina-Habenicht, Olga; Rupp, Andre A.; Wilhelm, Oliver

2012-01-01

Using a complex simulation study we investigated parameter recovery, classification accuracy, and performance of two item-fit statistics for correct and misspecified diagnostic classification models within a log-linear modeling framework. The basic manipulated test design factors included the number of respondents (1,000 vs. 10,000), attributes (3…

A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation

PubMed Central

Rajeswaran, Jeevanantham; Blackstone, Eugene H.

2014-01-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830

Model-Free CUSUM Methods for Person Fit

ERIC Educational Resources Information Center

Armstrong, Ronald D.; Shi, Min

2009-01-01

This article demonstrates the use of a new class of model-free cumulative sum (CUSUM) statistics to detect person fit given the responses to a linear test. The fundamental statistic being accumulated is the likelihood ratio of two probabilities. The detection performance of this CUSUM scheme is compared to other model-free person-fit statistics…

Identifying the Factors That Influence Change in SEBD Using Logistic Regression Analysis

ERIC Educational Resources Information Center

Camilleri, Liberato; Cefai, Carmel

2013-01-01

Multiple linear regression and ANOVA models are widely used in applications since they provide effective statistical tools for assessing the relationship between a continuous dependent variable and several predictors. However these models rely heavily on linearity and normality assumptions and they do not accommodate categorical dependent…

Commentary on the statistical properties of noise and its implication on general linear models in functional near-infrared spectroscopy.

PubMed

Huppert, Theodore J

2016-01-01

Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of light to measure changes in cerebral blood oxygenation levels. In the majority of NIRS functional brain studies, analysis of this data is based on a statistical comparison of hemodynamic levels between a baseline and task or between multiple task conditions by means of a linear regression model: the so-called general linear model. Although these methods are similar to their implementation in other fields, particularly for functional magnetic resonance imaging, the specific application of these methods in fNIRS research differs in several key ways related to the sources of noise and artifacts unique to fNIRS. In this brief communication, we discuss the application of linear regression models in fNIRS and the modifications needed to generalize these models in order to deal with structured (colored) noise due to systemic physiology and noise heteroscedasticity due to motion artifacts. The objective of this work is to present an overview of these noise properties in the context of the linear model as it applies to fNIRS data. This work is aimed at explaining these mathematical issues to the general fNIRS experimental researcher but is not intended to be a complete mathematical treatment of these concepts.

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

PubMed

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

Correcting for population structure and kinship using the linear mixed model: theory and extensions.

PubMed

Hoffman, Gabriel E

2013-01-01

Population structure and kinship are widespread confounding factors in genome-wide association studies (GWAS). It has been standard practice to include principal components of the genotypes in a regression model in order to account for population structure. More recently, the linear mixed model (LMM) has emerged as a powerful method for simultaneously accounting for population structure and kinship. The statistical theory underlying the differences in empirical performance between modeling principal components as fixed versus random effects has not been thoroughly examined. We undertake an analysis to formalize the relationship between these widely used methods and elucidate the statistical properties of each. Moreover, we introduce a new statistic, effective degrees of freedom, that serves as a metric of model complexity and a novel low rank linear mixed model (LRLMM) to learn the dimensionality of the correction for population structure and kinship, and we assess its performance through simulations. A comparison of the results of LRLMM and a standard LMM analysis applied to GWAS data from the Multi-Ethnic Study of Atherosclerosis (MESA) illustrates how our theoretical results translate into empirical properties of the mixed model. Finally, the analysis demonstrates the ability of the LRLMM to substantially boost the strength of an association for HDL cholesterol in Europeans.

Adaptive Error Estimation in Linearized Ocean General Circulation Models

NASA Technical Reports Server (NTRS)

Chechelnitsky, Michael Y.

1999-01-01

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

Mixed models, linear dependency, and identification in age-period-cohort models.

PubMed

O'Brien, Robert M

2017-07-20

This paper examines the identification problem in age-period-cohort models that use either linear or categorically coded ages, periods, and cohorts or combinations of these parameterizations. These models are not identified using the traditional fixed effect regression model approach because of a linear dependency between the ages, periods, and cohorts. However, these models can be identified if the researcher introduces a single just identifying constraint on the model coefficients. The problem with such constraints is that the results can differ substantially depending on the constraint chosen. Somewhat surprisingly, age-period-cohort models that specify one or more of ages and/or periods and/or cohorts as random effects are identified. This is the case without introducing an additional constraint. I label this identification as statistical model identification and show how statistical model identification comes about in mixed models and why which effects are treated as fixed and which are treated as random can substantially change the estimates of the age, period, and cohort effects. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Evaluation of airborne lidar data to predict vegetation Presence/Absence

USGS Publications Warehouse

Palaseanu-Lovejoy, M.; Nayegandhi, A.; Brock, J.; Woodman, R.; Wright, C.W.

2009-01-01

This study evaluates the capabilities of the Experimental Advanced Airborne Research Lidar (EAARL) in delineating vegetation assemblages in Jean Lafitte National Park, Louisiana. Five-meter-resolution grids of bare earth, canopy height, canopy-reflection ratio, and height of median energy were derived from EAARL data acquired in September 2006. Ground-truth data were collected along transects to assess species composition, canopy cover, and ground cover. To decide which model is more accurate, comparisons of general linear models and generalized additive models were conducted using conventional evaluation methods (i.e., sensitivity, specificity, Kappa statistics, and area under the curve) and two new indexes, net reclassification improvement and integrated discrimination improvement. Generalized additive models were superior to general linear models in modeling presence/absence in training vegetation categories, but no statistically significant differences between the two models were achieved in determining the classification accuracy at validation locations using conventional evaluation methods, although statistically significant improvements in net reclassifications were observed. ?? 2009 Coastal Education and Research Foundation.

Two Paradoxes in Linear Regression Analysis.

PubMed

Feng, Ge; Peng, Jing; Tu, Dongke; Zheng, Julia Z; Feng, Changyong

2016-12-25

Regression is one of the favorite tools in applied statistics. However, misuse and misinterpretation of results from regression analysis are common in biomedical research. In this paper we use statistical theory and simulation studies to clarify some paradoxes around this popular statistical method. In particular, we show that a widely used model selection procedure employed in many publications in top medical journals is wrong. Formal procedures based on solid statistical theory should be used in model selection.

Reliability Analysis of the Gradual Degradation of Semiconductor Devices.

DTIC Science & Technology

1983-07-20

under the heading of linear models or linear statistical models . 3 ,4 We have not used this material in this report. Assuming catastrophic failure when...assuming a catastrophic model . In this treatment we first modify our system loss formula and then proceed to the actual analysis. II. ANALYSIS OF...Failure Time 1 Ti Ti 2 T2 T2 n Tn n and are easily analyzed by simple linear regression. Since we have assumed a log normal/Arrhenius activation

Comparing the Fit of Item Response Theory and Factor Analysis Models

ERIC Educational Resources Information Center

Maydeu-Olivares, Alberto; Cai, Li; Hernandez, Adolfo

2011-01-01

Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be…

A note about high blood pressure in childhood

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena; Simão, Carla

2017-06-01

In medical, behavioral and social sciences it is usual to get a binary outcome. In the present work is collected information where some of the outcomes are binary variables (1='yes'/ 0='no'). In [14] a preliminary study about the caregivers perception of pediatric hypertension was introduced. An experimental questionnaire was designed to be answered by the caregivers of routine pediatric consultation attendees in the Santa Maria's hospital (HSM). The collected data was statistically analyzed, where a descriptive analysis and a predictive model were performed. Significant relations between some socio-demographic variables and the assessed knowledge were obtained. In [14] can be found a statistical data analysis using partial questionnaire's information. The present article completes the statistical approach estimating a model for relevant remaining questions of questionnaire by Generalized Linear Models (GLM). Exploring the binary outcome issue, we intend to extend this approach using Generalized Linear Mixed Models (GLMM), but the process is still ongoing.

A Refined Model for Radar Homing Intercepts.

DTIC Science & Technology

1983-10-27

Helge Toutenburq, Prior Information in Linear Models ,(Wiley, NY, 1982). 7. F. A. Graybill , Introduction to Matrices with Applications in StatisticF... linear target trajectory model z i = 0 + 1 r i + wi () where w i i=I,..., N is a sequence of uncorrelated zero-mean A noise, the general formula for...z i (i=l,..., N) at r. and a linear regression model 1 z i = a0 + a1 r i + w i =(Al) where wi is the corruption noise; the problem is to estimate a0

Understanding the relationship between duration of untreated psychosis and outcomes: A statistical perspective.

PubMed

Hannigan, Ailish; Bargary, Norma; Kinsella, Anthony; Clarke, Mary

2017-06-14

Although the relationships between duration of untreated psychosis (DUP) and outcomes are often assumed to be linear, few studies have explored the functional form of these relationships. The aim of this study is to demonstrate the potential of recent advances in curve fitting approaches (splines) to explore the form of the relationship between DUP and global assessment of functioning (GAF). Curve fitting approaches were used in models to predict change in GAF at long-term follow-up using DUP for a sample of 83 individuals with schizophrenia. The form of the relationship between DUP and GAF was non-linear. Accounting for non-linearity increased the percentage of variance in GAF explained by the model, resulting in better prediction and understanding of the relationship. The relationship between DUP and outcomes may be complex and model fit may be improved by accounting for the form of the relationship. This should be routinely assessed and new statistical approaches for non-linear relationships exploited, if appropriate. © 2017 John Wiley & Sons Australia, Ltd.

A general science-based framework for dynamical spatio-temporal models

USGS Publications Warehouse

Wikle, C.K.; Hooten, M.B.

2010-01-01

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially-explicit processes that evolve over time. Correspondingly, in recent years there has been a significant amount of research on new statistical methodology for such models. Although descriptive models that approach the problem from the second-order (covariance) perspective are important, and innovative work is being done in this regard, many real-world processes are dynamic, and it can be more efficient in some cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The chief challenge with the specification of such dynamical models has been related to the curse of dimensionality. Even in fairly simple linear, first-order Markovian, Gaussian error settings, statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters. In addition, this framework has allowed for the specification of science based parameterizations (and associated prior distributions) in which classes of deterministic dynamical models (e. g., partial differential equations (PDEs), integro-difference equations (IDEs), matrix models, and agent-based models) are used to guide specific parameterizations. Most of the focus for the application of such models in statistics has been in the linear case. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models. In this sense, the need for coherent and sensible model parameterizations is not only helpful, it is essential. Here, we present an overview of a framework for incorporating scientific information to motivate dynamical spatio-temporal models. First, we illustrate the methodology with the linear case. We then develop a general nonlinear spatio-temporal framework that we call general quadratic nonlinearity and demonstrate that it accommodates many different classes of scientific-based parameterizations as special cases. The model is presented in a hierarchical Bayesian framework and is illustrated with examples from ecology and oceanography. ?? 2010 Sociedad de Estad??stica e Investigaci??n Operativa.

Advanced statistics: linear regression, part II: multiple linear regression.

PubMed

Marill, Keith A

2004-01-01

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Cosmological Constraints from Fourier Phase Statistics

NASA Astrophysics Data System (ADS)

Ali, Kamran; Obreschkow, Danail; Howlett, Cullan; Bonvin, Camille; Llinares, Claudio; Oliveira Franco, Felipe; Power, Chris

2018-06-01

Most statistical inference from cosmic large-scale structure relies on two-point statistics, i.e. on the galaxy-galaxy correlation function (2PCF) or the power spectrum. These statistics capture the full information encoded in the Fourier amplitudes of the galaxy density field but do not describe the Fourier phases of the field. Here, we quantify the information contained in the line correlation function (LCF), a three-point Fourier phase correlation function. Using cosmological simulations, we estimate the Fisher information (at redshift z = 0) of the 2PCF, LCF and their combination, regarding the cosmological parameters of the standard ΛCDM model, as well as a Warm Dark Matter (WDM) model and the f(R) and Symmetron modified gravity models. The galaxy bias is accounted for at the level of a linear bias. The relative information of the 2PCF and the LCF depends on the survey volume, sampling density (shot noise) and the bias uncertainty. For a volume of 1h^{-3}Gpc^3, sampled with points of mean density \\bar{n} = 2× 10^{-3} h3 Mpc^{-3} and a bias uncertainty of 13%, the LCF improves the parameter constraints by about 20% in the ΛCDM cosmology and potentially even more in alternative models. Finally, since a linear bias only affects the Fourier amplitudes (2PCF), but not the phases (LCF), the combination of the 2PCF and the LCF can be used to break the degeneracy between the linear bias and σ8, present in 2-point statistics.

Gene Level Meta-Analysis of Quantitative Traits by Functional Linear Models.

PubMed

Fan, Ruzong; Wang, Yifan; Boehnke, Michael; Chen, Wei; Li, Yun; Ren, Haobo; Lobach, Iryna; Xiong, Momiao

2015-08-01

Meta-analysis of genetic data must account for differences among studies including study designs, markers genotyped, and covariates. The effects of genetic variants may differ from population to population, i.e., heterogeneity. Thus, meta-analysis of combining data of multiple studies is difficult. Novel statistical methods for meta-analysis are needed. In this article, functional linear models are developed for meta-analyses that connect genetic data to quantitative traits, adjusting for covariates. The models can be used to analyze rare variants, common variants, or a combination of the two. Both likelihood-ratio test (LRT) and F-distributed statistics are introduced to test association between quantitative traits and multiple variants in one genetic region. Extensive simulations are performed to evaluate empirical type I error rates and power performance of the proposed tests. The proposed LRT and F-distributed statistics control the type I error very well and have higher power than the existing methods of the meta-analysis sequence kernel association test (MetaSKAT). We analyze four blood lipid levels in data from a meta-analysis of eight European studies. The proposed methods detect more significant associations than MetaSKAT and the P-values of the proposed LRT and F-distributed statistics are usually much smaller than those of MetaSKAT. The functional linear models and related test statistics can be useful in whole-genome and whole-exome association studies. Copyright © 2015 by the Genetics Society of America.

Conjoint Analysis: A Study of the Effects of Using Person Variables.

ERIC Educational Resources Information Center

Fraas, John W.; Newman, Isadore

Three statistical techniques--conjoint analysis, a multiple linear regression model, and a multiple linear regression model with a surrogate person variable--were used to estimate the relative importance of five university attributes for students in the process of selecting a college. The five attributes include: availability and variety of…

Comparison of Statistical Models for Analyzing Wheat Yield Time Series

PubMed Central

Michel, Lucie; Makowski, David

2013-01-01

The world's population is predicted to exceed nine billion by 2050 and there is increasing concern about the capability of agriculture to feed such a large population. Foresight studies on food security are frequently based on crop yield trends estimated from yield time series provided by national and regional statistical agencies. Various types of statistical models have been proposed for the analysis of yield time series, but the predictive performances of these models have not yet been evaluated in detail. In this study, we present eight statistical models for analyzing yield time series and compare their ability to predict wheat yield at the national and regional scales, using data provided by the Food and Agriculture Organization of the United Nations and by the French Ministry of Agriculture. The Holt-Winters and dynamic linear models performed equally well, giving the most accurate predictions of wheat yield. However, dynamic linear models have two advantages over Holt-Winters models: they can be used to reconstruct past yield trends retrospectively and to analyze uncertainty. The results obtained with dynamic linear models indicated a stagnation of wheat yields in many countries, but the estimated rate of increase of wheat yield remained above 0.06 t ha−1 year−1 in several countries in Europe, Asia, Africa and America, and the estimated values were highly uncertain for several major wheat producing countries. The rate of yield increase differed considerably between French regions, suggesting that efforts to identify the main causes of yield stagnation should focus on a subnational scale. PMID:24205280

Two Paradoxes in Linear Regression Analysis

PubMed Central

FENG, Ge; PENG, Jing; TU, Dongke; ZHENG, Julia Z.; FENG, Changyong

2016-01-01

Summary Regression is one of the favorite tools in applied statistics. However, misuse and misinterpretation of results from regression analysis are common in biomedical research. In this paper we use statistical theory and simulation studies to clarify some paradoxes around this popular statistical method. In particular, we show that a widely used model selection procedure employed in many publications in top medical journals is wrong. Formal procedures based on solid statistical theory should be used in model selection. PMID:28638214

Comparison of linear, skewed-linear, and proportional hazard models for the analysis of lambing interval in Ripollesa ewes.

PubMed

Casellas, J; Bach, R

2012-06-01

Lambing interval is a relevant reproductive indicator for sheep populations under continuous mating systems, although there is a shortage of selection programs accounting for this trait in the sheep industry. Both the historical assumption of small genetic background and its unorthodox distribution pattern have limited its implementation as a breeding objective. In this manuscript, statistical performances of 3 alternative parametrizations [i.e., symmetric Gaussian mixed linear (GML) model, skew-Gaussian mixed linear (SGML) model, and piecewise Weibull proportional hazard (PWPH) model] have been compared to elucidate the preferred methodology to handle lambing interval data. More specifically, flock-by-flock analyses were performed on 31,986 lambing interval records (257.3 ± 0.2 d) from 6 purebred Ripollesa flocks. Model performances were compared in terms of deviance information criterion (DIC) and Bayes factor (BF). For all flocks, PWPH models were clearly preferred; they generated a reduction of 1,900 or more DIC units and provided BF estimates larger than 100 (i.e., PWPH models against linear models). These differences were reduced when comparing PWPH models with different number of change points for the baseline hazard function. In 4 flocks, only 2 change points were required to minimize the DIC, whereas 4 and 6 change points were needed for the 2 remaining flocks. These differences demonstrated a remarkable degree of heterogeneity across sheep flocks that must be properly accounted for in genetic evaluation models to avoid statistical biases and suboptimal genetic trends. Within this context, all 6 Ripollesa flocks revealed substantial genetic background for lambing interval with heritabilities ranging between 0.13 and 0.19. This study provides the first evidence of the suitability of PWPH models for lambing interval analysis, clearly discarding previous parametrizations focused on mixed linear models.

Linear regression models and k-means clustering for statistical analysis of fNIRS data.

PubMed

Bonomini, Viola; Zucchelli, Lucia; Re, Rebecca; Ieva, Francesca; Spinelli, Lorenzo; Contini, Davide; Paganoni, Anna; Torricelli, Alessandro

2015-02-01

We propose a new algorithm, based on a linear regression model, to statistically estimate the hemodynamic activations in fNIRS data sets. The main concern guiding the algorithm development was the minimization of assumptions and approximations made on the data set for the application of statistical tests. Further, we propose a K-means method to cluster fNIRS data (i.e. channels) as activated or not activated. The methods were validated both on simulated and in vivo fNIRS data. A time domain (TD) fNIRS technique was preferred because of its high performances in discriminating cortical activation and superficial physiological changes. However, the proposed method is also applicable to continuous wave or frequency domain fNIRS data sets.

Linear regression models and k-means clustering for statistical analysis of fNIRS data

PubMed Central

Bonomini, Viola; Zucchelli, Lucia; Re, Rebecca; Ieva, Francesca; Spinelli, Lorenzo; Contini, Davide; Paganoni, Anna; Torricelli, Alessandro

2015-01-01

We propose a new algorithm, based on a linear regression model, to statistically estimate the hemodynamic activations in fNIRS data sets. The main concern guiding the algorithm development was the minimization of assumptions and approximations made on the data set for the application of statistical tests. Further, we propose a K-means method to cluster fNIRS data (i.e. channels) as activated or not activated. The methods were validated both on simulated and in vivo fNIRS data. A time domain (TD) fNIRS technique was preferred because of its high performances in discriminating cortical activation and superficial physiological changes. However, the proposed method is also applicable to continuous wave or frequency domain fNIRS data sets. PMID:25780751

Normality of raw data in general linear models: The most widespread myth in statistics

USGS Publications Warehouse

Kery, Marc; Hatfield, Jeff S.

2003-01-01

In years of statistical consulting for ecologists and wildlife biologists, by far the most common misconception we have come across has been the one about normality in general linear models. These comprise a very large part of the statistical models used in ecology and include t tests, simple and multiple linear regression, polynomial regression, and analysis of variance (ANOVA) and covariance (ANCOVA). There is a widely held belief that the normality assumption pertains to the raw data rather than to the model residuals. We suspect that this error may also occur in countless published studies, whenever the normality assumption is tested prior to analysis. This may lead to the use of nonparametric alternatives (if there are any), when parametric tests would indeed be appropriate, or to use of transformations of raw data, which may introduce hidden assumptions such as multiplicative effects on the natural scale in the case of log-transformed data. Our aim here is to dispel this myth. We very briefly describe relevant theory for two cases of general linear models to show that the residuals need to be normally distributed if tests requiring normality are to be used, such as t and F tests. We then give two examples demonstrating that the distribution of the response variable may be nonnormal, and yet the residuals are well behaved. We do not go into the issue of how to test normality; instead we display the distributions of response variables and residuals graphically.

Agent based reasoning for the non-linear stochastic models of long-range memory

NASA Astrophysics Data System (ADS)

Kononovicius, A.; Gontis, V.

2012-02-01

We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. The agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.

Linear and nonlinear methods in modeling the aqueous solubility of organic compounds.

PubMed

Catana, Cornel; Gao, Hua; Orrenius, Christian; Stouten, Pieter F W

2005-01-01

Solubility data for 930 diverse compounds have been analyzed using linear Partial Least Square (PLS) and nonlinear PLS methods, Continuum Regression (CR), and Neural Networks (NN). 1D and 2D descriptors from MOE package in combination with E-state or ISIS keys have been used. The best model was obtained using linear PLS for a combination between 22 MOE descriptors and 65 ISIS keys. It has a correlation coefficient (r2) of 0.935 and a root-mean-square error (RMSE) of 0.468 log molar solubility (log S(w)). The model validated on a test set of 177 compounds not included in the training set has r2 0.911 and RMSE 0.475 log S(w). The descriptors were ranked according to their importance, and at the top of the list have been found the 22 MOE descriptors. The CR model produced results as good as PLS, and because of the way in which cross-validation has been done it is expected to be a valuable tool in prediction besides PLS model. The statistics obtained using nonlinear methods did not surpass those got with linear ones. The good statistic obtained for linear PLS and CR recommends these models to be used in prediction when it is difficult or impossible to make experimental measurements, for virtual screening, combinatorial library design, and efficient leads optimization.

[Quantitative structure-gas chromatographic retention relationship of polycyclic aromatic sulfur heterocycles using molecular electronegativity-distance vector].

PubMed

Li, Zhenghua; Cheng, Fansheng; Xia, Zhining

2011-01-01

The chemical structures of 114 polycyclic aromatic sulfur heterocycles (PASHs) have been studied by molecular electronegativity-distance vector (MEDV). The linear relationships between gas chromatographic retention index and the MEDV have been established by a multiple linear regression (MLR) model. The results of variable selection by stepwise multiple regression (SMR) and the powerful predictive abilities of the optimization model appraised by leave-one-out cross-validation showed that the optimization model with the correlation coefficient (R) of 0.994 7 and the cross-validated correlation coefficient (Rcv) of 0.994 0 possessed the best statistical quality. Furthermore, when the 114 PASHs compounds were divided into calibration and test sets in the ratio of 2:1, the statistical analysis showed our models possesses almost equal statistical quality, the very similar regression coefficients and the good robustness. The quantitative structure-retention relationship (QSRR) model established may provide a convenient and powerful method for predicting the gas chromatographic retention of PASHs.

Regression Model Term Selection for the Analysis of Strain-Gage Balance Calibration Data

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred; Volden, Thomas R.

2010-01-01

The paper discusses the selection of regression model terms for the analysis of wind tunnel strain-gage balance calibration data. Different function class combinations are presented that may be used to analyze calibration data using either a non-iterative or an iterative method. The role of the intercept term in a regression model of calibration data is reviewed. In addition, useful algorithms and metrics originating from linear algebra and statistics are recommended that will help an analyst (i) to identify and avoid both linear and near-linear dependencies between regression model terms and (ii) to make sure that the selected regression model of the calibration data uses only statistically significant terms. Three different tests are suggested that may be used to objectively assess the predictive capability of the final regression model of the calibration data. These tests use both the original data points and regression model independent confirmation points. Finally, data from a simplified manual calibration of the Ames MK40 balance is used to illustrate the application of some of the metrics and tests to a realistic calibration data set.

On Fitting Generalized Linear Mixed-effects Models for Binary Responses using Different Statistical Packages

PubMed Central

Zhang, Hui; Lu, Naiji; Feng, Changyong; Thurston, Sally W.; Xia, Yinglin; Tu, Xin M.

2011-01-01

Summary The generalized linear mixed-effects model (GLMM) is a popular paradigm to extend models for cross-sectional data to a longitudinal setting. When applied to modeling binary responses, different software packages and even different procedures within a package may give quite different results. In this report, we describe the statistical approaches that underlie these different procedures and discuss their strengths and weaknesses when applied to fit correlated binary responses. We then illustrate these considerations by applying these procedures implemented in some popular software packages to simulated and real study data. Our simulation results indicate a lack of reliability for most of the procedures considered, which carries significant implications for applying such popular software packages in practice. PMID:21671252

Statistical treatment for the wet bias in tree-ring chronologies: A case study from the InteriorWest, USA

Treesearch

Yan Sun; Matthew F. Bekker; R. Justin DeRose; Roger Kjelgren; S. -Y. Simon Wang

2017-01-01

Dendroclimatic research has long assumed a linear relationship between tree-ring increment and climate variables. However, ring width frequently underestimates extremely wet years, a phenomenon we refer to as ‘wet bias’. In this paper, we present statistical evidence for wet bias that is obscured by the assumption of linearity. To improve tree-ring-climate modeling, we...

The Effects of Measurement Error on Statistical Models for Analyzing Change. Final Report.

ERIC Educational Resources Information Center

Dunivant, Noel

The results of six major projects are discussed including a comprehensive mathematical and statistical analysis of the problems caused by errors of measurement in linear models for assessing change. In a general matrix representation of the problem, several new analytic results are proved concerning the parameters which affect bias in…

Linear theory for filtering nonlinear multiscale systems with model error

PubMed Central

Berry, Tyrus; Harlim, John

2014-01-01

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline. PMID:25002829

A Test Strategy for High Resolution Image Scanners.

DTIC Science & Technology

1983-10-01

for multivariate analysis. Holt, Richart and Winston, Inc., New York. Graybill , F.A., 1961: An introduction to linear statistical models . SVolume I...i , j i -(7) 02 1 )2 y 4n .i ij 13 The linear estimation model for the polynomial coefficients can be set up as - =; =(8) with T = ( x’ . . X-nn "X...Resolution Image Scanner MTF Geometrical and radiometric performance Dynamic range, linearity , noise - Dynamic scanning errors Response uniformity Skewness of

Interpretation of commonly used statistical regression models.

PubMed

Kasza, Jessica; Wolfe, Rory

2014-01-01

A review of some regression models commonly used in respiratory health applications is provided in this article. Simple linear regression, multiple linear regression, logistic regression and ordinal logistic regression are considered. The focus of this article is on the interpretation of the regression coefficients of each model, which are illustrated through the application of these models to a respiratory health research study. © 2013 The Authors. Respirology © 2013 Asian Pacific Society of Respirology.

Online Updating of Statistical Inference in the Big Data Setting.

PubMed

Schifano, Elizabeth D; Wu, Jing; Wang, Chun; Yan, Jun; Chen, Ming-Hui

2016-01-01

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.

Detecting temporal change in freshwater fisheries surveys: statistical power and the important linkages between management questions and monitoring objectives

USGS Publications Warehouse

Wagner, Tyler; Irwin, Brian J.; James R. Bence,; Daniel B. Hayes,

2016-01-01

Monitoring to detect temporal trends in biological and habitat indices is a critical component of fisheries management. Thus, it is important that management objectives are linked to monitoring objectives. This linkage requires a definition of what constitutes a management-relevant “temporal trend.” It is also important to develop expectations for the amount of time required to detect a trend (i.e., statistical power) and for choosing an appropriate statistical model for analysis. We provide an overview of temporal trends commonly encountered in fisheries management, review published studies that evaluated statistical power of long-term trend detection, and illustrate dynamic linear models in a Bayesian context, as an additional analytical approach focused on shorter term change. We show that monitoring programs generally have low statistical power for detecting linear temporal trends and argue that often management should be focused on different definitions of trends, some of which can be better addressed by alternative analytical approaches.

Comparison of statistical models to estimate parasite growth rate in the induced blood stage malaria model.

PubMed

Wockner, Leesa F; Hoffmann, Isabell; O'Rourke, Peter; McCarthy, James S; Marquart, Louise

2017-08-25

The efficacy of vaccines aimed at inhibiting the growth of malaria parasites in the blood can be assessed by comparing the growth rate of parasitaemia in the blood of subjects treated with a test vaccine compared to controls. In studies using induced blood stage malaria (IBSM), a type of controlled human malaria infection, parasite growth rate has been measured using models with the intercept on the y-axis fixed to the inoculum size. A set of statistical models was evaluated to determine an optimal methodology to estimate parasite growth rate in IBSM studies. Parasite growth rates were estimated using data from 40 subjects published in three IBSM studies. Data was fitted using 12 statistical models: log-linear, sine-wave with the period either fixed to 48 h or not fixed; these models were fitted with the intercept either fixed to the inoculum size or not fixed. All models were fitted by individual, and overall by study using a mixed effects model with a random effect for the individual. Log-linear models and sine-wave models, with the period fixed or not fixed, resulted in similar parasite growth rate estimates (within 0.05 log 10 parasites per mL/day). Average parasite growth rate estimates for models fitted by individual with the intercept fixed to the inoculum size were substantially lower by an average of 0.17 log 10 parasites per mL/day (range 0.06-0.24) compared with non-fixed intercept models. Variability of parasite growth rate estimates across the three studies analysed was substantially higher (3.5 times) for fixed-intercept models compared with non-fixed intercept models. The same tendency was observed in models fitted overall by study. Modelling data by individual or overall by study had minimal effect on parasite growth estimates. The analyses presented in this report confirm that fixing the intercept to the inoculum size influences parasite growth estimates. The most appropriate statistical model to estimate the growth rate of blood-stage parasites in IBSM studies appears to be a log-linear model fitted by individual and with the intercept estimated in the log-linear regression. Future studies should use this model to estimate parasite growth rates.

Identifying ontogenetic, environmental and individual components of forest tree growth

PubMed Central

Chaubert-Pereira, Florence; Caraglio, Yves; Lavergne, Christian; Guédon, Yann

2009-01-01

Background and Aims This study aimed to identify and characterize the ontogenetic, environmental and individual components of forest tree growth. In the proposed approach, the tree growth data typically correspond to the retrospective measurement of annual shoot characteristics (e.g. length) along the trunk. Methods Dedicated statistical models (semi-Markov switching linear mixed models) were applied to data sets of Corsican pine and sessile oak. In the semi-Markov switching linear mixed models estimated from these data sets, the underlying semi-Markov chain represents both the succession of growth phases and their lengths, while the linear mixed models represent both the influence of climatic factors and the inter-individual heterogeneity within each growth phase. Key Results On the basis of these integrative statistical models, it is shown that growth phases are not only defined by average growth level but also by growth fluctuation amplitudes in response to climatic factors and inter-individual heterogeneity and that the individual tree status within the population may change between phases. Species plasticity affected the response to climatic factors while tree origin, sampling strategy and silvicultural interventions impacted inter-individual heterogeneity. Conclusions The transposition of the proposed integrative statistical modelling approach to cambial growth in relation to climatic factors and the study of the relationship between apical growth and cambial growth constitute the next steps in this research. PMID:19684021

A question of separation: disentangling tracer bias and gravitational non-linearity with counts-in-cells statistics

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Feix, M.; Codis, S.; Pichon, C.; Bernardeau, F.; L'Huillier, B.; Kim, J.; Hong, S. E.; Laigle, C.; Park, C.; Shin, J.; Pogosyan, D.

2018-02-01

Starting from a very accurate model for density-in-cells statistics of dark matter based on large deviation theory, a bias model for the tracer density in spheres is formulated. It adopts a mean bias relation based on a quadratic bias model to relate the log-densities of dark matter to those of mass-weighted dark haloes in real and redshift space. The validity of the parametrized bias model is established using a parametrization-independent extraction of the bias function. This average bias model is then combined with the dark matter PDF, neglecting any scatter around it: it nevertheless yields an excellent model for densities-in-cells statistics of mass tracers that is parametrized in terms of the underlying dark matter variance and three bias parameters. The procedure is validated on measurements of both the one- and two-point statistics of subhalo densities in the state-of-the-art Horizon Run 4 simulation showing excellent agreement for measured dark matter variance and bias parameters. Finally, it is demonstrated that this formalism allows for a joint estimation of the non-linear dark matter variance and the bias parameters using solely the statistics of subhaloes. Having verified that galaxy counts in hydrodynamical simulations sampled on a scale of 10 Mpc h-1 closely resemble those of subhaloes, this work provides important steps towards making theoretical predictions for density-in-cells statistics applicable to upcoming galaxy surveys like Euclid or WFIRST.

Towards bridging the gap between climate change projections and maize producers in South Africa

NASA Astrophysics Data System (ADS)

Landman, Willem A.; Engelbrecht, Francois; Hewitson, Bruce; Malherbe, Johan; van der Merwe, Jacobus

2018-05-01

Multi-decadal regional projections of future climate change are introduced into a linear statistical model in order to produce an ensemble of austral mid-summer maximum temperature simulations for southern Africa. The statistical model uses atmospheric thickness fields from a high-resolution (0.5° × 0.5°) reanalysis-forced simulation as predictors in order to develop a linear recalibration model which represents the relationship between atmospheric thickness fields and gridded maximum temperatures across the region. The regional climate model, the conformal-cubic atmospheric model (CCAM), projects maximum temperatures increases over southern Africa to be in the order of 4 °C under low mitigation towards the end of the century or even higher. The statistical recalibration model is able to replicate these increasing temperatures, and the atmospheric thickness-maximum temperature relationship is shown to be stable under future climate conditions. Since dry land crop yields are not explicitly simulated by climate models but are sensitive to maximum temperature extremes, the effect of projected maximum temperature change on dry land crops of the Witbank maize production district of South Africa, assuming other factors remain unchanged, is then assessed by employing a statistical approach similar to the one used for maximum temperature projections.

Hypothesis testing in functional linear regression models with Neyman's truncation and wavelet thresholding for longitudinal data.

PubMed

Yang, Xiaowei; Nie, Kun

2008-03-15

Longitudinal data sets in biomedical research often consist of large numbers of repeated measures. In many cases, the trajectories do not look globally linear or polynomial, making it difficult to summarize the data or test hypotheses using standard longitudinal data analysis based on various linear models. An alternative approach is to apply the approaches of functional data analysis, which directly target the continuous nonlinear curves underlying discretely sampled repeated measures. For the purposes of data exploration, many functional data analysis strategies have been developed based on various schemes of smoothing, but fewer options are available for making causal inferences regarding predictor-outcome relationships, a common task seen in hypothesis-driven medical studies. To compare groups of curves, two testing strategies with good power have been proposed for high-dimensional analysis of variance: the Fourier-based adaptive Neyman test and the wavelet-based thresholding test. Using a smoking cessation clinical trial data set, this paper demonstrates how to extend the strategies for hypothesis testing into the framework of functional linear regression models (FLRMs) with continuous functional responses and categorical or continuous scalar predictors. The analysis procedure consists of three steps: first, apply the Fourier or wavelet transform to the original repeated measures; then fit a multivariate linear model in the transformed domain; and finally, test the regression coefficients using either adaptive Neyman or thresholding statistics. Since a FLRM can be viewed as a natural extension of the traditional multiple linear regression model, the development of this model and computational tools should enhance the capacity of medical statistics for longitudinal data.

Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems.

PubMed

Sapsis, Themistoklis P; Majda, Andrew J

2013-08-20

A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.

High-resolution vertical profiles of groundwater electrical conductivity (EC) and chloride from direct-push EC logs

NASA Astrophysics Data System (ADS)

Bourke, Sarah A.; Hermann, Kristian J.; Hendry, M. Jim

2017-11-01

Elevated groundwater salinity associated with produced water, leaching from landfills or secondary salinity can degrade arable soils and potable water resources. Direct-push electrical conductivity (EC) profiling enables rapid, relatively inexpensive, high-resolution in-situ measurements of subsurface salinity, without requiring core collection or installation of groundwater wells. However, because the direct-push tool measures the bulk EC of both solid and liquid phases (ECa), incorporation of ECa data into regional or historical groundwater data sets requires the prediction of pore water EC (ECw) or chloride (Cl-) concentrations from measured ECa. Statistical linear regression and physically based models for predicting ECw and Cl- from ECa profiles were tested on a brine plume in central Saskatchewan, Canada. A linear relationship between ECa/ECw and porosity was more accurate for predicting ECw and Cl- concentrations than a power-law relationship (Archie's Law). Despite clay contents of up to 96%, the addition of terms to account for electrical conductance in the solid phase did not improve model predictions. In the absence of porosity data, statistical linear regression models adequately predicted ECw and Cl- concentrations from direct-push ECa profiles (ECw = 5.48 ECa + 0.78, R 2 = 0.87; Cl- = 1,978 ECa - 1,398, R 2 = 0.73). These statistical models can be used to predict ECw in the absence of lithologic data and will be particularly useful for initial site assessments. The more accurate linear physically based model can be used to predict ECw and Cl- as porosity data become available and the site-specific ECw-Cl- relationship is determined.

On fitting generalized linear mixed-effects models for binary responses using different statistical packages.

PubMed

Zhang, Hui; Lu, Naiji; Feng, Changyong; Thurston, Sally W; Xia, Yinglin; Zhu, Liang; Tu, Xin M

2011-09-10

The generalized linear mixed-effects model (GLMM) is a popular paradigm to extend models for cross-sectional data to a longitudinal setting. When applied to modeling binary responses, different software packages and even different procedures within a package may give quite different results. In this report, we describe the statistical approaches that underlie these different procedures and discuss their strengths and weaknesses when applied to fit correlated binary responses. We then illustrate these considerations by applying these procedures implemented in some popular software packages to simulated and real study data. Our simulation results indicate a lack of reliability for most of the procedures considered, which carries significant implications for applying such popular software packages in practice. Copyright © 2011 John Wiley & Sons, Ltd.

VizieR Online Data Catalog: HARPS timeseries data for HD41248 (Jenkins+, 2014)

NASA Astrophysics Data System (ADS)

Jenkins, J. S.; Tuomi, M.

2017-05-01

We modeled the HARPS radial velocities of HD 42148 by adopting the analysis techniques and the statistical model applied in Tuomi et al. (2014, arXiv:1405.2016). This model contains Keplerian signals, a linear trend, a moving average component with exponential smoothing, and linear correlations with activity indices, namely, BIS, FWHM, and chromospheric activity S index. We applied our statistical model outlined above to the full data set of radial velocities for HD 41248, combining the previously published data in Jenkins et al. (2013ApJ...771...41J) with the newly published data in Santos et al. (2014, J/A+A/566/A35), giving rise to a total time series of 223 HARPS (Mayor et al. 2003Msngr.114...20M) velocities. (1 data file).

A SIGNIFICANCE TEST FOR THE LASSO1

PubMed Central

Lockhart, Richard; Taylor, Jonathan; Tibshirani, Ryan J.; Tibshirani, Robert

2014-01-01

In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic based on lasso fitted values, called the covariance test statistic, and show that when the true model is linear, this statistic has an Exp(1) asymptotic distribution under the null hypothesis (the null being that all truly active variables are contained in the current lasso model). Our proof of this result for the special case of the first predictor to enter the model (i.e., testing for a single significant predictor variable against the global null) requires only weak assumptions on the predictor matrix X. On the other hand, our proof for a general step in the lasso path places further technical assumptions on X and the generative model, but still allows for the important high-dimensional case p > n, and does not necessarily require that the current lasso model achieves perfect recovery of the truly active variables. Of course, for testing the significance of an additional variable between two nested linear models, one typically uses the chi-squared test, comparing the drop in residual sum of squares (RSS) to a χ12 distribution. But when this additional variable is not fixed, and has been chosen adaptively or greedily, this test is no longer appropriate: adaptivity makes the drop in RSS stochastically much larger than χ12 under the null hypothesis. Our analysis explicitly accounts for adaptivity, as it must, since the lasso builds an adaptive sequence of linear models as the tuning parameter λ decreases. In this analysis, shrinkage plays a key role: though additional variables are chosen adaptively, the coefficients of lasso active variables are shrunken due to the l1 penalty. Therefore, the test statistic (which is based on lasso fitted values) is in a sense balanced by these two opposing properties—adaptivity and shrinkage—and its null distribution is tractable and asymptotically Exp(1). PMID:25574062

Statistical Methods for Generalized Linear Models with Covariates Subject to Detection Limits.

PubMed

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

2015-05-01

Censored observations are a common occurrence in biomedical data sets. Although a large amount of research has been devoted to estimation and inference for data with censored responses, very little research has focused on proper statistical procedures when predictors are censored. In this paper, we consider statistical methods for dealing with multiple predictors subject to detection limits within the context of generalized linear models. We investigate and adapt several conventional methods and develop a new multiple imputation approach for analyzing data sets with predictors censored due to detection limits. We establish the consistency and asymptotic normality of the proposed multiple imputation estimator and suggest a computationally simple and consistent variance estimator. We also demonstrate that the conditional mean imputation method often leads to inconsistent estimates in generalized linear models, while several other methods are either computationally intensive or lead to parameter estimates that are biased or more variable compared to the proposed multiple imputation estimator. In an extensive simulation study, we assess the bias and variability of different approaches within the context of a logistic regression model and compare variance estimation methods for the proposed multiple imputation estimator. Lastly, we apply several methods to analyze the data set from a recently-conducted GenIMS study.

Online Statistical Modeling (Regression Analysis) for Independent Responses

NASA Astrophysics Data System (ADS)

Made Tirta, I.; Anggraeni, Dian; Pandutama, Martinus

2017-06-01

Regression analysis (statistical analmodelling) are among statistical methods which are frequently needed in analyzing quantitative data, especially to model relationship between response and explanatory variables. Nowadays, statistical models have been developed into various directions to model various type and complex relationship of data. Rich varieties of advanced and recent statistical modelling are mostly available on open source software (one of them is R). However, these advanced statistical modelling, are not very friendly to novice R users, since they are based on programming script or command line interface. Our research aims to developed web interface (based on R and shiny), so that most recent and advanced statistical modelling are readily available, accessible and applicable on web. We have previously made interface in the form of e-tutorial for several modern and advanced statistical modelling on R especially for independent responses (including linear models/LM, generalized linier models/GLM, generalized additive model/GAM and generalized additive model for location scale and shape/GAMLSS). In this research we unified them in the form of data analysis, including model using Computer Intensive Statistics (Bootstrap and Markov Chain Monte Carlo/ MCMC). All are readily accessible on our online Virtual Statistics Laboratory. The web (interface) make the statistical modeling becomes easier to apply and easier to compare them in order to find the most appropriate model for the data.

Modeling exposure–lag–response associations with distributed lag non-linear models

PubMed Central

Gasparrini, Antonio

2014-01-01

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094

The Development of Web-based Graphical User Interface for Unified Modeling Data with Multi (Correlated) Responses

NASA Astrophysics Data System (ADS)

Made Tirta, I.; Anggraeni, Dian

2018-04-01

Statistical models have been developed rapidly into various directions to accommodate various types of data. Data collected from longitudinal, repeated measured, clustered data (either continuous, binary, count, or ordinal), are more likely to be correlated. Therefore statistical model for independent responses, such as Generalized Linear Model (GLM), Generalized Additive Model (GAM) are not appropriate. There are several models available to apply for correlated responses including GEEs (Generalized Estimating Equations), for marginal model and various mixed effect model such as GLMM (Generalized Linear Mixed Models) and HGLM (Hierarchical Generalized Linear Models) for subject spesific models. These models are available on free open source software R, but they can only be accessed through command line interface (using scrit). On the othe hand, most practical researchers very much rely on menu based or Graphical User Interface (GUI). We develop, using Shiny framework, standard pull down menu Web-GUI that unifies most models for correlated responses. The Web-GUI has accomodated almost all needed features. It enables users to do and compare various modeling for repeated measure data (GEE, GLMM, HGLM, GEE for nominal responses) much more easily trough online menus. This paper discusses the features of the Web-GUI and illustrates the use of them. In General we find that GEE, GLMM, HGLM gave very closed results.

Transfer Student Success: Educationally Purposeful Activities Predictive of Undergraduate GPA

ERIC Educational Resources Information Center

Fauria, Renee M.; Fuller, Matthew B.

2015-01-01

Researchers evaluated the effects of Educationally Purposeful Activities (EPAs) on transfer and nontransfer students' cumulative GPAs. Hierarchical, linear, and multiple regression models yielded seven statistically significant educationally purposeful items that influenced undergraduate student GPAs. Statistically significant positive EPAs for…

Alternative approaches to predicting methane emissions from dairy cows.

PubMed

Mills, J A N; Kebreab, E; Yates, C M; Crompton, L A; Cammell, S B; Dhanoa, M S; Agnew, R E; France, J

2003-12-01

Previous attempts to apply statistical models, which correlate nutrient intake with methane production, have been of limited value where predictions are obtained for nutrient intakes and diet types outside those used in model construction. Dynamic mechanistic models have proved more suitable for extrapolation, but they remain computationally expensive and are not applied easily in practical situations. The first objective of this research focused on employing conventional techniques to generate statistical models of methane production appropriate to United Kingdom dairy systems. The second objective was to evaluate these models and a model published previously using both United Kingdom and North American data sets. Thirdly, nonlinear models were considered as alternatives to the conventional linear regressions. The United Kingdom calorimetry data used to construct the linear models also were used to develop the three nonlinear alternatives that were all of modified Mitscherlich (monomolecular) form. Of the linear models tested, an equation from the literature proved most reliable across the full range of evaluation data (root mean square prediction error = 21.3%). However, the Mitscherlich models demonstrated the greatest degree of adaptability across diet types and intake level. The most successful model for simulating the independent data was a modified Mitscherlich equation with the steepness parameter set to represent dietary starch-to-ADF ratio (root mean square prediction error = 20.6%). However, when such data were unavailable, simpler Mitscherlich forms relating dry matter or metabolizable energy intake to methane production remained better alternatives relative to their linear counterparts.

Performance Metrics, Error Modeling, and Uncertainty Quantification

NASA Technical Reports Server (NTRS)

Tian, Yudong; Nearing, Grey S.; Peters-Lidard, Christa D.; Harrison, Kenneth W.; Tang, Ling

2016-01-01

A common set of statistical metrics has been used to summarize the performance of models or measurements-­ the most widely used ones being bias, mean square error, and linear correlation coefficient. They assume linear, additive, Gaussian errors, and they are interdependent, incomplete, and incapable of directly quantifying un­certainty. The authors demonstrate that these metrics can be directly derived from the parameters of the simple linear error model. Since a correct error model captures the full error information, it is argued that the specification of a parametric error model should be an alternative to the metrics-based approach. The error-modeling meth­odology is applicable to both linear and nonlinear errors, while the metrics are only meaningful for linear errors. In addition, the error model expresses the error structure more naturally, and directly quantifies uncertainty. This argument is further explained by highlighting the intrinsic connections between the performance metrics, the error model, and the joint distribution between the data and the reference.

A semiempirical linear model of indirect, flat-panel x-ray detectors.

PubMed

Huang, Shih-Ying; Yang, Kai; Abbey, Craig K; Boone, John M

2012-04-01

It is important to understand signal and noise transfer in the indirect, flat-panel x-ray detector when developing and optimizing imaging systems. For optimization where simulating images is necessary, this study introduces a semiempirical model to simulate projection images with user-defined x-ray fluence interaction. The signal and noise transfer in the indirect, flat-panel x-ray detectors is characterized by statistics consistent with energy-integration of x-ray photons. For an incident x-ray spectrum, x-ray photons are attenuated and absorbed in the x-ray scintillator to produce light photons, which are coupled to photodiodes for signal readout. The signal mean and variance are linearly related to the energy-integrated x-ray spectrum by empirically determined factors. With the known first- and second-order statistics, images can be simulated by incorporating multipixel signal statistics and the modulation transfer function of the imaging system. To estimate the semiempirical input to this model, 500 projection images (using an indirect, flat-panel x-ray detector in the breast CT system) were acquired with 50-100 kilovolt (kV) x-ray spectra filtered with 0.1-mm tin (Sn), 0.2-mm copper (Cu), 1.5-mm aluminum (Al), or 0.05-mm silver (Ag). The signal mean and variance of each detector element and the noise power spectra (NPS) were calculated and incorporated into this model for accuracy. Additionally, the modulation transfer function of the detector system was physically measured and incorporated in the image simulation steps. For validation purposes, simulated and measured projection images of air scans were compared using 40 kV∕0.1-mm Sn, 65 kV∕0.2-mm Cu, 85 kV∕1.5-mm Al, and 95 kV∕0.05-mm Ag. The linear relationship between the measured signal statistics and the energy-integrated x-ray spectrum was confirmed and incorporated into the model. The signal mean and variance factors were linearly related to kV for each filter material (r(2) of signal mean to kV: 0.91, 0.93, 0.86, and 0.99 for 0.1-mm Sn, 0.2-mm Cu, 1.5-mm Al, and 0.05-mm Ag, respectively; r(2) of signal variance to kV: 0.99 for all four filters). The comparison of the signal and noise (mean, variance, and NPS) between the simulated and measured air scan images suggested that this model was reasonable in predicting accurate signal statistics of air scan images using absolute percent error. Overall, the model was found to be accurate in estimating signal statistics and spatial correlation between the detector elements of the images acquired with indirect, flat-panel x-ray detectors. The semiempirical linear model of the indirect, flat-panel x-ray detectors was described and validated with images of air scans. The model was found to be a useful tool in understanding the signal and noise transfer within indirect, flat-panel x-ray detector systems.

Generalized linear and generalized additive models in studies of species distributions: Setting the scene

USGS Publications Warehouse

Guisan, Antoine; Edwards, T.C.; Hastie, T.

2002-01-01

An important statistical development of the last 30 years has been the advance in regression analysis provided by generalized linear models (GLMs) and generalized additive models (GAMs). Here we introduce a series of papers prepared within the framework of an international workshop entitled: Advances in GLMs/GAMs modeling: from species distribution to environmental management, held in Riederalp, Switzerland, 6-11 August 2001. We first discuss some general uses of statistical models in ecology, as well as provide a short review of several key examples of the use of GLMs and GAMs in ecological modeling efforts. We next present an overview of GLMs and GAMs, and discuss some of their related statistics used for predictor selection, model diagnostics, and evaluation. Included is a discussion of several new approaches applicable to GLMs and GAMs, such as ridge regression, an alternative to stepwise selection of predictors, and methods for the identification of interactions by a combined use of regression trees and several other approaches. We close with an overview of the papers and how we feel they advance our understanding of their application to ecological modeling. ?? 2002 Elsevier Science B.V. All rights reserved.

Estimating the impact of mineral aerosols on crop yields in food insecure regions using statistical crop models

NASA Astrophysics Data System (ADS)

Hoffman, A.; Forest, C. E.; Kemanian, A.

2016-12-01

A significant number of food-insecure nations exist in regions of the world where dust plays a large role in the climate system. While the impacts of common climate variables (e.g. temperature, precipitation, ozone, and carbon dioxide) on crop yields are relatively well understood, the impact of mineral aerosols on yields have not yet been thoroughly investigated. This research aims to develop the data and tools to progress our understanding of mineral aerosol impacts on crop yields. Suspended dust affects crop yields by altering the amount and type of radiation reaching the plant, modifying local temperature and precipitation. While dust events (i.e. dust storms) affect crop yields by depleting the soil of nutrients or by defoliation via particle abrasion. The impact of dust on yields is modeled statistically because we are uncertain which impacts will dominate the response on national and regional scales considered in this study. Multiple linear regression is used in a number of large-scale statistical crop modeling studies to estimate yield responses to various climate variables. In alignment with previous work, we develop linear crop models, but build upon this simple method of regression with machine-learning techniques (e.g. random forests) to identify important statistical predictors and isolate how dust affects yields on the scales of interest. To perform this analysis, we develop a crop-climate dataset for maize, soybean, groundnut, sorghum, rice, and wheat for the regions of West Africa, East Africa, South Africa, and the Sahel. Random forest regression models consistently model historic crop yields better than the linear models. In several instances, the random forest models accurately capture the temperature and precipitation threshold behavior in crops. Additionally, improving agricultural technology has caused a well-documented positive trend that dominates time series of global and regional yields. This trend is often removed before regression with traditional crop models, but likely at the cost of removing climate information. Our random forest models consistently discover the positive trend without removing any additional data. The application of random forests as a statistical crop model provides insight into understanding the impact of dust on yields in marginal food producing regions.

Is There a Critical Distance for Fickian Transport? - a Statistical Approach to Sub-Fickian Transport Modelling in Porous Media

NASA Astrophysics Data System (ADS)

Most, S.; Nowak, W.; Bijeljic, B.

2014-12-01

Transport processes in porous media are frequently simulated as particle movement. This process can be formulated as a stochastic process of particle position increments. At the pore scale, the geometry and micro-heterogeneities prohibit the commonly made assumption of independent and normally distributed increments to represent dispersion. Many recent particle methods seek to loosen this assumption. Recent experimental data suggest that we have not yet reached the end of the need to generalize, because particle increments show statistical dependency beyond linear correlation and over many time steps. The goal of this work is to better understand the validity regions of commonly made assumptions. We are investigating after what transport distances can we observe: A statistical dependence between increments, that can be modelled as an order-k Markov process, boils down to order 1. This would be the Markovian distance for the process, where the validity of yet-unexplored non-Gaussian-but-Markovian random walks would start. A bivariate statistical dependence that simplifies to a multi-Gaussian dependence based on simple linear correlation (validity of correlated PTRW). Complete absence of statistical dependence (validity of classical PTRW/CTRW). The approach is to derive a statistical model for pore-scale transport from a powerful experimental data set via copula analysis. The model is formulated as a non-Gaussian, mutually dependent Markov process of higher order, which allows us to investigate the validity ranges of simpler models.

Enrichment of statistical power for genome-wide association studies

USDA-ARS?s Scientific Manuscript database

The inheritance of most human diseases and agriculturally important traits is controlled by many genes with small effects. Identifying these genes, while simultaneously controlling false positives, is challenging. Among available statistical methods, the mixed linear model (MLM) has been the most fl...

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

The Impact of a Flipped Classroom Model of Learning on a Large Undergraduate Statistics Class

ERIC Educational Resources Information Center

Nielson, Perpetua Lynne; Bean, Nathan William Bean; Larsen, Ross Allen Andrew

2018-01-01

We examine the impact of a flipped classroom model of learning on student performance and satisfaction in a large undergraduate introductory statistics class. Two professors each taught a lecture-section and a flipped-class section. Using MANCOVA, a linear combination of final exam scores, average quiz scores, and course ratings was compared for…

Improving the Power of GWAS and Avoiding Confounding from Population Stratification with PC-Select

PubMed Central

Tucker, George; Price, Alkes L.; Berger, Bonnie

2014-01-01

Using a reduced subset of SNPs in a linear mixed model can improve power for genome-wide association studies, yet this can result in insufficient correction for population stratification. We propose a hybrid approach using principal components that does not inflate statistics in the presence of population stratification and improves power over standard linear mixed models. PMID:24788602

Towards a General Turbulence Model for Planetary Boundary Layers Based on Direct Statistical Simulation

NASA Astrophysics Data System (ADS)

Skitka, J.; Marston, B.; Fox-Kemper, B.

2016-02-01

Sub-grid turbulence models for planetary boundary layers are typically constructed additively, starting with local flow properties and including non-local (KPP) or higher order (Mellor-Yamada) parameters until a desired level of predictive capacity is achieved or a manageable threshold of complexity is surpassed. Such approaches are necessarily limited in general circumstances, like global circulation models, by their being optimized for particular flow phenomena. By building a model reductively, starting with the infinite hierarchy of turbulence statistics, truncating at a given order, and stripping degrees of freedom from the flow, we offer the prospect a turbulence model and investigative tool that is equally applicable to all flow types and able to take full advantage of the wealth of nonlocal information in any flow. Direct statistical simulation (DSS) that is based upon expansion in equal-time cumulants can be used to compute flow statistics of arbitrary order. We investigate the feasibility of a second-order closure (CE2) by performing simulations of the ocean boundary layer in a quasi-linear approximation for which CE2 is exact. As oceanographic examples, wind-driven Langmuir turbulence and thermal convection are studied by comparison of the quasi-linear and fully nonlinear statistics. We also characterize the computational advantages and physical uncertainties of CE2 defined on a reduced basis determined via proper orthogonal decomposition (POD) of the flow fields.

Advanced statistics: linear regression, part I: simple linear regression.

PubMed

Marill, Keith A

2004-01-01

Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

Regularized learning of linear ordered-statistic constant false alarm rate filters (Conference Presentation)

NASA Astrophysics Data System (ADS)

Havens, Timothy C.; Cummings, Ian; Botts, Jonathan; Summers, Jason E.

2017-05-01

The linear ordered statistic (LOS) is a parameterized ordered statistic (OS) that is a weighted average of a rank-ordered sample. LOS operators are useful generalizations of aggregation as they can represent any linear aggregation, from minimum to maximum, including conventional aggregations, such as mean and median. In the fuzzy logic field, these aggregations are called ordered weighted averages (OWAs). Here, we present a method for learning LOS operators from training data, viz., data for which you know the output of the desired LOS. We then extend the learning process with regularization, such that a lower complexity or sparse LOS can be learned. Hence, we discuss what 'lower complexity' means in this context and how to represent that in the optimization procedure. Finally, we apply our learning methods to the well-known constant-false-alarm-rate (CFAR) detection problem, specifically for the case of background levels modeled by long-tailed distributions, such as the K-distribution. These backgrounds arise in several pertinent imaging problems, including the modeling of clutter in synthetic aperture radar and sonar (SAR and SAS) and in wireless communications.

Nonparametric estimation and testing of fixed effects panel data models

PubMed Central

Henderson, Daniel J.; Carroll, Raymond J.; Li, Qi

2009-01-01

In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We introduce an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear fixed effects model. To determine whether a parametric, semiparametric or nonparametric model is appropriate, we propose test statistics to test between the three alternatives in practice. We further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model. Simulations are used to examine the finite sample performance of the proposed estimators and the test statistics. PMID:19444335

Tracking Electroencephalographic Changes Using Distributions of Linear Models: Application to Propofol-Based Depth of Anesthesia Monitoring.

PubMed

Kuhlmann, Levin; Manton, Jonathan H; Heyse, Bjorn; Vereecke, Hugo E M; Lipping, Tarmo; Struys, Michel M R F; Liley, David T J

2017-04-01

Tracking brain states with electrophysiological measurements often relies on short-term averages of extracted features and this may not adequately capture the variability of brain dynamics. The objective is to assess the hypotheses that this can be overcome by tracking distributions of linear models using anesthesia data, and that anesthetic brain state tracking performance of linear models is comparable to that of a high performing depth of anesthesia monitoring feature. Individuals' brain states are classified by comparing the distribution of linear (auto-regressive moving average-ARMA) model parameters estimated from electroencephalographic (EEG) data obtained with a sliding window to distributions of linear model parameters for each brain state. The method is applied to frontal EEG data from 15 subjects undergoing propofol anesthesia and classified by the observers assessment of alertness/sedation (OAA/S) scale. Classification of the OAA/S score was performed using distributions of either ARMA parameters or the benchmark feature, Higuchi fractal dimension. The highest average testing sensitivity of 59% (chance sensitivity: 17%) was found for ARMA (2,1) models and Higuchi fractal dimension achieved 52%, however, no statistical difference was observed. For the same ARMA case, there was no statistical difference if medians are used instead of distributions (sensitivity: 56%). The model-based distribution approach is not necessarily more effective than a median/short-term average approach, however, it performs well compared with a distribution approach based on a high performing anesthesia monitoring measure. These techniques hold potential for anesthesia monitoring and may be generally applicable for tracking brain states.

Tooth-size discrepancy: A comparison between manual and digital methods

PubMed Central

Correia, Gabriele Dória Cabral; Habib, Fernando Antonio Lima; Vogel, Carlos Jorge

2014-01-01

Introduction Technological advances in Dentistry have emerged primarily in the area of diagnostic tools. One example is the 3D scanner, which can transform plaster models into three-dimensional digital models. Objective This study aimed to assess the reliability of tooth size-arch length discrepancy analysis measurements performed on three-dimensional digital models, and compare these measurements with those obtained from plaster models. Material and Methods To this end, plaster models of lower dental arches and their corresponding three-dimensional digital models acquired with a 3Shape R700T scanner were used. All of them had lower permanent dentition. Four different tooth size-arch length discrepancy calculations were performed on each model, two of which by manual methods using calipers and brass wire, and two by digital methods using linear measurements and parabolas. Results Data were statistically assessed using Friedman test and no statistically significant differences were found between the two methods (P > 0.05), except for values found by the linear digital method which revealed a slight, non-significant statistical difference. Conclusions Based on the results, it is reasonable to assert that any of these resources used by orthodontists to clinically assess tooth size-arch length discrepancy can be considered reliable. PMID:25279529

Minimal agent based model for financial markets II. Statistical properties of the linear and multiplicative dynamics

NASA Astrophysics Data System (ADS)

Alfi, V.; Cristelli, M.; Pietronero, L.; Zaccaria, A.

2009-02-01

We present a detailed study of the statistical properties of the Agent Based Model introduced in paper I [Eur. Phys. J. B, DOI: 10.1140/epjb/e2009-00028-4] and of its generalization to the multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the stylized facts and their self-organization. The key elements are fundamentalist agents, chartist agents, herding dynamics and price behavior. The first two elements correspond to the competition between stability and instability tendencies in the market. The herding behavior governs the possibility of the agents to change strategy and it is a crucial element of this class of models. We consider a linear approximation for the price dynamics which permits a simple interpretation of the model dynamics and, for many properties, it is possible to derive analytical results. The generalized non linear dynamics results to be extremely more sensible to the parameter space and much more difficult to analyze and control. The main results for the nature and self-organization of the stylized facts are, however, very similar in the two cases. The main peculiarity of the non linear dynamics is an enhancement of the fluctuations and a more marked evidence of the stylized facts. We will also discuss some modifications of the model to introduce more realistic elements with respect to the real markets.

Group Influences on Young Adult Warfighters’ Risk Taking

DTIC Science & Technology

2016-12-01

Statistical Analysis Latent linear growth models were fitted using the maximum likelihood estimation method in Mplus (version 7.0; Muthen & Muthen...condition had a higher net score than those in the alone condition (b = 20.53, SE = 6.29, p < .001). Results of the relevant statistical analyses are...8.56 110.86*** 22.01 158.25*** 29.91 Model fit statistics BIC 4004.50 5302.539 5540.58 Chi-square (df) 41.51*** (16) 38.10** (20) 42.19** (20

On the Statistical Errors of RADAR Location Sensor Networks with Built-In Wi-Fi Gaussian Linear Fingerprints

PubMed Central

Zhou, Mu; Xu, Yu Bin; Ma, Lin; Tian, Shuo

2012-01-01

The expected errors of RADAR sensor networks with linear probabilistic location fingerprints inside buildings with varying Wi-Fi Gaussian strength are discussed. As far as we know, the statistical errors of equal and unequal-weighted RADAR networks have been suggested as a better way to evaluate the behavior of different system parameters and the deployment of reference points (RPs). However, up to now, there is still not enough related work on the relations between the statistical errors, system parameters, number and interval of the RPs, let alone calculating the correlated analytical expressions of concern. Therefore, in response to this compelling problem, under a simple linear distribution model, much attention will be paid to the mathematical relations of the linear expected errors, number of neighbors, number and interval of RPs, parameters in logarithmic attenuation model and variations of radio signal strength (RSS) at the test point (TP) with the purpose of constructing more practical and reliable RADAR location sensor networks (RLSNs) and also guaranteeing the accuracy requirements for the location based services in future ubiquitous context-awareness environments. Moreover, the numerical results and some real experimental evaluations of the error theories addressed in this paper will also be presented for our future extended analysis. PMID:22737027

On the statistical errors of RADAR location sensor networks with built-in Wi-Fi Gaussian linear fingerprints.

PubMed

Zhou, Mu; Xu, Yu Bin; Ma, Lin; Tian, Shuo

2012-01-01

The expected errors of RADAR sensor networks with linear probabilistic location fingerprints inside buildings with varying Wi-Fi Gaussian strength are discussed. As far as we know, the statistical errors of equal and unequal-weighted RADAR networks have been suggested as a better way to evaluate the behavior of different system parameters and the deployment of reference points (RPs). However, up to now, there is still not enough related work on the relations between the statistical errors, system parameters, number and interval of the RPs, let alone calculating the correlated analytical expressions of concern. Therefore, in response to this compelling problem, under a simple linear distribution model, much attention will be paid to the mathematical relations of the linear expected errors, number of neighbors, number and interval of RPs, parameters in logarithmic attenuation model and variations of radio signal strength (RSS) at the test point (TP) with the purpose of constructing more practical and reliable RADAR location sensor networks (RLSNs) and also guaranteeing the accuracy requirements for the location based services in future ubiquitous context-awareness environments. Moreover, the numerical results and some real experimental evaluations of the error theories addressed in this paper will also be presented for our future extended analysis.

Random-effects linear modeling and sample size tables for two special crossover designs of average bioequivalence studies: the four-period, two-sequence, two-formulation and six-period, three-sequence, three-formulation designs.

PubMed

Diaz, Francisco J; Berg, Michel J; Krebill, Ron; Welty, Timothy; Gidal, Barry E; Alloway, Rita; Privitera, Michael

2013-12-01

Due to concern and debate in the epilepsy medical community and to the current interest of the US Food and Drug Administration (FDA) in revising approaches to the approval of generic drugs, the FDA is currently supporting ongoing bioequivalence studies of antiepileptic drugs, the EQUIGEN studies. During the design of these crossover studies, the researchers could not find commercial or non-commercial statistical software that quickly allowed computation of sample sizes for their designs, particularly software implementing the FDA requirement of using random-effects linear models for the analyses of bioequivalence studies. This article presents tables for sample-size evaluations of average bioequivalence studies based on the two crossover designs used in the EQUIGEN studies: the four-period, two-sequence, two-formulation design, and the six-period, three-sequence, three-formulation design. Sample-size computations assume that random-effects linear models are used in bioequivalence analyses with crossover designs. Random-effects linear models have been traditionally viewed by many pharmacologists and clinical researchers as just mathematical devices to analyze repeated-measures data. In contrast, a modern view of these models attributes an important mathematical role in theoretical formulations in personalized medicine to them, because these models not only have parameters that represent average patients, but also have parameters that represent individual patients. Moreover, the notation and language of random-effects linear models have evolved over the years. Thus, another goal of this article is to provide a presentation of the statistical modeling of data from bioequivalence studies that highlights the modern view of these models, with special emphasis on power analyses and sample-size computations.

Critical Fluctuations in Cortical Models Near Instability

PubMed Central

Aburn, Matthew J.; Holmes, C. A.; Roberts, James A.; Boonstra, Tjeerd W.; Breakspear, Michael

2012-01-01

Computational studies often proceed from the premise that cortical dynamics operate in a linearly stable domain, where fluctuations dissipate quickly and show only short memory. Studies of human electroencephalography (EEG), however, have shown significant autocorrelation at time lags on the scale of minutes, indicating the need to consider regimes where non-linearities influence the dynamics. Statistical properties such as increased autocorrelation length, increased variance, power law scaling, and bistable switching have been suggested as generic indicators of the approach to bifurcation in non-linear dynamical systems. We study temporal fluctuations in a widely-employed computational model (the Jansen–Rit model) of cortical activity, examining the statistical signatures that accompany bifurcations. Approaching supercritical Hopf bifurcations through tuning of the background excitatory input, we find a dramatic increase in the autocorrelation length that depends sensitively on the direction in phase space of the input fluctuations and hence on which neuronal subpopulation is stochastically perturbed. Similar dependence on the input direction is found in the distribution of fluctuation size and duration, which show power law scaling that extends over four orders of magnitude at the Hopf bifurcation. We conjecture that the alignment in phase space between the input noise vector and the center manifold of the Hopf bifurcation is directly linked to these changes. These results are consistent with the possibility of statistical indicators of linear instability being detectable in real EEG time series. However, even in a simple cortical model, we find that these indicators may not necessarily be visible even when bifurcations are present because their expression can depend sensitively on the neuronal pathway of incoming fluctuations. PMID:22952464

The consentaneous model of the financial markets exhibiting spurious nature of long-range memory

NASA Astrophysics Data System (ADS)

Gontis, V.; Kononovicius, A.

2018-09-01

It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based on the non-linear stochastic differential equations. The consentaneous model successfully reproduces empirical probability and power spectral densities of volatility. This approach is qualitatively different from models built using fractional Brownian motion. In this contribution we investigate burst and inter-burst duration statistics of volatility in the financial markets employing the consentaneous model. Our analysis provides an evidence that empirical statistical properties of burst and inter-burst duration can be explained by non-linear stochastic differential equations driving the volatility in the financial markets. This serves as an strong argument that long-range memory in finance can have spurious nature.

Low-complexity stochastic modeling of wall-bounded shear flows

NASA Astrophysics Data System (ADS)

Zare, Armin

Turbulent flows are ubiquitous in nature and they appear in many engineering applications. Transition to turbulence, in general, increases skin-friction drag in air/water vehicles compromising their fuel-efficiency and reduces the efficiency and longevity of wind turbines. While traditional flow control techniques combine physical intuition with costly experiments, their effectiveness can be significantly enhanced by control design based on low-complexity models and optimization. In this dissertation, we develop a theoretical and computational framework for the low-complexity stochastic modeling of wall-bounded shear flows. Part I of the dissertation is devoted to the development of a modeling framework which incorporates data-driven techniques to refine physics-based models. We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate optimization problems to identify the dynamics and directionality of input excitation in order to explain and complete available covariance data. For problem sizes that general-purpose solvers cannot handle, we develop customized optimization algorithms based on alternating direction methods. The solution to the optimization problem provides information about critical directions that have maximal effect in bringing model and statistics in agreement. In Part II, we employ our modeling framework to account for statistical signatures of turbulent channel flow using low-complexity stochastic dynamical models. We demonstrate that white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics and develop models for colored-in-time forcing of the linearized Navier-Stokes equations. We also examine the efficacy of stochastically forced linearized NS equations and their parabolized equivalents in the receptivity analysis of velocity fluctuations to external sources of excitation as well as capturing the effect of the slowly-varying base flow on streamwise streaks and Tollmien-Schlichting waves. In Part III, we develop a model-based approach to design surface actuation of turbulent channel flow in the form of streamwise traveling waves. This approach is capable of identifying the drag reducing trends of traveling waves in a simulation-free manner. We also use the stochastically forced linearized NS equations to examine the Reynolds number independent effects of spanwise wall oscillations on drag reduction in turbulent channel flows. This allows us to extend the predictive capability of our simulation-free approach to high Reynolds numbers.

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

PubMed Central

Guan, Yongtao; Li, Yehua; Sinha, Rajita

2011-01-01

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

Multi-Parameter Linear Least-Squares Fitting to Poisson Data One Count at a Time

NASA Technical Reports Server (NTRS)

Wheaton, W.; Dunklee, A.; Jacobson, A.; Ling, J.; Mahoney, W.; Radocinski, R.

1993-01-01

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multi-component linear model, with underlying physical count rates or fluxes which are to be estimated from the data.

A Generalization of Pythagoras's Theorem and Application to Explanations of Variance Contributions in Linear Models. Research Report. ETS RR-14-18

ERIC Educational Resources Information Center

Carlson, James E.

2014-01-01

Many aspects of the geometry of linear statistical models and least squares estimation are well known. Discussions of the geometry may be found in many sources. Some aspects of the geometry relating to the partitioning of variation that can be explained using a little-known theorem of Pappus and have not been discussed previously are the topic of…

Regression assumptions in clinical psychology research practice-a systematic review of common misconceptions.

PubMed

Ernst, Anja F; Albers, Casper J

2017-01-01

Misconceptions about the assumptions behind the standard linear regression model are widespread and dangerous. These lead to using linear regression when inappropriate, and to employing alternative procedures with less statistical power when unnecessary. Our systematic literature review investigated employment and reporting of assumption checks in twelve clinical psychology journals. Findings indicate that normality of the variables themselves, rather than of the errors, was wrongfully held for a necessary assumption in 4% of papers that use regression. Furthermore, 92% of all papers using linear regression were unclear about their assumption checks, violating APA-recommendations. This paper appeals for a heightened awareness for and increased transparency in the reporting of statistical assumption checking.

Regression assumptions in clinical psychology research practice—a systematic review of common misconceptions

PubMed Central

Ernst, Anja F.

2017-01-01

Misconceptions about the assumptions behind the standard linear regression model are widespread and dangerous. These lead to using linear regression when inappropriate, and to employing alternative procedures with less statistical power when unnecessary. Our systematic literature review investigated employment and reporting of assumption checks in twelve clinical psychology journals. Findings indicate that normality of the variables themselves, rather than of the errors, was wrongfully held for a necessary assumption in 4% of papers that use regression. Furthermore, 92% of all papers using linear regression were unclear about their assumption checks, violating APA-recommendations. This paper appeals for a heightened awareness for and increased transparency in the reporting of statistical assumption checking. PMID:28533971

Statistical Package User’s Guide.

DTIC Science & Technology

1980-08-01

261 C. STACH Nonparametric Descriptive Statistics ... ......... ... 265 D. CHIRA Coefficient of Concordance...135 I.- -a - - W 7- Test Data: This program was tested using data from John Neter and William Wasserman, Applied Linear Statistical Models: Regression...length of data file e. new fileý name (not same as raw data file) 5. Printout as optioned for only. Comments: Ranked data are used for program CHIRA

A General Accelerated Degradation Model Based on the Wiener Process.

PubMed

Liu, Le; Li, Xiaoyang; Sun, Fuqiang; Wang, Ning

2016-12-06

Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses.

A General Accelerated Degradation Model Based on the Wiener Process

PubMed Central

Liu, Le; Li, Xiaoyang; Sun, Fuqiang; Wang, Ning

2016-01-01

Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses. PMID:28774107

Patterns of medicinal plant use: an examination of the Ecuadorian Shuar medicinal flora using contingency table and binomial analyses.

PubMed

Bennett, Bradley C; Husby, Chad E

2008-03-28

Botanical pharmacopoeias are non-random subsets of floras, with some taxonomic groups over- or under-represented. Moerman [Moerman, D.E., 1979. Symbols and selectivity: a statistical analysis of Native American medical ethnobotany, Journal of Ethnopharmacology 1, 111-119] introduced linear regression/residual analysis to examine these patterns. However, regression, the commonly-employed analysis, suffers from several statistical flaws. We use contingency table and binomial analyses to examine patterns of Shuar medicinal plant use (from Amazonian Ecuador). We first analyzed the Shuar data using Moerman's approach, modified to better meet requirements of linear regression analysis. Second, we assessed the exact randomization contingency table test for goodness of fit. Third, we developed a binomial model to test for non-random selection of plants in individual families. Modified regression models (which accommodated assumptions of linear regression) reduced R(2) to from 0.59 to 0.38, but did not eliminate all problems associated with regression analyses. Contingency table analyses revealed that the entire flora departs from the null model of equal proportions of medicinal plants in all families. In the binomial analysis, only 10 angiosperm families (of 115) differed significantly from the null model. These 10 families are largely responsible for patterns seen at higher taxonomic levels. Contingency table and binomial analyses offer an easy and statistically valid alternative to the regression approach.

Statistical modelling of networked human-automation performance using working memory capacity.

PubMed

Ahmed, Nisar; de Visser, Ewart; Shaw, Tyler; Mohamed-Ameen, Amira; Campbell, Mark; Parasuraman, Raja

2014-01-01

This study examines the challenging problem of modelling the interaction between individual attentional limitations and decision-making performance in networked human-automation system tasks. Analysis of real experimental data from a task involving networked supervision of multiple unmanned aerial vehicles by human participants shows that both task load and network message quality affect performance, but that these effects are modulated by individual differences in working memory (WM) capacity. These insights were used to assess three statistical approaches for modelling and making predictions with real experimental networked supervisory performance data: classical linear regression, non-parametric Gaussian processes and probabilistic Bayesian networks. It is shown that each of these approaches can help designers of networked human-automated systems cope with various uncertainties in order to accommodate future users by linking expected operating conditions and performance from real experimental data to observable cognitive traits like WM capacity. Practitioner Summary: Working memory (WM) capacity helps account for inter-individual variability in operator performance in networked unmanned aerial vehicle supervisory tasks. This is useful for reliable performance prediction near experimental conditions via linear models; robust statistical prediction beyond experimental conditions via Gaussian process models and probabilistic inference about unknown task conditions/WM capacities via Bayesian network models.

Does competition improve financial stability of the banking sector in ASEAN countries? An empirical analysis.

PubMed

Noman, Abu Hanifa Md; Gee, Chan Sok; Isa, Che Ruhana

2017-01-01

This study examines the influence of competition on the financial stability of the commercial banks of Association of Southeast Asian Nation (ASEAN) over the 1990 to 2014 period. Panzar-Rosse H-statistic, Lerner index and Herfindahl-Hirschman Index (HHI) are used as measures of competition, while Z-score, non-performing loan (NPL) ratio and equity ratio are used as measures of financial stability. Two-step system Generalized Method of Moments (GMM) estimates demonstrate that competition measured by H-statistic is positively related to Z-score and equity ratio, and negatively related to non-performing loan ratio. Conversely, market power measured by Lerner index is negatively related to Z-score and equity ratio and positively related to NPL ratio. These results strongly support the competition-stability view for ASEAN banks. We also capture the non-linear relationship between competition and financial stability by incorporating a quadratic term of competition in our models. The results show that the coefficient of the quadratic term of H-statistic is negative for the Z-score model given a positive coefficient of the linear term in the same model. These results support the non-linear relationship between competition and financial stability of the banking sector. The study contains significant policy implications for improving the financial stability of the commercial banks.

Does competition improve financial stability of the banking sector in ASEAN countries? An empirical analysis

PubMed Central

Gee, Chan Sok; Isa, Che Ruhana

2017-01-01

This study examines the influence of competition on the financial stability of the commercial banks of Association of Southeast Asian Nation (ASEAN) over the 1990 to 2014 period. Panzar-Rosse H-statistic, Lerner index and Herfindahl-Hirschman Index (HHI) are used as measures of competition, while Z-score, non-performing loan (NPL) ratio and equity ratio are used as measures of financial stability. Two-step system Generalized Method of Moments (GMM) estimates demonstrate that competition measured by H-statistic is positively related to Z-score and equity ratio, and negatively related to non-performing loan ratio. Conversely, market power measured by Lerner index is negatively related to Z-score and equity ratio and positively related to NPL ratio. These results strongly support the competition-stability view for ASEAN banks. We also capture the non-linear relationship between competition and financial stability by incorporating a quadratic term of competition in our models. The results show that the coefficient of the quadratic term of H-statistic is negative for the Z-score model given a positive coefficient of the linear term in the same model. These results support the non-linear relationship between competition and financial stability of the banking sector. The study contains significant policy implications for improving the financial stability of the commercial banks. PMID:28486548

Primal/dual linear programming and statistical atlases for cartilage segmentation.

PubMed

Glocker, Ben; Komodakis, Nikos; Paragios, Nikos; Glaser, Christian; Tziritas, Georgios; Navab, Nassir

2007-01-01

In this paper we propose a novel approach for automatic segmentation of cartilage using a statistical atlas and efficient primal/dual linear programming. To this end, a novel statistical atlas construction is considered from registered training examples. Segmentation is then solved through registration which aims at deforming the atlas such that the conditional posterior of the learned (atlas) density is maximized with respect to the image. Such a task is reformulated using a discrete set of deformations and segmentation becomes equivalent to finding the set of local deformations which optimally match the model to the image. We evaluate our method on 56 MRI data sets (28 used for the model and 28 used for evaluation) and obtain a fully automatic segmentation of patella cartilage volume with an overlap ratio of 0.84 with a sensitivity and specificity of 94.06% and 99.92%, respectively.

Teaching "Instant Experience" with Graphical Model Validation Techniques

ERIC Educational Resources Information Center

Ekstrøm, Claus Thorn

2014-01-01

Graphical model validation techniques for linear normal models are often used to check the assumptions underlying a statistical model. We describe an approach to provide "instant experience" in looking at a graphical model validation plot, so it becomes easier to validate if any of the underlying assumptions are violated.

Role of Statistical Random-Effects Linear Models in Personalized Medicine.

PubMed

Diaz, Francisco J; Yeh, Hung-Wen; de Leon, Jose

2012-03-01

Some empirical studies and recent developments in pharmacokinetic theory suggest that statistical random-effects linear models are valuable tools that allow describing simultaneously patient populations as a whole and patients as individuals. This remarkable characteristic indicates that these models may be useful in the development of personalized medicine, which aims at finding treatment regimes that are appropriate for particular patients, not just appropriate for the average patient. In fact, published developments show that random-effects linear models may provide a solid theoretical framework for drug dosage individualization in chronic diseases. In particular, individualized dosages computed with these models by means of an empirical Bayesian approach may produce better results than dosages computed with some methods routinely used in therapeutic drug monitoring. This is further supported by published empirical and theoretical findings that show that random effects linear models may provide accurate representations of phase III and IV steady-state pharmacokinetic data, and may be useful for dosage computations. These models have applications in the design of clinical algorithms for drug dosage individualization in chronic diseases; in the computation of dose correction factors; computation of the minimum number of blood samples from a patient that are necessary for calculating an optimal individualized drug dosage in therapeutic drug monitoring; measure of the clinical importance of clinical, demographic, environmental or genetic covariates; study of drug-drug interactions in clinical settings; the implementation of computational tools for web-site-based evidence farming; design of pharmacogenomic studies; and in the development of a pharmacological theory of dosage individualization.

On the Convenience of Using the Complete Linearization Method in Modelling the BLR of AGN

NASA Astrophysics Data System (ADS)

Patriarchi, P.; Perinotto, M.

The Complete Linearization Method (Mihalas, 1978) consists in the determination of the radiation field (at a set of frequency points), atomic level populations, temperature, electron density etc., by resolving the system of radiative transfer, thermal equilibrium, statistical equilibrium equations simultaneously and self-consistently. Since the system is not linear, it must be solved by iteration after linearization, using a perturbative method, starting from an initial guess solution. Of course the Complete Linearization Method is more time consuming than the previous one. But how great can this disadvantage be in the age of supercomputers? It is possible to approximately evaluate the CPU time needed to run a model by computing the number of multiplications necessary to solve the system.

Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems

NASA Technical Reports Server (NTRS)

He, Yuning; Davies, Misty Dawn

2014-01-01

The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries.

DEVELOPMENT OF THE VIRTUAL BEACH MODEL, PHASE 1: AN EMPIRICAL MODEL

EPA Science Inventory

With increasing attention focused on the use of multiple linear regression (MLR) modeling of beach fecal bacteria concentration, the validity of the entire statistical process should be carefully evaluated to assure satisfactory predictions. This work aims to identify pitfalls an...

Application of Multiregressive Linear Models, Dynamic Kriging Models and Neural Network Models to Predictive Maintenance of Hydroelectric Power Systems

NASA Astrophysics Data System (ADS)

Lucifredi, A.; Mazzieri, C.; Rossi, M.

2000-05-01

Since the operational conditions of a hydroelectric unit can vary within a wide range, the monitoring system must be able to distinguish between the variations of the monitored variable caused by variations of the operation conditions and those due to arising and progressing of failures and misoperations. The paper aims to identify the best technique to be adopted for the monitoring system. Three different methods have been implemented and compared. Two of them use statistical techniques: the first, the linear multiple regression, expresses the monitored variable as a linear function of the process parameters (independent variables), while the second, the dynamic kriging technique, is a modified technique of multiple linear regression representing the monitored variable as a linear combination of the process variables in such a way as to minimize the variance of the estimate error. The third is based on neural networks. Tests have shown that the monitoring system based on the kriging technique is not affected by some problems common to the other two models e.g. the requirement of a large amount of data for their tuning, both for training the neural network and defining the optimum plane for the multiple regression, not only in the system starting phase but also after a trivial operation of maintenance involving the substitution of machinery components having a direct impact on the observed variable. Or, in addition, the necessity of different models to describe in a satisfactory way the different ranges of operation of the plant. The monitoring system based on the kriging statistical technique overrides the previous difficulties: it does not require a large amount of data to be tuned and is immediately operational: given two points, the third can be immediately estimated; in addition the model follows the system without adapting itself to it. The results of the experimentation performed seem to indicate that a model based on a neural network or on a linear multiple regression is not optimal, and that a different approach is necessary to reduce the amount of work during the learning phase using, when available, all the information stored during the initial phase of the plant to build the reference baseline, elaborating, if it is the case, the raw information available. A mixed approach using the kriging statistical technique and neural network techniques could optimise the result.

Summary goodness-of-fit statistics for binary generalized linear models with noncanonical link functions.

PubMed

Canary, Jana D; Blizzard, Leigh; Barry, Ronald P; Hosmer, David W; Quinn, Stephen J

2016-05-01

Generalized linear models (GLM) with a canonical logit link function are the primary modeling technique used to relate a binary outcome to predictor variables. However, noncanonical links can offer more flexibility, producing convenient analytical quantities (e.g., probit GLMs in toxicology) and desired measures of effect (e.g., relative risk from log GLMs). Many summary goodness-of-fit (GOF) statistics exist for logistic GLM. Their properties make the development of GOF statistics relatively straightforward, but it can be more difficult under noncanonical links. Although GOF tests for logistic GLM with continuous covariates (GLMCC) have been applied to GLMCCs with log links, we know of no GOF tests in the literature specifically developed for GLMCCs that can be applied regardless of link function chosen. We generalize the Tsiatis GOF statistic originally developed for logistic GLMCCs, (TG), so that it can be applied under any link function. Further, we show that the algebraically related Hosmer-Lemeshow (HL) and Pigeon-Heyse (J(2) ) statistics can be applied directly. In a simulation study, TG, HL, and J(2) were used to evaluate the fit of probit, log-log, complementary log-log, and log models, all calculated with a common grouping method. The TG statistic consistently maintained Type I error rates, while those of HL and J(2) were often lower than expected if terms with little influence were included. Generally, the statistics had similar power to detect an incorrect model. An exception occurred when a log GLMCC was incorrectly fit to data generated from a logistic GLMCC. In this case, TG had more power than HL or J(2) . © 2015 John Wiley & Sons Ltd/London School of Economics.

Application of linear regression analysis in accuracy assessment of rolling force calculations

NASA Astrophysics Data System (ADS)

Poliak, E. I.; Shim, M. K.; Kim, G. S.; Choo, W. Y.

1998-10-01

Efficient operation of the computational models employed in process control systems require periodical assessment of the accuracy of their predictions. Linear regression is proposed as a tool which allows separate systematic and random prediction errors from those related to measurements. A quantitative characteristic of the model predictive ability is introduced in addition to standard statistical tests for model adequacy. Rolling force calculations are considered as an example for the application. However, the outlined approach can be used to assess the performance of any computational model.

Longitudinal data analyses using linear mixed models in SPSS: concepts, procedures and illustrations.

PubMed

Shek, Daniel T L; Ma, Cecilia M S

2011-01-05

Although different methods are available for the analyses of longitudinal data, analyses based on generalized linear models (GLM) are criticized as violating the assumption of independence of observations. Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear models) are outlined. Although SPSS is a statistical analyses package commonly used by researchers, documentation on LMM procedures in SPSS is not thorough or user friendly. With reference to this limitation, the related procedures for performing analyses based on LMM in SPSS are described. To demonstrate the application of LMM analyses in SPSS, findings based on six waves of data collected in the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in Hong Kong are presented.

Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations

PubMed Central

Shek, Daniel T. L.; Ma, Cecilia M. S.

2011-01-01

Although different methods are available for the analyses of longitudinal data, analyses based on generalized linear models (GLM) are criticized as violating the assumption of independence of observations. Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear models) are outlined. Although SPSS is a statistical analyses package commonly used by researchers, documentation on LMM procedures in SPSS is not thorough or user friendly. With reference to this limitation, the related procedures for performing analyses based on LMM in SPSS are described. To demonstrate the application of LMM analyses in SPSS, findings based on six waves of data collected in the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in Hong Kong are presented. PMID:21218263

Using Artificial Neural Networks in Educational Research: Some Comparisons with Linear Statistical Models.

ERIC Educational Resources Information Center

Everson, Howard T.; And Others

This paper explores the feasibility of neural computing methods such as artificial neural networks (ANNs) and abductory induction mechanisms (AIM) for use in educational measurement. ANNs and AIMS methods are contrasted with more traditional statistical techniques, such as multiple regression and discriminant function analyses, for making…

Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool.

PubMed

Aqil, Muhammad; Kita, Ichiro; Yano, Akira; Nishiyama, Soichi

2007-10-01

Traditionally, the multiple linear regression technique has been one of the most widely used models in simulating hydrological time series. However, when the nonlinear phenomenon is significant, the multiple linear will fail to develop an appropriate predictive model. Recently, neuro-fuzzy systems have gained much popularity for calibrating the nonlinear relationships. This study evaluated the potential of a neuro-fuzzy system as an alternative to the traditional statistical regression technique for the purpose of predicting flow from a local source in a river basin. The effectiveness of the proposed identification technique was demonstrated through a simulation study of the river flow time series of the Citarum River in Indonesia. Furthermore, in order to provide the uncertainty associated with the estimation of river flow, a Monte Carlo simulation was performed. As a comparison, a multiple linear regression analysis that was being used by the Citarum River Authority was also examined using various statistical indices. The simulation results using 95% confidence intervals indicated that the neuro-fuzzy model consistently underestimated the magnitude of high flow while the low and medium flow magnitudes were estimated closer to the observed data. The comparison of the prediction accuracy of the neuro-fuzzy and linear regression methods indicated that the neuro-fuzzy approach was more accurate in predicting river flow dynamics. The neuro-fuzzy model was able to improve the root mean square error (RMSE) and mean absolute percentage error (MAPE) values of the multiple linear regression forecasts by about 13.52% and 10.73%, respectively. Considering its simplicity and efficiency, the neuro-fuzzy model is recommended as an alternative tool for modeling of flow dynamics in the study area.

Are V1 Simple Cells Optimized for Visual Occlusions? A Comparative Study

PubMed Central

Bornschein, Jörg; Henniges, Marc; Lücke, Jörg

2013-01-01

Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges. Sparse coding and independent component analysis (ICA) emerged as the standard computational models for simple cell coding because they linked their receptive fields to the statistics of visual stimuli. However, a salient feature of image statistics, occlusions of image components, is not considered by these models. Here we ask if occlusions have an effect on the predicted shapes of simple cell receptive fields. We use a comparative approach to answer this question and investigate two models for simple cells: a standard linear model and an occlusive model. For both models we simultaneously estimate optimal receptive fields, sparsity and stimulus noise. The two models are identical except for their component superposition assumption. We find the image encoding and receptive fields predicted by the models to differ significantly. While both models predict many Gabor-like fields, the occlusive model predicts a much sparser encoding and high percentages of ‘globular’ receptive fields. This relatively new center-surround type of simple cell response is observed since reverse correlation is used in experimental studies. While high percentages of ‘globular’ fields can be obtained using specific choices of sparsity and overcompleteness in linear sparse coding, no or only low proportions are reported in the vast majority of studies on linear models (including all ICA models). Likewise, for the here investigated linear model and optimal sparsity, only low proportions of ‘globular’ fields are observed. In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of ‘globular’ fields well. Our computational study, therefore, suggests that ‘globular’ fields may be evidence for an optimal encoding of visual occlusions in primary visual cortex. PMID:23754938

A new statistical approach to climate change detection and attribution

NASA Astrophysics Data System (ADS)

Ribes, Aurélien; Zwiers, Francis W.; Azaïs, Jean-Marc; Naveau, Philippe

2017-01-01

We propose here a new statistical approach to climate change detection and attribution that is based on additive decomposition and simple hypothesis testing. Most current statistical methods for detection and attribution rely on linear regression models where the observations are regressed onto expected response patterns to different external forcings. These methods do not use physical information provided by climate models regarding the expected response magnitudes to constrain the estimated responses to the forcings. Climate modelling uncertainty is difficult to take into account with regression based methods and is almost never treated explicitly. As an alternative to this approach, our statistical model is only based on the additivity assumption; the proposed method does not regress observations onto expected response patterns. We introduce estimation and testing procedures based on likelihood maximization, and show that climate modelling uncertainty can easily be accounted for. Some discussion is provided on how to practically estimate the climate modelling uncertainty based on an ensemble of opportunity. Our approach is based on the " models are statistically indistinguishable from the truth" paradigm, where the difference between any given model and the truth has the same distribution as the difference between any pair of models, but other choices might also be considered. The properties of this approach are illustrated and discussed based on synthetic data. Lastly, the method is applied to the linear trend in global mean temperature over the period 1951-2010. Consistent with the last IPCC assessment report, we find that most of the observed warming over this period (+0.65 K) is attributable to anthropogenic forcings (+0.67 ± 0.12 K, 90 % confidence range), with a very limited contribution from natural forcings (-0.01± 0.02 K).

Robust Combining of Disparate Classifiers Through Order Statistics

NASA Technical Reports Server (NTRS)

Tumer, Kagan; Ghosh, Joydeep

2001-01-01

Integrating the outputs of multiple classifiers via combiners or meta-learners has led to substantial improvements in several difficult pattern recognition problems. In this article we investigate a family of combiners based on order statistics, for robust handling of situations where there are large discrepancies in performance of individual classifiers. Based on a mathematical modeling of how the decision boundaries are affected by order statistic combiners, we derive expressions for the reductions in error expected when simple output combination methods based on the the median, the maximum and in general, the ith order statistic, are used. Furthermore, we analyze the trim and spread combiners, both based on linear combinations of the ordered classifier outputs, and show that in the presence of uneven classifier performance, they often provide substantial gains over both linear and simple order statistics combiners. Experimental results on both real world data and standard public domain data sets corroborate these findings.

Community air pollution and mortality: Analysis of 1980 data from US metropolitan areas. 1: Particulate air pollution

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

Lipfert, F.W.

1992-11-01

1980 data from up to 149 metropolitan areas were used to define cross-sectional associations between community air pollution and excess human mortality. The regression model proposed by Oezkaynak and Thurston, which accounted for age, race, education, poverty, and population density, was evaluated and several new models were developed. The new models also accounted for population change, drinking water hardness, and smoking, and included a more detailed description of race. Cause-of-death categories analyzed include all causes, all non-external causes, major cardiovascular diseases, and chronic obstructive pulmonary diseases (COPD). Both annual mortality rates and their logarithms were analyzed. The data on particulatesmore » were averaged across all monitoring stations available for each SMSA and the TSP data were restricted to the year 1980. The associations between mortality and air pollution were found to be dependent on the socioeconomic factors included in the models, the specific locations included din the data set, and the type of statistical model used. Statistically significant associations were found between TSP and mortality due to non-external causes with log-linear models, but not with a linear model, and between TS and COPD mortality for both linear and log-linear models. When the sulfate contribution to TSP was subtracted, the relationship with COPD mortality was strengthened. Scatter plots and quintile analyses suggested a TSP threshold for COPD mortality at around 65 ug/m{sup 3} (annual average). SO{sub 4}{sup {minus}2}, Mn, PM{sup 15}, and PM{sub 2.5} were not significantly associated with mortality using the new models.« less

A d-statistic for single-case designs that is equivalent to the usual between-groups d-statistic.

PubMed

Shadish, William R; Hedges, Larry V; Pustejovsky, James E; Boyajian, Jonathan G; Sullivan, Kristynn J; Andrade, Alma; Barrientos, Jeannette L

2014-01-01

We describe a standardised mean difference statistic (d) for single-case designs that is equivalent to the usual d in between-groups experiments. We show how it can be used to summarise treatment effects over cases within a study, to do power analyses in planning new studies and grant proposals, and to meta-analyse effects across studies of the same question. We discuss limitations of this d-statistic, and possible remedies to them. Even so, this d-statistic is better founded statistically than other effect size measures for single-case design, and unlike many general linear model approaches such as multilevel modelling or generalised additive models, it produces a standardised effect size that can be integrated over studies with different outcome measures. SPSS macros for both effect size computation and power analysis are available.

Model Checking Techniques for Assessing Functional Form Specifications in Censored Linear Regression Models.

PubMed

León, Larry F; Cai, Tianxi

2012-04-01

In this paper we develop model checking techniques for assessing functional form specifications of covariates in censored linear regression models. These procedures are based on a censored data analog to taking cumulative sums of "robust" residuals over the space of the covariate under investigation. These cumulative sums are formed by integrating certain Kaplan-Meier estimators and may be viewed as "robust" censored data analogs to the processes considered by Lin, Wei & Ying (2002). The null distributions of these stochastic processes can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be generated by computer simulation. Each observed process can then be graphically compared with a few realizations from the Gaussian process. We also develop formal test statistics for numerical comparison. Such comparisons enable one to assess objectively whether an apparent trend seen in a residual plot reects model misspecification or natural variation. We illustrate the methods with a well known dataset. In addition, we examine the finite sample performance of the proposed test statistics in simulation experiments. In our simulation experiments, the proposed test statistics have good power of detecting misspecification while at the same time controlling the size of the test.

Statistical downscaling of precipitation using long short-term memory recurrent neural networks

NASA Astrophysics Data System (ADS)

Misra, Saptarshi; Sarkar, Sudeshna; Mitra, Pabitra

2017-11-01

Hydrological impacts of global climate change on regional scale are generally assessed by downscaling large-scale climatic variables, simulated by General Circulation Models (GCMs), to regional, small-scale hydrometeorological variables like precipitation, temperature, etc. In this study, we propose a new statistical downscaling model based on Recurrent Neural Network with Long Short-Term Memory which captures the spatio-temporal dependencies in local rainfall. The previous studies have used several other methods such as linear regression, quantile regression, kernel regression, beta regression, and artificial neural networks. Deep neural networks and recurrent neural networks have been shown to be highly promising in modeling complex and highly non-linear relationships between input and output variables in different domains and hence we investigated their performance in the task of statistical downscaling. We have tested this model on two datasets—one on precipitation in Mahanadi basin in India and the second on precipitation in Campbell River basin in Canada. Our autoencoder coupled long short-term memory recurrent neural network model performs the best compared to other existing methods on both the datasets with respect to temporal cross-correlation, mean squared error, and capturing the extremes.

Evaluating Differential Effects Using Regression Interactions and Regression Mixture Models

ERIC Educational Resources Information Center

Van Horn, M. Lee; Jaki, Thomas; Masyn, Katherine; Howe, George; Feaster, Daniel J.; Lamont, Andrea E.; George, Melissa R. W.; Kim, Minjung

2015-01-01

Research increasingly emphasizes understanding differential effects. This article focuses on understanding regression mixture models, which are relatively new statistical methods for assessing differential effects by comparing results to using an interactive term in linear regression. The research questions which each model answers, their…

Locating suppression resources by travel times to wildfires

Treesearch

Romain M. Mees

1986-01-01

Two mathematical models are given to determine the best locations for initial attack resources in terms of travel time: a linear programmingmodel and a statistical model. An example for the Clearwater National Forest in Idaho illustrates some of the differences between the two models.

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

Modeling the microstructurally dependent mechanical properties of poly(ester-urethane-urea)s.

PubMed

Warren, P Daniel; Sycks, Dalton G; McGrath, Dominic V; Vande Geest, Jonathan P

2013-12-01

Poly(ester-urethane-urea) (PEUU) is one of many synthetic biodegradable elastomers under scrutiny for biomedical and soft tissue applications. The goal of this study was to investigate the effect of the experimental parameters on mechanical properties of PEUUs following exposure to different degrading environments, similar to that of the human body, using linear regression, producing one predictive model. The model utilizes two independent variables of poly(caprolactone) (PCL) type and copolymer crystallinity to predict the dependent variable of maximum tangential modulus (MTM). Results indicate that comparisons between PCLs at different degradation states are statistically different (p < 0.0003), while the difference between experimental and predicted average MTM is statistically negligible (p < 0.02). The linear correlation between experimental and predicted MTM values is R(2) = 0.75. Copyright © 2013 Wiley Periodicals, Inc., a Wiley Company.

The Fermi-Pasta-Ulam Problem and Its Underlying Integrable Dynamics: An Approach Through Lyapunov Exponents

NASA Astrophysics Data System (ADS)

Benettin, G.; Pasquali, S.; Ponno, A.

2018-05-01

FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual β -model, perturbations of Toda include the usual α +β model. In this paper we explore and compare two families, or hierarchies, of FPU models, closer and closer to either the linear or the Toda model, by computing numerically, for each model, the maximal Lyapunov exponent χ . More precisely, we consider statistically typical trajectories and study the asymptotics of χ for large N (the number of particles) and small ɛ (the specific energy E / N), and find, for all models, asymptotic power laws χ ˜eq Cɛ ^a, C and a depending on the model. The asymptotics turns out to be, in general, rather slow, and producing accurate results requires a great computational effort. We also revisit and extend the analytic computation of χ introduced by Casetti, Livi and Pettini, originally formulated for the β -model. With great evidence the theory extends successfully to all models of the linear hierarchy, but not to models close to Toda.

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

NASA Technical Reports Server (NTRS)

Melott, A. L.; Buchert, T.; Weib, A. G.

1995-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action

NASA Astrophysics Data System (ADS)

Barra, Adriano; Contucci, Pierluigi; Sandell, Rickard; Vernia, Cecilia

2014-02-01

How does immigrant integration in a country change with immigration density? Guided by a statistical mechanics perspective we propose a novel approach to this problem. The analysis focuses on classical integration quantifiers such as the percentage of jobs (temporary and permanent) given to immigrants, mixed marriages, and newborns with parents of mixed origin. We find that the average values of different quantifiers may exhibit either linear or non-linear growth on immigrant density and we suggest that social action, a concept identified by Max Weber, causes the observed non-linearity. Using the statistical mechanics notion of interaction to quantitatively emulate social action, a unified mathematical model for integration is proposed and it is shown to explain both growth behaviors observed. The linear theory instead, ignoring the possibility of interaction effects would underestimate the quantifiers up to 30% when immigrant densities are low, and overestimate them as much when densities are high. The capacity to quantitatively isolate different types of integration mechanisms makes our framework a suitable tool in the quest for more efficient integration policies.

The Influence Factor Model for the Popularity of Mobile Phone without Considering the Price Factor

NASA Astrophysics Data System (ADS)

Long, Hongming; Peng, Diefei; Wu, Hailin; Yang, Zihui

2018-01-01

Based on the statistical data like economic development, social development, population indicator and so on, this paper establishes the linear regression model which influences the popularity rate of mobile phone users.

A heteroscedastic generalized linear model with a non-normal speed factor for responses and response times.

PubMed

Molenaar, Dylan; Bolsinova, Maria

2017-05-01

In generalized linear modelling of responses and response times, the observed response time variables are commonly transformed to make their distribution approximately normal. A normal distribution for the transformed response times is desirable as it justifies the linearity and homoscedasticity assumptions in the underlying linear model. Past research has, however, shown that the transformed response times are not always normal. Models have been developed to accommodate this violation. In the present study, we propose a modelling approach for responses and response times to test and model non-normality in the transformed response times. Most importantly, we distinguish between non-normality due to heteroscedastic residual variances, and non-normality due to a skewed speed factor. In a simulation study, we establish parameter recovery and the power to separate both effects. In addition, we apply the model to a real data set. © 2017 The Authors. British Journal of Mathematical and Statistical Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

Protein linear indices of the 'macromolecular pseudograph alpha-carbon atom adjacency matrix' in bioinformatics. Part 1: prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor.

PubMed

Marrero-Ponce, Yovani; Medina-Marrero, Ricardo; Castillo-Garit, Juan A; Romero-Zaldivar, Vicente; Torrens, Francisco; Castro, Eduardo A

2005-04-15

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

Statistical Models for the Analysis of Zero-Inflated Pain Intensity Numeric Rating Scale Data.

PubMed

Goulet, Joseph L; Buta, Eugenia; Bathulapalli, Harini; Gueorguieva, Ralitza; Brandt, Cynthia A

2017-03-01

Pain intensity is often measured in clinical and research settings using the 0 to 10 numeric rating scale (NRS). NRS scores are recorded as discrete values, and in some samples they may display a high proportion of zeroes and a right-skewed distribution. Despite this, statistical methods for normally distributed data are frequently used in the analysis of NRS data. We present results from an observational cross-sectional study examining the association of NRS scores with patient characteristics using data collected from a large cohort of 18,935 veterans in Department of Veterans Affairs care diagnosed with a potentially painful musculoskeletal disorder. The mean (variance) NRS pain was 3.0 (7.5), and 34% of patients reported no pain (NRS = 0). We compared the following statistical models for analyzing NRS scores: linear regression, generalized linear models (Poisson and negative binomial), zero-inflated and hurdle models for data with an excess of zeroes, and a cumulative logit model for ordinal data. We examined model fit, interpretability of results, and whether conclusions about the predictor effects changed across models. In this study, models that accommodate zero inflation provided a better fit than the other models. These models should be considered for the analysis of NRS data with a large proportion of zeroes. We examined and analyzed pain data from a large cohort of veterans with musculoskeletal disorders. We found that many reported no current pain on the NRS on the diagnosis date. We present several alternative statistical methods for the analysis of pain intensity data with a large proportion of zeroes. Published by Elsevier Inc.

Distributed Monitoring of the R(sup 2) Statistic for Linear Regression

NASA Technical Reports Server (NTRS)

Bhaduri, Kanishka; Das, Kamalika; Giannella, Chris R.

2011-01-01

The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and one or more dependent target variables. This problem becomes challenging for large scale data in a distributed computing environment when only a subset of instances is available at individual nodes and the local data changes frequently. Data centralization and periodic model recomputation can add high overhead to tasks like anomaly detection in such dynamic settings. Therefore, the goal is to develop techniques for monitoring and updating the model over the union of all nodes data in a communication-efficient fashion. Correctness guarantees on such techniques are also often highly desirable, especially in safety-critical application scenarios. In this paper we develop DReMo a distributed algorithm with very low resource overhead, for monitoring the quality of a regression model in terms of its coefficient of determination (R2 statistic). When the nodes collectively determine that R2 has dropped below a fixed threshold, the linear regression model is recomputed via a network-wide convergecast and the updated model is broadcast back to all nodes. We show empirically, using both synthetic and real data, that our proposed method is highly communication-efficient and scalable, and also provide theoretical guarantees on correctness.

Energy-balance climate models

NASA Technical Reports Server (NTRS)

North, G. R.; Cahalan, R. F.; Coakley, J. A., Jr.

1980-01-01

An introductory survey of the global energy balance climate models is presented with an emphasis on analytical results. A sequence of increasingly complicated models involving ice cap and radiative feedback processes are solved and the solutions and parameter sensitivities are studied. The model parameterizations are examined critically in light of many current uncertainties. A simple seasonal model is used to study the effects of changes in orbital elements on the temperature field. A linear stability theorem and a complete nonlinear stability analysis for the models are developed. Analytical solutions are also obtained for the linearized models driven by stochastic forcing elements. In this context the relation between natural fluctuation statistics and climate sensitivity is stressed.

Energy balance climate models

NASA Technical Reports Server (NTRS)

North, G. R.; Cahalan, R. F.; Coakley, J. A., Jr.

1981-01-01

An introductory survey of the global energy balance climate models is presented with an emphasis on analytical results. A sequence of increasingly complicated models involving ice cap and radiative feedback processes are solved, and the solutions and parameter sensitivities are studied. The model parameterizations are examined critically in light of many current uncertainties. A simple seasonal model is used to study the effects of changes in orbital elements on the temperature field. A linear stability theorem and a complete nonlinear stability analysis for the models are developed. Analytical solutions are also obtained for the linearized models driven by stochastic forcing elements. In this context the relation between natural fluctuation statistics and climate sensitivity is stressed.

Focal activation of primary visual cortex following supra-choroidal electrical stimulation of the retina: Intrinsic signal imaging and linear model analysis.

PubMed

Cloherty, Shaun L; Hietanen, Markus A; Suaning, Gregg J; Ibbotson, Michael R

2010-01-01

We performed optical intrinsic signal imaging of cat primary visual cortex (Area 17 and 18) while delivering bipolar electrical stimulation to the retina by way of a supra-choroidal electrode array. Using a general linear model (GLM) analysis we identified statistically significant (p < 0.01) activation in a localized region of cortex following supra-threshold electrical stimulation at a single retinal locus. (1) demonstrate that intrinsic signal imaging combined with linear model analysis provides a powerful tool for assessing cortical responses to prosthetic stimulation, and (2) confirm that supra-choroidal electrical stimulation can achieve localized activation of the cortex consistent with focal activation of the retina.

Robust Linear Models for Cis-eQTL Analysis.

PubMed

Rantalainen, Mattias; Lindgren, Cecilia M; Holmes, Christopher C

2015-01-01

Expression Quantitative Trait Loci (eQTL) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes. In outbread populations, including humans, eQTLs are commonly analysed using the conventional linear model, adjusting for relevant covariates, assuming an allelic dosage model and a Gaussian error term. However, gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations, or outliers. Such departures from modelling assumptions can lead to an increased rate of type II errors (false negatives), and to some extent also type I errors (false positives). Careful model checking can reduce the risk of type-I errors but often not type II errors, since it is generally too time-consuming to carefully check all models with a non-significant effect in large-scale and genome-wide studies. Here we propose the application of a robust linear model for eQTL analysis to reduce adverse effects of deviations from the assumption of Gaussian residuals. We present results from a simulation study as well as results from the analysis of real eQTL data sets. Our findings suggest that in many situations robust models have the potential to provide more reliable eQTL results compared to conventional linear models, particularly in respect to reducing type II errors due to non-Gaussian noise. Post-genomic data, such as that generated in genome-wide eQTL studies, are often noisy and frequently contain atypical observations. Robust statistical models have the potential to provide more reliable results and increased statistical power under non-Gaussian conditions. The results presented here suggest that robust models should be considered routinely alongside other commonly used methodologies for eQTL analysis.

Steganalysis of recorded speech

NASA Astrophysics Data System (ADS)

Johnson, Micah K.; Lyu, Siwei; Farid, Hany

2005-03-01

Digital audio provides a suitable cover for high-throughput steganography. At 16 bits per sample and sampled at a rate of 44,100 Hz, digital audio has the bit-rate to support large messages. In addition, audio is often transient and unpredictable, facilitating the hiding of messages. Using an approach similar to our universal image steganalysis, we show that hidden messages alter the underlying statistics of audio signals. Our statistical model begins by building a linear basis that captures certain statistical properties of audio signals. A low-dimensional statistical feature vector is extracted from this basis representation and used by a non-linear support vector machine for classification. We show the efficacy of this approach on LSB embedding and Hide4PGP. While no explicit assumptions about the content of the audio are made, our technique has been developed and tested on high-quality recorded speech.

Identifying pleiotropic genes in genome-wide association studies from related subjects using the linear mixed model and Fisher combination function.

PubMed

Yang, James J; Williams, L Keoki; Buu, Anne

2017-08-24

A multivariate genome-wide association test is proposed for analyzing data on multivariate quantitative phenotypes collected from related subjects. The proposed method is a two-step approach. The first step models the association between the genotype and marginal phenotype using a linear mixed model. The second step uses the correlation between residuals of the linear mixed model to estimate the null distribution of the Fisher combination test statistic. The simulation results show that the proposed method controls the type I error rate and is more powerful than the marginal tests across different population structures (admixed or non-admixed) and relatedness (related or independent). The statistical analysis on the database of the Study of Addiction: Genetics and Environment (SAGE) demonstrates that applying the multivariate association test may facilitate identification of the pleiotropic genes contributing to the risk for alcohol dependence commonly expressed by four correlated phenotypes. This study proposes a multivariate method for identifying pleiotropic genes while adjusting for cryptic relatedness and population structure between subjects. The two-step approach is not only powerful but also computationally efficient even when the number of subjects and the number of phenotypes are both very large.

Predicting the performance of linear optical detectors in free space laser communication links

NASA Astrophysics Data System (ADS)

Farrell, Thomas C.

2018-05-01

While the fundamental performance limit for optical communications is set by the quantum nature of light, in practical systems background light, dark current, and thermal noise of the electronics also degrade performance. In this paper, we derive a set of equations predicting the performance of PIN diodes and linear mode avalanche photo diodes (APDs) in the presence of such noise sources. Electrons generated by signal, background, and dark current shot noise are well modeled in PIN diodes as Poissonian statistical processes. In APDs, on the other hand, the amplifying effects of the device result in statistics that are distinctly non-Poissonian. Thermal noise is well modeled as Gaussian. In this paper, we appeal to the central limit theorem and treat both the variability of the signal and the sum of noise sources as Gaussian. Comparison against Monte-Carlo simulation of PIN diode performance (where we do model shot noise with draws from a Poissonian distribution) validates the legitimacy of this approximation. On-off keying, M-ary pulse position, and binary differential phase shift keying modulation are modeled. We conclude with examples showing how the equations may be used in a link budget to estimate the performance of optical links using linear receivers.

Estimation for the Linear Model With Uncertain Covariance Matrices

NASA Astrophysics Data System (ADS)

Zachariah, Dave; Shariati, Nafiseh; Bengtsson, Mats; Jansson, Magnus; Chatterjee, Saikat

2014-03-01

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior inverse-Wishart distributions. The nonconvex problem of jointly estimating the signal of interest and the covariance matrices is tackled by a computationally efficient fixed-point iteration as well as an approximate variational Bayes solution. The statistical performance of estimators is compared numerically to state-of-the-art estimators from the literature and shown to perform favorably.

Predicting oropharyngeal tumor volume throughout the course of radiation therapy from pretreatment computed tomography data using general linear models.

PubMed

Yock, Adam D; Rao, Arvind; Dong, Lei; Beadle, Beth M; Garden, Adam S; Kudchadker, Rajat J; Court, Laurence E

2014-05-01

The purpose of this work was to develop and evaluate the accuracy of several predictive models of variation in tumor volume throughout the course of radiation therapy. Nineteen patients with oropharyngeal cancers were imaged daily with CT-on-rails for image-guided alignment per an institutional protocol. The daily volumes of 35 tumors in these 19 patients were determined and used to generate (1) a linear model in which tumor volume changed at a constant rate, (2) a general linear model that utilized the power fit relationship between the daily and initial tumor volumes, and (3) a functional general linear model that identified and exploited the primary modes of variation between time series describing the changing tumor volumes. Primary and nodal tumor volumes were examined separately. The accuracy of these models in predicting daily tumor volumes were compared with those of static and linear reference models using leave-one-out cross-validation. In predicting the daily volume of primary tumors, the general linear model and the functional general linear model were more accurate than the static reference model by 9.9% (range: -11.6%-23.8%) and 14.6% (range: -7.3%-27.5%), respectively, and were more accurate than the linear reference model by 14.2% (range: -6.8%-40.3%) and 13.1% (range: -1.5%-52.5%), respectively. In predicting the daily volume of nodal tumors, only the 14.4% (range: -11.1%-20.5%) improvement in accuracy of the functional general linear model compared to the static reference model was statistically significant. A general linear model and a functional general linear model trained on data from a small population of patients can predict the primary tumor volume throughout the course of radiation therapy with greater accuracy than standard reference models. These more accurate models may increase the prognostic value of information about the tumor garnered from pretreatment computed tomography images and facilitate improved treatment management.

Sensitivity of airborne fluorosensor measurements to linear vertical gradients in chlorophyll concentration

NASA Technical Reports Server (NTRS)

Venable, D. D.; Punjabi, A. R.; Poole, L. R.

1984-01-01

A semianalytic Monte Carlo radiative transfer simulation model for airborne laser fluorosensors has been extended to investigate the effects of inhomogeneities in the vertical distribution of phytoplankton concentrations in clear seawater. Simulation results for linearly varying step concentrations of chlorophyll are presented. The results indicate that statistically significant differences can be seen under certain conditions in the water Raman-normalized fluorescence signals between nonhomogeneous and homogeneous cases. A statistical test has been used to establish ranges of surface concentrations and/or verticl gradients in which calibration by surface samples would by inappropriate, and the results are discussed.

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

NASA Astrophysics Data System (ADS)

Benaych-Georges, Florent; Guionnet, Alice; Male, Camille

2014-07-01

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.

Role of Statistical Random-Effects Linear Models in Personalized Medicine

PubMed Central

Diaz, Francisco J; Yeh, Hung-Wen; de Leon, Jose

2012-01-01

Some empirical studies and recent developments in pharmacokinetic theory suggest that statistical random-effects linear models are valuable tools that allow describing simultaneously patient populations as a whole and patients as individuals. This remarkable characteristic indicates that these models may be useful in the development of personalized medicine, which aims at finding treatment regimes that are appropriate for particular patients, not just appropriate for the average patient. In fact, published developments show that random-effects linear models may provide a solid theoretical framework for drug dosage individualization in chronic diseases. In particular, individualized dosages computed with these models by means of an empirical Bayesian approach may produce better results than dosages computed with some methods routinely used in therapeutic drug monitoring. This is further supported by published empirical and theoretical findings that show that random effects linear models may provide accurate representations of phase III and IV steady-state pharmacokinetic data, and may be useful for dosage computations. These models have applications in the design of clinical algorithms for drug dosage individualization in chronic diseases; in the computation of dose correction factors; computation of the minimum number of blood samples from a patient that are necessary for calculating an optimal individualized drug dosage in therapeutic drug monitoring; measure of the clinical importance of clinical, demographic, environmental or genetic covariates; study of drug-drug interactions in clinical settings; the implementation of computational tools for web-site-based evidence farming; design of pharmacogenomic studies; and in the development of a pharmacological theory of dosage individualization. PMID:23467392

Acceleration of the direct reconstruction of linear parametric images using nested algorithms.

PubMed

Wang, Guobao; Qi, Jinyi

2010-03-07

Parametric imaging using dynamic positron emission tomography (PET) provides important information for biological research and clinical diagnosis. Indirect and direct methods have been developed for reconstructing linear parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the image reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from raw PET data and are statistically more efficient. However, the convergence rate of direct algorithms can be slow due to the coupling between the reconstruction and kinetic modeling. Here we present two fast gradient-type algorithms for direct reconstruction of linear parametric images. The new algorithms decouple the reconstruction and linear parametric modeling at each iteration by employing the principle of optimization transfer. Convergence speed is accelerated by running more sub-iterations of linear parametric estimation because the computation cost of the linear parametric modeling is much less than that of the image reconstruction. Computer simulation studies demonstrated that the new algorithms converge much faster than the traditional expectation maximization (EM) and the preconditioned conjugate gradient algorithms for dynamic PET.

Quantifying the evolution of flow boiling bubbles by statistical testing and image analysis: toward a general model.

PubMed

Xiao, Qingtai; Xu, Jianxin; Wang, Hua

2016-08-16

A new index, the estimate of the error variance, which can be used to quantify the evolution of the flow patterns when multiphase components or tracers are difficultly distinguishable, was proposed. The homogeneity degree of the luminance space distribution behind the viewing windows in the direct contact boiling heat transfer process was explored. With image analysis and a linear statistical model, the F-test of the statistical analysis was used to test whether the light was uniform, and a non-linear method was used to determine the direction and position of a fixed source light. The experimental results showed that the inflection point of the new index was approximately equal to the mixing time. The new index has been popularized and applied to a multiphase macro mixing process by top blowing in a stirred tank. Moreover, a general quantifying model was introduced for demonstrating the relationship between the flow patterns of the bubble swarms and heat transfer. The results can be applied to investigate other mixing processes that are very difficult to recognize the target.

Quantifying the evolution of flow boiling bubbles by statistical testing and image analysis: toward a general model

PubMed Central

Xiao, Qingtai; Xu, Jianxin; Wang, Hua

2016-01-01

A new index, the estimate of the error variance, which can be used to quantify the evolution of the flow patterns when multiphase components or tracers are difficultly distinguishable, was proposed. The homogeneity degree of the luminance space distribution behind the viewing windows in the direct contact boiling heat transfer process was explored. With image analysis and a linear statistical model, the F-test of the statistical analysis was used to test whether the light was uniform, and a non-linear method was used to determine the direction and position of a fixed source light. The experimental results showed that the inflection point of the new index was approximately equal to the mixing time. The new index has been popularized and applied to a multiphase macro mixing process by top blowing in a stirred tank. Moreover, a general quantifying model was introduced for demonstrating the relationship between the flow patterns of the bubble swarms and heat transfer. The results can be applied to investigate other mixing processes that are very difficult to recognize the target. PMID:27527065

Nonclassical point of view of the Brownian motion generation via fractional deterministic model

NASA Astrophysics Data System (ADS)

Gilardi-Velázquez, H. E.; Campos-Cantón, E.

In this paper, we present a dynamical system based on the Langevin equation without stochastic term and using fractional derivatives that exhibit properties of Brownian motion, i.e. a deterministic model to generate Brownian motion is proposed. The stochastic process is replaced by considering an additional degree of freedom in the second-order Langevin equation. Thus, it is transformed into a system of three first-order linear differential equations, additionally α-fractional derivative are considered which allow us to obtain better statistical properties. Switching surfaces are established as a part of fluctuating acceleration. The final system of three α-order linear differential equations does not contain a stochastic term, so the system generates motion in a deterministic way. Nevertheless, from the time series analysis, we found that the behavior of the system exhibits statistics properties of Brownian motion, such as, a linear growth in time of mean square displacement, a Gaussian distribution. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion.

Introduction to statistical modelling 2: categorical variables and interactions in linear regression.

PubMed

Lunt, Mark

2015-07-01

In the first article in this series we explored the use of linear regression to predict an outcome variable from a number of predictive factors. It assumed that the predictive factors were measured on an interval scale. However, this article shows how categorical variables can also be included in a linear regression model, enabling predictions to be made separately for different groups and allowing for testing the hypothesis that the outcome differs between groups. The use of interaction terms to measure whether the effect of a particular predictor variable differs between groups is also explained. An alternative approach to testing the difference between groups of the effect of a given predictor, which consists of measuring the effect in each group separately and seeing whether the statistical significance differs between the groups, is shown to be misleading. © The Author 2013. Published by Oxford University Press on behalf of the British Society for Rheumatology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Variability aware compact model characterization for statistical circuit design optimization

NASA Astrophysics Data System (ADS)

Qiao, Ying; Qian, Kun; Spanos, Costas J.

2012-03-01

Variability modeling at the compact transistor model level can enable statistically optimized designs in view of limitations imposed by the fabrication technology. In this work we propose an efficient variabilityaware compact model characterization methodology based on the linear propagation of variance. Hierarchical spatial variability patterns of selected compact model parameters are directly calculated from transistor array test structures. This methodology has been implemented and tested using transistor I-V measurements and the EKV-EPFL compact model. Calculation results compare well to full-wafer direct model parameter extractions. Further studies are done on the proper selection of both compact model parameters and electrical measurement metrics used in the method.

Universal Capacitance Model for Real-Time Biomass in Cell Culture.

PubMed

Konakovsky, Viktor; Yagtu, Ali Civan; Clemens, Christoph; Müller, Markus Michael; Berger, Martina; Schlatter, Stefan; Herwig, Christoph

2015-09-02

: Capacitance probes have the potential to revolutionize bioprocess control due to their safe and robust use and ability to detect even the smallest capacitors in the form of biological cells. Several techniques have evolved to model biomass statistically, however, there are problems with model transfer between cell lines and process conditions. Errors of transferred models in the declining phase of the culture range for linear models around +100% or worse, causing unnecessary delays with test runs during bioprocess development. The goal of this work was to develop one single universal model which can be adapted by considering a potentially mechanistic factor to estimate biomass in yet untested clones and scales. The novelty of this work is a methodology to select sensitive frequencies to build a statistical model which can be shared among fermentations with an error between 9% and 38% (mean error around 20%) for the whole process, including the declining phase. A simple linear factor was found to be responsible for the transferability of biomass models between cell lines, indicating a link to their phenotype or physiology.

Unveiling Galaxy Bias via the Halo Model, KiDS and GAMA

NASA Astrophysics Data System (ADS)

Dvornik, Andrej; Hoekstra, Henk; Kuijken, Konrad; Schneider, Peter; Amon, Alexandra; Nakajima, Reiko; Viola, Massimo; Choi, Ami; Erben, Thomas; Farrow, Daniel J.; Heymans, Catherine; Hildebrandt, Hendrik; Sifón, Cristóbal; Wang, Lingyu

2018-06-01

We measure the projected galaxy clustering and galaxy-galaxy lensing signals using the Galaxy And Mass Assembly (GAMA) survey and Kilo-Degree Survey (KiDS) to study galaxy bias. We use the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics to constrain the parameters of the halo occupation statistics and to unveil the origin of galaxy biasing. The bias function Γgm(rp), where rp is the projected comoving separation, is evaluated using the analytical halo model from which the scale dependence of Γgm(rp), and the origin of the non-linearity and stochasticity in halo occupation models can be inferred. Our observations unveil the physical reason for the non-linearity and stochasticity, further explored using hydrodynamical simulations, with the stochasticity mostly originating from the non-Poissonian behaviour of satellite galaxies in the dark matter haloes and their spatial distribution, which does not follow the spatial distribution of dark matter in the halo. The observed non-linearity is mostly due to the presence of the central galaxies, as was noted from previous theoretical work on the same topic. We also see that overall, more massive galaxies reveal a stronger scale dependence, and out to a larger radius. Our results show that a wealth of information about galaxy bias is hidden in halo occupation models. These models should therefore be used to determine the influence of galaxy bias in cosmological studies.

Examining Elementary Social Studies Marginalization: A Multilevel Model

ERIC Educational Resources Information Center

Fitchett, Paul G.; Heafner, Tina L.; Lambert, Richard G.

2014-01-01

Utilizing data from the National Center for Education Statistics Schools and Staffing Survey (SASS), a multilevel model (Hierarchical Linear Model) was developed to examine the association of teacher/classroom and state level indicators on reported elementary social studies instructional time. Findings indicated that state testing policy was a…

Modeling Systematicity and Individuality in Nonlinear Second Language Development: The Case of English Grammatical Morphemes

ERIC Educational Resources Information Center

Murakami, Akira

2016-01-01

This article introduces two sophisticated statistical modeling techniques that allow researchers to analyze systematicity, individual variation, and nonlinearity in second language (L2) development. Generalized linear mixed-effects models can be used to quantify individual variation and examine systematic effects simultaneously, and generalized…

On Generalizations of Cochran’s Theorem and Projection Matrices.

DTIC Science & Technology

1980-08-01

Definiteness of the Estimated Dispersion Matrix in a Multivariate Linear Model ," F. Pukelsheim and George P.H. Styan, May 1978. TECHNICAL REPORTS...with applications to the analysis of covariance," Proc. Cambridge Philos. Soc., 30, pp. 178-191. Graybill , F. A. and Marsaglia, G. (1957...34Idempotent matrices and quad- ratic forms in the general linear hypothesis," Ann. Math. Statist., 28, pp. 678-686. Greub, W. (1975). Linear Algebra (4th ed

Implementing Restricted Maximum Likelihood Estimation in Structural Equation Models

ERIC Educational Resources Information Center

Cheung, Mike W.-L.

2013-01-01

Structural equation modeling (SEM) is now a generic modeling framework for many multivariate techniques applied in the social and behavioral sciences. Many statistical models can be considered either as special cases of SEM or as part of the latent variable modeling framework. One popular extension is the use of SEM to conduct linear mixed-effects…

Estimating cosmic velocity fields from density fields and tidal tensors

NASA Astrophysics Data System (ADS)

Kitaura, Francisco-Shu; Angulo, Raul E.; Hoffman, Yehuda; Gottlöber, Stefan

2012-10-01

In this work we investigate the non-linear and non-local relation between cosmological density and peculiar velocity fields. Our goal is to provide an algorithm for the reconstruction of the non-linear velocity field from the fully non-linear density. We find that including the gravitational tidal field tensor using second-order Lagrangian perturbation theory based upon an estimate of the linear component of the non-linear density field significantly improves the estimate of the cosmic flow in comparison to linear theory not only in the low density, but also and more dramatically in the high-density regions. In particular we test two estimates of the linear component: the lognormal model and the iterative Lagrangian linearization. The present approach relies on a rigorous higher order Lagrangian perturbation theory analysis which incorporates a non-local relation. It does not require additional fitting from simulations being in this sense parameter free, it is independent of statistical-geometrical optimization and it is straightforward and efficient to compute. The method is demonstrated to yield an unbiased estimator of the velocity field on scales ≳5 h-1 Mpc with closely Gaussian distributed errors. Moreover, the statistics of the divergence of the peculiar velocity field is extremely well recovered showing a good agreement with the true one from N-body simulations. The typical errors of about 10 km s-1 (1σ confidence intervals) are reduced by more than 80 per cent with respect to linear theory in the scale range between 5 and 10 h-1 Mpc in high-density regions (δ > 2). We also find that iterative Lagrangian linearization is significantly superior in the low-density regime with respect to the lognormal model.

Using structural equation modeling for network meta-analysis.

PubMed

Tu, Yu-Kang; Wu, Yun-Chun

2017-07-14

Network meta-analysis overcomes the limitations of traditional pair-wise meta-analysis by incorporating all available evidence into a general statistical framework for simultaneous comparisons of several treatments. Currently, network meta-analyses are undertaken either within the Bayesian hierarchical linear models or frequentist generalized linear mixed models. Structural equation modeling (SEM) is a statistical method originally developed for modeling causal relations among observed and latent variables. As random effect is explicitly modeled as a latent variable in SEM, it is very flexible for analysts to specify complex random effect structure and to make linear and nonlinear constraints on parameters. The aim of this article is to show how to undertake a network meta-analysis within the statistical framework of SEM. We used an example dataset to demonstrate the standard fixed and random effect network meta-analysis models can be easily implemented in SEM. It contains results of 26 studies that directly compared three treatment groups A, B and C for prevention of first bleeding in patients with liver cirrhosis. We also showed that a new approach to network meta-analysis based on the technique of unrestricted weighted least squares (UWLS) method can also be undertaken using SEM. For both the fixed and random effect network meta-analysis, SEM yielded similar coefficients and confidence intervals to those reported in the previous literature. The point estimates of two UWLS models were identical to those in the fixed effect model but the confidence intervals were greater. This is consistent with results from the traditional pairwise meta-analyses. Comparing to UWLS model with common variance adjusted factor, UWLS model with unique variance adjusted factor has greater confidence intervals when the heterogeneity was larger in the pairwise comparison. The UWLS model with unique variance adjusted factor reflects the difference in heterogeneity within each comparison. SEM provides a very flexible framework for univariate and multivariate meta-analysis, and its potential as a powerful tool for advanced meta-analysis is still to be explored.

A multivariate model and statistical method for validating tree grade lumber yield equations

Treesearch

Donald W. Seegrist

1975-01-01

Lumber yields within lumber grades can be described by a multivariate linear model. A method for validating lumber yield prediction equations when there are several tree grades is presented. The method is based on multivariate simultaneous test procedures.

The linearized multistage model and the future of quantitative risk assessment.

PubMed

Crump, K S

1996-10-01

The linearized multistage (LMS) model has for over 15 years been the default dose-response model used by the U.S. Environmental Protection Agency (USEPA) and other federal and state regulatory agencies in the United States for calculating quantitative estimates of low-dose carcinogenic risks from animal data. The LMS model is in essence a flexible statistical model that can describe both linear and non-linear dose-response patterns, and that produces an upper confidence bound on the linear low-dose slope of the dose-response curve. Unlike its namesake, the Armitage-Doll multistage model, the parameters of the LMS do not correspond to actual physiological phenomena. Thus the LMS is 'biological' only to the extent that the true biological dose response is linear at low dose and that low-dose slope is reflected in the experimental data. If the true dose response is non-linear the LMS upper bound may overestimate the true risk by many orders of magnitude. However, competing low-dose extrapolation models, including those derived from 'biologically-based models' that are capable of incorporating additional biological information, have not shown evidence to date of being able to produce quantitative estimates of low-dose risks that are any more accurate than those obtained from the LMS model. Further, even if these attempts were successful, the extent to which more accurate estimates of low-dose risks in a test animal species would translate into improved estimates of human risk is questionable. Thus, it does not appear possible at present to develop a quantitative approach that would be generally applicable and that would offer significant improvements upon the crude bounding estimates of the type provided by the LMS model. Draft USEPA guidelines for cancer risk assessment incorporate an approach similar to the LMS for carcinogens having a linear mode of action. However, under these guidelines quantitative estimates of low-dose risks would not be developed for carcinogens having a non-linear mode of action; instead dose-response modelling would be used in the experimental range to calculate an LED10* (a statistical lower bound on the dose corresponding to a 10% increase in risk), and safety factors would be applied to the LED10* to determine acceptable exposure levels for humans. This approach is very similar to the one presently used by USEPA for non-carcinogens. Rather than using one approach for carcinogens believed to have a linear mode of action and a different approach for all other health effects, it is suggested herein that it would be more appropriate to use an approach conceptually similar to the 'LED10*-safety factor' approach for all health effects, and not to routinely develop quantitative risk estimates from animal data.

Sea surface temperature anomalies, planetary waves, and air-sea feedback in the middle latitudes

NASA Technical Reports Server (NTRS)

Frankignoul, C.

1985-01-01

Current analytical models for large-scale air-sea interactions in the middle latitudes are reviewed in terms of known sea-surface temperature (SST) anomalies. The scales and strength of different atmospheric forcing mechanisms are discussed, along with the damping and feedback processes controlling the evolution of the SST. Difficulties with effective SST modeling are described in terms of the techniques and results of case studies, numerical simulations of mixed-layer variability and statistical modeling. The relationship between SST and diabatic heating anomalies is considered and a linear model is developed for the response of the stationary atmosphere to the air-sea feedback. The results obtained with linear wave models are compared with the linear model results. Finally, sample data are presented from experiments with general circulation models into which specific SST anomaly data for the middle latitudes were introduced.

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

NASA Astrophysics Data System (ADS)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

On Fluctuations of Eigenvalues of Random Band Matrices

NASA Astrophysics Data System (ADS)

Shcherbina, M.

2015-10-01

We consider the fluctuations of linear eigenvalue statistics of random band matrices whose entries have the form with i.i.d. possessing the th moment, where the function u has a finite support , so that M has only nonzero diagonals. The parameter b (called the bandwidth) is assumed to grow with n in a way such that . Without any additional assumptions on the growth of b we prove CLT for linear eigenvalue statistics for a rather wide class of test functions. Thus we improve and generalize the results of the previous papers (Jana et al., arXiv:1412.2445; Li et al. Random Matrices 2:04, 2013), where CLT was proven under the assumption . Moreover, we develop a method which allows to prove automatically the CLT for linear eigenvalue statistics of the smooth test functions for almost all classical models of random matrix theory: deformed Wigner and sample covariance matrices, sparse matrices, diluted random matrices, matrices with heavy tales etc.

How Do Microphysical Processes Influence Large-Scale Precipitation Variability and Extremes?

DOE PAGES

Hagos, Samson; Ruby Leung, L.; Zhao, Chun; ...

2018-02-10

Convection permitting simulations using the Model for Prediction Across Scales-Atmosphere (MPAS-A) are used to examine how microphysical processes affect large-scale precipitation variability and extremes. An episode of the Madden-Julian Oscillation is simulated using MPAS-A with a refined region at 4-km grid spacing over the Indian Ocean. It is shown that cloud microphysical processes regulate the precipitable water (PW) statistics. Because of the non-linear relationship between precipitation and PW, PW exceeding a certain critical value (PWcr) contributes disproportionately to precipitation variability. However, the frequency of PW exceeding PWcr decreases rapidly with PW, so changes in microphysical processes that shift the columnmore » PW statistics relative to PWcr even slightly have large impacts on precipitation variability. Furthermore, precipitation variance and extreme precipitation frequency are approximately linearly related to the difference between the mean and critical PW values. Thus observed precipitation statistics could be used to directly constrain model microphysical parameters as this study demonstrates using radar observations from DYNAMO field campaign.« less

How Do Microphysical Processes Influence Large-Scale Precipitation Variability and Extremes?

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

Hagos, Samson; Ruby Leung, L.; Zhao, Chun

Convection permitting simulations using the Model for Prediction Across Scales-Atmosphere (MPAS-A) are used to examine how microphysical processes affect large-scale precipitation variability and extremes. An episode of the Madden-Julian Oscillation is simulated using MPAS-A with a refined region at 4-km grid spacing over the Indian Ocean. It is shown that cloud microphysical processes regulate the precipitable water (PW) statistics. Because of the non-linear relationship between precipitation and PW, PW exceeding a certain critical value (PWcr) contributes disproportionately to precipitation variability. However, the frequency of PW exceeding PWcr decreases rapidly with PW, so changes in microphysical processes that shift the columnmore » PW statistics relative to PWcr even slightly have large impacts on precipitation variability. Furthermore, precipitation variance and extreme precipitation frequency are approximately linearly related to the difference between the mean and critical PW values. Thus observed precipitation statistics could be used to directly constrain model microphysical parameters as this study demonstrates using radar observations from DYNAMO field campaign.« less

Linear mixed-effects models for within-participant psychology experiments: an introductory tutorial and free, graphical user interface (LMMgui).

PubMed

Magezi, David A

2015-01-01

Linear mixed-effects models (LMMs) are increasingly being used for data analysis in cognitive neuroscience and experimental psychology, where within-participant designs are common. The current article provides an introductory review of the use of LMMs for within-participant data analysis and describes a free, simple, graphical user interface (LMMgui). LMMgui uses the package lme4 (Bates et al., 2014a,b) in the statistical environment R (R Core Team).

qFeature

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

2015-09-14

This package contains statistical routines for extracting features from multivariate time-series data which can then be used for subsequent multivariate statistical analysis to identify patterns and anomalous behavior. It calculates local linear or quadratic regression model fits to moving windows for each series and then summarizes the model coefficients across user-defined time intervals for each series. These methods are domain agnostic-but they have been successfully applied to a variety of domains, including commercial aviation and electric power grid data.

Improving mass-univariate analysis of neuroimaging data by modelling important unknown covariates: Application to Epigenome-Wide Association Studies.

PubMed

Guillaume, Bryan; Wang, Changqing; Poh, Joann; Shen, Mo Jun; Ong, Mei Lyn; Tan, Pei Fang; Karnani, Neerja; Meaney, Michael; Qiu, Anqi

2018-06-01

Statistical inference on neuroimaging data is often conducted using a mass-univariate model, equivalent to fitting a linear model at every voxel with a known set of covariates. Due to the large number of linear models, it is challenging to check if the selection of covariates is appropriate and to modify this selection adequately. The use of standard diagnostics, such as residual plotting, is clearly not practical for neuroimaging data. However, the selection of covariates is crucial for linear regression to ensure valid statistical inference. In particular, the mean model of regression needs to be reasonably well specified. Unfortunately, this issue is often overlooked in the field of neuroimaging. This study aims to adopt the existing Confounder Adjusted Testing and Estimation (CATE) approach and to extend it for use with neuroimaging data. We propose a modification of CATE that can yield valid statistical inferences using Principal Component Analysis (PCA) estimators instead of Maximum Likelihood (ML) estimators. We then propose a non-parametric hypothesis testing procedure that can improve upon parametric testing. Monte Carlo simulations show that the modification of CATE allows for more accurate modelling of neuroimaging data and can in turn yield a better control of False Positive Rate (FPR) and Family-Wise Error Rate (FWER). We demonstrate its application to an Epigenome-Wide Association Study (EWAS) on neonatal brain imaging and umbilical cord DNA methylation data obtained as part of a longitudinal cohort study. Software for this CATE study is freely available at http://www.bioeng.nus.edu.sg/cfa/Imaging_Genetics2.html. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

Estimation of aboveground biomass in Mediterranean forests by statistical modelling of ASTER fraction images

NASA Astrophysics Data System (ADS)

Fernández-Manso, O.; Fernández-Manso, A.; Quintano, C.

2014-09-01

Aboveground biomass (AGB) estimation from optical satellite data is usually based on regression models of original or synthetic bands. To overcome the poor relation between AGB and spectral bands due to mixed-pixels when a medium spatial resolution sensor is considered, we propose to base the AGB estimation on fraction images from Linear Spectral Mixture Analysis (LSMA). Our study area is a managed Mediterranean pine woodland (Pinus pinaster Ait.) in central Spain. A total of 1033 circular field plots were used to estimate AGB from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) optical data. We applied Pearson correlation statistics and stepwise multiple regression to identify suitable predictors from the set of variables of original bands, fraction imagery, Normalized Difference Vegetation Index and Tasselled Cap components. Four linear models and one nonlinear model were tested. A linear combination of ASTER band 2 (red, 0.630-0.690 μm), band 8 (short wave infrared 5, 2.295-2.365 μm) and green vegetation fraction (from LSMA) was the best AGB predictor (Radj2=0.632, the root-mean-squared error of estimated AGB was 13.3 Mg ha-1 (or 37.7%), resulting from cross-validation), rather than other combinations of the above cited independent variables. Results indicated that using ASTER fraction images in regression models improves the AGB estimation in Mediterranean pine forests. The spatial distribution of the estimated AGB, based on a multiple linear regression model, may be used as baseline information for forest managers in future studies, such as quantifying the regional carbon budget, fuel accumulation or monitoring of management practices.

Components of a Flipped Classroom Influencing Student Success in an Undergraduate Business Statistics Course

ERIC Educational Resources Information Center

Shinaberger, Lee

2017-01-01

An instructor transformed an undergraduate business statistics course over 10 semesters from a traditional lecture course to a flipped classroom course. The researcher used a linear mixed model to explore the effectiveness of the evolution on student success as measured by exam performance. The results provide guidance to successfully implement a…

(Draft) Community air pollution and mortality: Analysis of 1980 data from US metropolitan areas

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

Lipfert, F.W.

1992-11-01

1980 data from up to 149 metropolitan areas were used to define cross-sectional associations between community air pollution and ``excess`` human mortality. The regression model proposed by Ozkaynak and Thurston (1987), which accounted for age, race, education, poverty, and population density, was evaluated and several new models were developed. The new models also accounted for migration, drinking water hardness, and smoking, and included a more detailed description of race. Cause-of-death categories analyzed include all causes, all ``non-external`` causes, major cardiovascular diseases, and chronic obstructive pulmonary diseases (COPD). Both annual mortality rates and their logarithms were analyzed. Air quality data weremore » obtained from the EPA AIRS database (TSP, SO{sub 4}{sup =}, Mn, and ozone) and from the inhalable particulate network (PM{sub 15}, PM{sub 2.5} and SO{sub 4}{sup =}, for 63{sup 4} locations). The data on particulates were averaged across all monitoring stations available for each SMSA and the TSP data were restricted to the year 1980. The associations between mortality and air pollution were found to be dependent on the socioeconomic factors included in the models, the specific locations included in the data set, and the type of statistical model used. Statistically significant associations were found as follows: between TSP and mortality due to non-external causes with log-linear models, but not with a linear model betweenestimated 10-year average (1980--90) ozone levels and 1980 non-external and cardiovascular deaths; and between TSP and COPD mortality for both linear and log-linear models. When the sulfate contribution to TSP was subtracted, the relationship with COPD mortality was strengthened.« less

(Draft) Community air pollution and mortality: Analysis of 1980 data from US metropolitan areas

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

Lipfert, F.W.

1992-11-01

1980 data from up to 149 metropolitan areas were used to define cross-sectional associations between community air pollution and excess'' human mortality. The regression model proposed by Ozkaynak and Thurston (1987), which accounted for age, race, education, poverty, and population density, was evaluated and several new models were developed. The new models also accounted for migration, drinking water hardness, and smoking, and included a more detailed description of race. Cause-of-death categories analyzed include all causes, all non-external'' causes, major cardiovascular diseases, and chronic obstructive pulmonary diseases (COPD). Both annual mortality rates and their logarithms were analyzed. Air quality data weremore » obtained from the EPA AIRS database (TSP, SO[sub 4][sup =], Mn, and ozone) and from the inhalable particulate network (PM[sub 15], PM[sub 2.5] and SO[sub 4][sup =], for 63[sup 4] locations). The data on particulates were averaged across all monitoring stations available for each SMSA and the TSP data were restricted to the year 1980. The associations between mortality and air pollution were found to be dependent on the socioeconomic factors included in the models, the specific locations included in the data set, and the type of statistical model used. Statistically significant associations were found as follows: between TSP and mortality due to non-external causes with log-linear models, but not with a linear model betweenestimated 10-year average (1980--90) ozone levels and 1980 non-external and cardiovascular deaths; and between TSP and COPD mortality for both linear and log-linear models. When the sulfate contribution to TSP was subtracted, the relationship with COPD mortality was strengthened.« less

Introducing linear functions: an alternative statistical approach

NASA Astrophysics Data System (ADS)

Nolan, Caroline; Herbert, Sandra

2015-12-01

The introduction of linear functions is the turning point where many students decide if mathematics is useful or not. This means the role of parameters and variables in linear functions could be considered to be `threshold concepts'. There is recognition that linear functions can be taught in context through the exploration of linear modelling examples, but this has its limitations. Currently, statistical data is easily attainable, and graphics or computer algebra system (CAS) calculators are common in many classrooms. The use of this technology provides ease of access to different representations of linear functions as well as the ability to fit a least-squares line for real-life data. This means these calculators could support a possible alternative approach to the introduction of linear functions. This study compares the results of an end-of-topic test for two classes of Australian middle secondary students at a regional school to determine if such an alternative approach is feasible. In this study, test questions were grouped by concept and subjected to concept by concept analysis of the means of test results of the two classes. This analysis revealed that the students following the alternative approach demonstrated greater competence with non-standard questions.

Statistical Modelling of Temperature and Moisture Uptake of Biochars Exposed to Selected Relative Humidity of Air.

PubMed

Bastistella, Luciane; Rousset, Patrick; Aviz, Antonio; Caldeira-Pires, Armando; Humbert, Gilles; Nogueira, Manoel

2018-02-09

New experimental techniques, as well as modern variants on known methods, have recently been employed to investigate the fundamental reactions underlying the oxidation of biochar. The purpose of this paper was to experimentally and statistically study how the relative humidity of air, mass, and particle size of four biochars influenced the adsorption of water and the increase in temperature. A random factorial design was employed using the intuitive statistical software Xlstat. A simple linear regression model and an analysis of variance with a pairwise comparison were performed. The experimental study was carried out on the wood of Quercus pubescens , Cyclobalanopsis glauca , Trigonostemon huangmosun , and Bambusa vulgaris , and involved five relative humidity conditions (22, 43, 75, 84, and 90%), two mass samples (0.1 and 1 g), and two particle sizes (powder and piece). Two response variables including water adsorption and temperature increase were analyzed and discussed. The temperature did not increase linearly with the adsorption of water. Temperature was modeled by nine explanatory variables, while water adsorption was modeled by eight. Five variables, including factors and their interactions, were found to be common to the two models. Sample mass and relative humidity influenced the two qualitative variables, while particle size and biochar type only influenced the temperature.

Extreme value statistics analysis of fracture strengths of a sintered silicon nitride failing from pores

NASA Technical Reports Server (NTRS)

Chao, Luen-Yuan; Shetty, Dinesh K.

1992-01-01

Statistical analysis and correlation between pore-size distribution and fracture strength distribution using the theory of extreme-value statistics is presented for a sintered silicon nitride. The pore-size distribution on a polished surface of this material was characterized, using an automatic optical image analyzer. The distribution measured on the two-dimensional plane surface was transformed to a population (volume) distribution, using the Schwartz-Saltykov diameter method. The population pore-size distribution and the distribution of the pore size at the fracture origin were correllated by extreme-value statistics. Fracture strength distribution was then predicted from the extreme-value pore-size distribution, usin a linear elastic fracture mechanics model of annular crack around pore and the fracture toughness of the ceramic. The predicted strength distribution was in good agreement with strength measurements in bending. In particular, the extreme-value statistics analysis explained the nonlinear trend in the linearized Weibull plot of measured strengths without postulating a lower-bound strength.

Analytic Methods for Adjusting Subjective Rating Schemes.

ERIC Educational Resources Information Center

Cooper, Richard V. L.; Nelson, Gary R.

Statistical and econometric techniques of correcting for supervisor bias in models of individual performance appraisal were developed, using a variant of the classical linear regression model. Location bias occurs when individual performance is systematically overestimated or underestimated, while scale bias results when raters either exaggerate…

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

NASA Technical Reports Server (NTRS)

Buchert, T.; Melott, A. L.; Weiss, A. G.

1993-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Reaction times to weak test lights. [psychophysics biological model

NASA Technical Reports Server (NTRS)

Wandell, B. A.; Ahumada, P.; Welsh, D.

1984-01-01

Maloney and Wandell (1984) describe a model of the response of a single visual channel to weak test lights. The initial channel response is a linearly filtered version of the stimulus. The filter output is randomly sampled over time. Each time a sample occurs there is some probability increasing with the magnitude of the sampled response - that a discrete detection event is generated. Maloney and Wandell derive the statistics of the detection events. In this paper a test is conducted of the hypothesis that the reaction time responses to the presence of a weak test light are initiated at the first detection event. This makes it possible to extend the application of the model to lights that are slightly above threshold, but still within the linear operating range of the visual system. A parameter-free prediction of the model proposed by Maloney and Wandell for lights detected by this statistic is tested. The data are in agreement with the prediction.

Non-linear mixed effects modeling - from methodology and software development to driving implementation in drug development science.

PubMed

Pillai, Goonaseelan Colin; Mentré, France; Steimer, Jean-Louis

2005-04-01

Few scientific contributions have made significant impact unless there was a champion who had the vision to see the potential for its use in seemingly disparate areas-and who then drove active implementation. In this paper, we present a historical summary of the development of non-linear mixed effects (NLME) modeling up to the more recent extensions of this statistical methodology. The paper places strong emphasis on the pivotal role played by Lewis B. Sheiner (1940-2004), who used this statistical methodology to elucidate solutions to real problems identified in clinical practice and in medical research and on how he drove implementation of the proposed solutions. A succinct overview of the evolution of the NLME modeling methodology is presented as well as ideas on how its expansion helped to provide guidance for a more scientific view of (model-based) drug development that reduces empiricism in favor of critical quantitative thinking and decision making.

Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape

PubMed Central

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for ‘difficult’ variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we assess a range of candidate distributions, including the Sichel, Delaporte, Box-Cox Green and Cole, and Box-Cox t distributions. We find that the Box-Cox t distribution, with appropriate modeling of its parameters, best fits the conditional distribution of phonemic inventory size. We finally discuss the specificities of phoneme counts, weak effects, and how GAMLSS should be considered for other linguistic variables. PMID:29713298

Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape.

PubMed

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for 'difficult' variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we assess a range of candidate distributions, including the Sichel, Delaporte, Box-Cox Green and Cole, and Box-Cox t distributions. We find that the Box-Cox t distribution, with appropriate modeling of its parameters, best fits the conditional distribution of phonemic inventory size. We finally discuss the specificities of phoneme counts, weak effects, and how GAMLSS should be considered for other linguistic variables.

Estimating PM2.5 Concentrations in Xi'an City Using a Generalized Additive Model with Multi-Source Monitoring Data

PubMed Central

Song, Yong-Ze; Yang, Hong-Lei; Peng, Jun-Huan; Song, Yi-Rong; Sun, Qian; Li, Yuan

2015-01-01

Particulate matter with an aerodynamic diameter <2.5 μm (PM2.5) represents a severe environmental problem and is of negative impact on human health. Xi'an City, with a population of 6.5 million, is among the highest concentrations of PM2.5 in China. In 2013, in total, there were 191 days in Xi’an City on which PM2.5 concentrations were greater than 100 μg/m3. Recently, a few studies have explored the potential causes of high PM2.5 concentration using remote sensing data such as the MODIS aerosol optical thickness (AOT) product. Linear regression is a commonly used method to find statistical relationships among PM2.5 concentrations and other pollutants, including CO, NO2, SO2, and O3, which can be indicative of emission sources. The relationships of these variables, however, are usually complicated and non-linear. Therefore, a generalized additive model (GAM) is used to estimate the statistical relationships between potential variables and PM2.5 concentrations. This model contains linear functions of SO2 and CO, univariate smoothing non-linear functions of NO2, O3, AOT and temperature, and bivariate smoothing non-linear functions of location and wind variables. The model can explain 69.50% of PM2.5 concentrations, with R2 = 0.691, which improves the result of a stepwise linear regression (R2 = 0.582) by 18.73%. The two most significant variables, CO concentration and AOT, represent 20.65% and 19.54% of the deviance, respectively, while the three other gas-phase concentrations, SO2, NO2, and O3 account for 10.88% of the total deviance. These results show that in Xi'an City, the traffic and other industrial emissions are the primary source of PM2.5. Temperature, location, and wind variables also non-linearly related with PM2.5. PMID:26540446

Comparing a single case to a control group - Applying linear mixed effects models to repeated measures data.

PubMed

Huber, Stefan; Klein, Elise; Moeller, Korbinian; Willmes, Klaus

2015-10-01

In neuropsychological research, single-cases are often compared with a small control sample. Crawford and colleagues developed inferential methods (i.e., the modified t-test) for such a research design. In the present article, we suggest an extension of the methods of Crawford and colleagues employing linear mixed models (LMM). We first show that a t-test for the significance of a dummy coded predictor variable in a linear regression is equivalent to the modified t-test of Crawford and colleagues. As an extension to this idea, we then generalized the modified t-test to repeated measures data by using LMMs to compare the performance difference in two conditions observed in a single participant to that of a small control group. The performance of LMMs regarding Type I error rates and statistical power were tested based on Monte-Carlo simulations. We found that starting with about 15-20 participants in the control sample Type I error rates were close to the nominal Type I error rate using the Satterthwaite approximation for the degrees of freedom. Moreover, statistical power was acceptable. Therefore, we conclude that LMMs can be applied successfully to statistically evaluate performance differences between a single-case and a control sample. Copyright © 2015 Elsevier Ltd. All rights reserved.

Extending local canonical correlation analysis to handle general linear contrasts for FMRI data.

PubMed

Jin, Mingwu; Nandy, Rajesh; Curran, Tim; Cordes, Dietmar

2012-01-01

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic.

Extending Local Canonical Correlation Analysis to Handle General Linear Contrasts for fMRI Data

PubMed Central

Jin, Mingwu; Nandy, Rajesh; Curran, Tim; Cordes, Dietmar

2012-01-01

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic. PMID:22461786

Prescriptive Statements and Educational Practice: What Can Structural Equation Modeling (SEM) Offer?

ERIC Educational Resources Information Center

Martin, Andrew J.

2011-01-01

Longitudinal structural equation modeling (SEM) can be a basis for making prescriptive statements on educational practice and offers yields over "traditional" statistical techniques under the general linear model. The extent to which prescriptive statements can be made will rely on the appropriate accommodation of key elements of research design,…

Determinants of Linear Judgment: A Meta-Analysis of Lens Model Studies

ERIC Educational Resources Information Center

Karelaia, Natalia; Hogarth, Robin M.

2008-01-01

The mathematical representation of E. Brunswik's (1952) lens model has been used extensively to study human judgment and provides a unique opportunity to conduct a meta-analysis of studies that covers roughly 5 decades. Specifically, the authors analyzed statistics of the "lens model equation" (L. R. Tucker, 1964) associated with 249 different…

Power Analysis for Complex Mediational Designs Using Monte Carlo Methods

ERIC Educational Resources Information Center

Thoemmes, Felix; MacKinnon, David P.; Reiser, Mark R.

2010-01-01

Applied researchers often include mediation effects in applications of advanced methods such as latent variable models and linear growth curve models. Guidance on how to estimate statistical power to detect mediation for these models has not yet been addressed in the literature. We describe a general framework for power analyses for complex…

Modeling Success: Using Preenrollment Data to Identify Academically At-Risk Students

ERIC Educational Resources Information Center

Gansemer-Topf, Ann M.; Compton, Jonathan; Wohlgemuth, Darin; Forbes, Greg; Ralston, Ekaterina

2015-01-01

Improving student success and degree completion is one of the core principles of strategic enrollment management. To address this principle, institutional data were used to develop a statistical model to identify academically at-risk students. The model employs multiple linear regression techniques to predict students at risk of earning below a…

Post-Modeling Histogram Matching of Maps Produced Using Regression Trees

Treesearch

Andrew J. Lister; Tonya W. Lister

2006-01-01

Spatial predictive models often use statistical techniques that in some way rely on averaging of values. Estimates from linear modeling are known to be susceptible to truncation of variance when the independent (predictor) variables are measured with error. A straightforward post-processing technique (histogram matching) for attempting to mitigate this effect is...

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

PubMed

Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William

2016-01-01

Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p < 0.001) when using a linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p < 0.001) and slopes (p < 0.001) of the individual growth trajectories. We also identified important serial correlation within the structure of the data (ρ = 0.66; 95 % CI 0.64 to 0.68; p < 0.001), which we modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather than the coefficients. Moreover, use of cubic regression splines provides biological meaningful growth velocity and acceleration curves despite increased complexity in coefficient interpretation. Through this stepwise approach, we provide a set of tools to model longitudinal childhood data for non-statisticians using linear mixed-effect models.

Statistical analysis of water-quality data containing multiple detection limits: S-language software for regression on order statistics

USGS Publications Warehouse

Lee, L.; Helsel, D.

2005-01-01

Trace contaminants in water, including metals and organics, often are measured at sufficiently low concentrations to be reported only as values below the instrument detection limit. Interpretation of these "less thans" is complicated when multiple detection limits occur. Statistical methods for multiply censored, or multiple-detection limit, datasets have been developed for medical and industrial statistics, and can be employed to estimate summary statistics or model the distributions of trace-level environmental data. We describe S-language-based software tools that perform robust linear regression on order statistics (ROS). The ROS method has been evaluated as one of the most reliable procedures for developing summary statistics of multiply censored data. It is applicable to any dataset that has 0 to 80% of its values censored. These tools are a part of a software library, or add-on package, for the R environment for statistical computing. This library can be used to generate ROS models and associated summary statistics, plot modeled distributions, and predict exceedance probabilities of water-quality standards. ?? 2005 Elsevier Ltd. All rights reserved.

Age related neuromuscular changes in sEMG of m. Tibialis Anterior using higher order statistics (Gaussianity & linearity test).

PubMed

Siddiqi, Ariba; Arjunan, Sridhar P; Kumar, Dinesh K

2016-08-01

Age-associated changes in the surface electromyogram (sEMG) of Tibialis Anterior (TA) muscle can be attributable to neuromuscular alterations that precede strength loss. We have used our sEMG model of the Tibialis Anterior to interpret the age-related changes and compared with the experimental sEMG. Eighteen young (20-30 years) and 18 older (60-85 years) performed isometric dorsiflexion at 6 different percentage levels of maximum voluntary contractions (MVC), and their sEMG from the TA muscle was recorded. Six different age-related changes in the neuromuscular system were simulated using the sEMG model at the same MVCs as the experiment. The maximal power of the spectrum, Gaussianity and Linearity Test Statistics were computed from the simulated and experimental sEMG. A correlation analysis at α=0.05 was performed between the simulated and experimental age-related change in the sEMG features. The results show the loss in motor units was distinguished by the Gaussianity and Linearity test statistics; while the maximal power of the PSD distinguished between the muscular factors. The simulated condition of 40% loss of motor units with halved the number of fast fibers best correlated with the age-related change observed in the experimental sEMG higher order statistical features. The simulated aging condition found by this study corresponds with the moderate motor unit remodelling and negligible strength loss reported in literature for the cohorts aged 60-70 years.

Scoring and staging systems using cox linear regression modeling and recursive partitioning.

PubMed

Lee, J W; Um, S H; Lee, J B; Mun, J; Cho, H

2006-01-01

Scoring and staging systems are used to determine the order and class of data according to predictors. Systems used for medical data, such as the Child-Turcotte-Pugh scoring and staging systems for ordering and classifying patients with liver disease, are often derived strictly from physicians' experience and intuition. We construct objective and data-based scoring/staging systems using statistical methods. We consider Cox linear regression modeling and recursive partitioning techniques for censored survival data. In particular, to obtain a target number of stages we propose cross-validation and amalgamation algorithms. We also propose an algorithm for constructing scoring and staging systems by integrating local Cox linear regression models into recursive partitioning, so that we can retain the merits of both methods such as superior predictive accuracy, ease of use, and detection of interactions between predictors. The staging system construction algorithms are compared by cross-validation evaluation of real data. The data-based cross-validation comparison shows that Cox linear regression modeling is somewhat better than recursive partitioning when there are only continuous predictors, while recursive partitioning is better when there are significant categorical predictors. The proposed local Cox linear recursive partitioning has better predictive accuracy than Cox linear modeling and simple recursive partitioning. This study indicates that integrating local linear modeling into recursive partitioning can significantly improve prediction accuracy in constructing scoring and staging systems.

Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses.

PubMed

Faul, Franz; Erdfelder, Edgar; Buchner, Axel; Lang, Albert-Georg

2009-11-01

G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.

Quantum description of light propagation in generalized media

NASA Astrophysics Data System (ADS)

Häyrynen, Teppo; Oksanen, Jani

2016-02-01

Linear quantum input-output relation based models are widely applied to describe the light propagation in a lossy medium. The details of the interaction and the associated added noise depend on whether the device is configured to operate as an amplifier or an attenuator. Using the traveling wave (TW) approach, we generalize the linear material model to simultaneously account for both the emission and absorption processes and to have point-wise defined noise field statistics and intensity dependent interaction strengths. Thus, our approach describes the quantum input-output relations of linear media with net attenuation, amplification or transparency without pre-selection of the operation point. The TW approach is then applied to investigate materials at thermal equilibrium, inverted materials, the transparency limit where losses are compensated, and the saturating amplifiers. We also apply the approach to investigate media in nonuniform states which can be e.g. consequences of a temperature gradient over the medium or a position dependent inversion of the amplifier. Furthermore, by using the generalized model we investigate devices with intensity dependent interactions and show how an initial thermal field transforms to a field having coherent statistics due to gain saturation.

Simplified biased random walk model for RecA-protein-mediated homology recognition offers rapid and accurate self-assembly of long linear arrays of binding sites

NASA Astrophysics Data System (ADS)

Kates-Harbeck, Julian; Tilloy, Antoine; Prentiss, Mara

2013-07-01

Inspired by RecA-protein-based homology recognition, we consider the pairing of two long linear arrays of binding sites. We propose a fully reversible, physically realizable biased random walk model for rapid and accurate self-assembly due to the spontaneous pairing of matching binding sites, where the statistics of the searched sample are included. In the model, there are two bound conformations, and the free energy for each conformation is a weakly nonlinear function of the number of contiguous matched bound sites.

Representing Micro-Macro Linkages by Actor-Based Dynamic Network Models

PubMed Central

Snijders, Tom A.B.; Steglich, Christian E.G.

2014-01-01

Stochastic actor-based models for network dynamics have the primary aim of statistical inference about processes of network change, but may be regarded as a kind of agent-based models. Similar to many other agent-based models, they are based on local rules for actor behavior. Different from many other agent-based models, by including elements of generalized linear statistical models they aim to be realistic detailed representations of network dynamics in empirical data sets. Statistical parallels to micro-macro considerations can be found in the estimation of parameters determining local actor behavior from empirical data, and the assessment of goodness of fit from the correspondence with network-level descriptives. This article studies several network-level consequences of dynamic actor-based models applied to represent cross-sectional network data. Two examples illustrate how network-level characteristics can be obtained as emergent features implied by micro-specifications of actor-based models. PMID:25960578

Fourier transform infrared reflectance spectra of latent fingerprints: a biometric gauge for the age of an individual.

PubMed

Hemmila, April; McGill, Jim; Ritter, David

2008-03-01

To determine if changes in fingerprint infrared spectra linear with age can be found, partial least squares (PLS1) regression of 155 fingerprint infrared spectra against the person's age was constructed. The regression produced a linear model of age as a function of spectrum with a root mean square error of calibration of less than 4 years, showing an inflection at about 25 years of age. The spectral ranges emphasized by the regression do not correspond to the highest concentration constituents of the fingerprints. Separate linear regression models for old and young people can be constructed with even more statistical rigor. The success of the regression demonstrates that a combination of constituents can be found that changes linearly with age, with a significant shift around puberty.

MIDAS: Regionally linear multivariate discriminative statistical mapping.

PubMed

Varol, Erdem; Sotiras, Aristeidis; Davatzikos, Christos

2018-07-01

Statistical parametric maps formed via voxel-wise mass-univariate tests, such as the general linear model, are commonly used to test hypotheses about regionally specific effects in neuroimaging cross-sectional studies where each subject is represented by a single image. Despite being informative, these techniques remain limited as they ignore multivariate relationships in the data. Most importantly, the commonly employed local Gaussian smoothing, which is important for accounting for registration errors and making the data follow Gaussian distributions, is usually chosen in an ad hoc fashion. Thus, it is often suboptimal for the task of detecting group differences and correlations with non-imaging variables. Information mapping techniques, such as searchlight, which use pattern classifiers to exploit multivariate information and obtain more powerful statistical maps, have become increasingly popular in recent years. However, existing methods may lead to important interpretation errors in practice (i.e., misidentifying a cluster as informative, or failing to detect truly informative voxels), while often being computationally expensive. To address these issues, we introduce a novel efficient multivariate statistical framework for cross-sectional studies, termed MIDAS, seeking highly sensitive and specific voxel-wise brain maps, while leveraging the power of regional discriminant analysis. In MIDAS, locally linear discriminative learning is applied to estimate the pattern that best discriminates between two groups, or predicts a variable of interest. This pattern is equivalent to local filtering by an optimal kernel whose coefficients are the weights of the linear discriminant. By composing information from all neighborhoods that contain a given voxel, MIDAS produces a statistic that collectively reflects the contribution of the voxel to the regional classifiers as well as the discriminative power of the classifiers. Critically, MIDAS efficiently assesses the statistical significance of the derived statistic by analytically approximating its null distribution without the need for computationally expensive permutation tests. The proposed framework was extensively validated using simulated atrophy in structural magnetic resonance imaging (MRI) and further tested using data from a task-based functional MRI study as well as a structural MRI study of cognitive performance. The performance of the proposed framework was evaluated against standard voxel-wise general linear models and other information mapping methods. The experimental results showed that MIDAS achieves relatively higher sensitivity and specificity in detecting group differences. Together, our results demonstrate the potential of the proposed approach to efficiently map effects of interest in both structural and functional data. Copyright © 2018. Published by Elsevier Inc.

An empirical comparison of statistical tests for assessing the proportional hazards assumption of Cox's model.

PubMed

Ng'andu, N H

1997-03-30

In the analysis of survival data using the Cox proportional hazard (PH) model, it is important to verify that the explanatory variables analysed satisfy the proportional hazard assumption of the model. This paper presents results of a simulation study that compares five test statistics to check the proportional hazard assumption of Cox's model. The test statistics were evaluated under proportional hazards and the following types of departures from the proportional hazard assumption: increasing relative hazards; decreasing relative hazards; crossing hazards; diverging hazards, and non-monotonic hazards. The test statistics compared include those based on partitioning of failure time and those that do not require partitioning of failure time. The simulation results demonstrate that the time-dependent covariate test, the weighted residuals score test and the linear correlation test have equally good power for detection of non-proportionality in the varieties of non-proportional hazards studied. Using illustrative data from the literature, these test statistics performed similarly.

Modelling of Dictyostelium discoideum movement in a linear gradient of chemoattractant.

PubMed

Eidi, Zahra; Mohammad-Rafiee, Farshid; Khorrami, Mohammad; Gholami, Azam

2017-11-15

Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the statistical features of the chemotactic motion of the social amoeba Dictyostelium discoideum in a linear gradient of cAMP (cyclic adenosine monophosphate). We fit the model to experimental trajectories that are recorded in a microfluidic setup with stationary cAMP gradients and extract the diffusion and drift coefficients in the gradient direction. Our analysis shows that for the majority of gradients, both coefficients decrease over time and become negative as the cells crawl up the gradient. The extracted model parameters also show that besides the expected drift in the direction of the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on time, which can be explained by the model. Furthermore, the results of the model show that the non-linear term in the mean squared displacement of the cell trajectories can dominate the linear term on large time scales.

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

Evaluating a linearized Euler equations model for strong turbulence effects on sound propagation.

PubMed

Ehrhardt, Loïc; Cheinet, Sylvain; Juvé, Daniel; Blanc-Benon, Philippe

2013-04-01

Sound propagation outdoors is strongly affected by atmospheric turbulence. Under strongly perturbed conditions or long propagation paths, the sound fluctuations reach their asymptotic behavior, e.g., the intensity variance progressively saturates. The present study evaluates the ability of a numerical propagation model based on the finite-difference time-domain solving of the linearized Euler equations in quantitatively reproducing the wave statistics under strong and saturated intensity fluctuations. It is the continuation of a previous study where weak intensity fluctuations were considered. The numerical propagation model is presented and tested with two-dimensional harmonic sound propagation over long paths and strong atmospheric perturbations. The results are compared to quantitative theoretical or numerical predictions available on the wave statistics, including the log-amplitude variance and the probability density functions of the complex acoustic pressure. The match is excellent for the evaluated source frequencies and all sound fluctuations strengths. Hence, this model captures these many aspects of strong atmospheric turbulence effects on sound propagation. Finally, the model results for the intensity probability density function are compared with a standard fit by a generalized gamma function.

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.

Dynamic Modeling and Very Short-term Prediction of Wind Power Output Using Box-Cox Transformation

NASA Astrophysics Data System (ADS)

Urata, Kengo; Inoue, Masaki; Murayama, Dai; Adachi, Shuichi

2016-09-01

We propose a statistical modeling method of wind power output for very short-term prediction. The modeling method with a nonlinear model has cascade structure composed of two parts. One is a linear dynamic part that is driven by a Gaussian white noise and described by an autoregressive model. The other is a nonlinear static part that is driven by the output of the linear part. This nonlinear part is designed for output distribution matching: we shape the distribution of the model output to match with that of the wind power output. The constructed model is utilized for one-step ahead prediction of the wind power output. Furthermore, we study the relation between the prediction accuracy and the prediction horizon.

Key Results of Interaction Models with Centering

ERIC Educational Resources Information Center

Afshartous, David; Preston, Richard A.

2011-01-01

We consider the effect on estimation of simultaneous variable centering and interaction effects in linear regression. We technically define, review, and amplify many of the statistical issues for interaction models with centering in order to create a useful and compact reference for teachers, students, and applied researchers. In addition, we…

A General Approach to Causal Mediation Analysis

ERIC Educational Resources Information Center

Imai, Kosuke; Keele, Luke; Tingley, Dustin

2010-01-01

Traditionally in the social sciences, causal mediation analysis has been formulated, understood, and implemented within the framework of linear structural equation models. We argue and demonstrate that this is problematic for 3 reasons: the lack of a general definition of causal mediation effects independent of a particular statistical model, the…

A comparative study between nonlinear regression and nonparametric approaches for modelling Phalaris paradoxa seedling emergence

USDA-ARS?s Scientific Manuscript database

Parametric non-linear regression (PNR) techniques commonly are used to develop weed seedling emergence models. Such techniques, however, require statistical assumptions that are difficult to meet. To examine and overcome these limitations, we compared PNR with a nonparametric estimation technique. F...

INTERANNUAL VARIATION IN METEOROLOGICALLY ADJUSTED OZONE LEVELS IN THE EASTERN UNITED STATES: A COMPARISON OF TWO APPROACHED

EPA Science Inventory

Assessing the influence of abatement efforts and other human activities on ozone levels is complicated by the atmosphere's changeable nature. Two statistical methods, the dynamic linear model(DLM) and the generalized additive model (GAM), are used to estimate ozone trends in the...

A Kp-based model of auroral boundaries

NASA Astrophysics Data System (ADS)

Carbary, James F.

2005-10-01

The auroral oval can serve as both a representation and a prediction of space weather on a global scale, so a competent model of the oval as a function of a geomagnetic index could conveniently appraise space weather itself. A simple model of the auroral boundaries is constructed by binning several months of images from the Polar Ultraviolet Imager by Kp index. The pixel intensities are first averaged into magnetic latitude-magnetic local time (MLT-MLAT) and local time bins, and intensity profiles are then derived for each Kp level at 1 hour intervals of MLT. After background correction, the boundary latitudes of each profile are determined at a threshold of 4 photons cm-2 s1. The peak locations and peak intensities are also found. The boundary and peak locations vary linearly with Kp index, and the coefficients of the linear fits are tabulated for each MLT. As a general rule of thumb, the UV intensity peak shifts 1° in magnetic latitude for each increment in Kp. The fits are surprisingly good for Kp < 6 but begin to deteriorate at high Kp because of auroral boundary irregularities and poor statistics. The statistical model allows calculation of the auroral boundaries at most MLTs as a function of Kp and can serve as an approximation to the shape and extent of the statistical oval.

[Application of ordinary Kriging method in entomologic ecology].

PubMed

Zhang, Runjie; Zhou, Qiang; Chen, Cuixian; Wang, Shousong

2003-01-01

Geostatistics is a statistic method based on regional variables and using the tool of variogram to analyze the spatial structure and the patterns of organism. In simulating the variogram within a great range, though optimal simulation cannot be obtained, the simulation method of a dialogue between human and computer can be used to optimize the parameters of the spherical models. In this paper, the method mentioned above and the weighted polynomial regression were utilized to simulate the one-step spherical model, the two-step spherical model and linear function model, and the available nearby samples were used to draw on the ordinary Kriging procedure, which provided a best linear unbiased estimate of the constraint of the unbiased estimation. The sum of square deviation between the estimating and measuring values of varying theory models were figured out, and the relative graphs were shown. It was showed that the simulation based on the two-step spherical model was the best simulation, and the one-step spherical model was better than the linear function model.

On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series

NASA Astrophysics Data System (ADS)

Gottwald, Georg A.; Wormell, J. P.; Wouters, Jeroen

2016-09-01

Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model of the observations, based on results for central limit theorems for deterministic dynamical systems, and used to detect linear response breakdown. We apply the method to discrete maps which do not obey linear response and show that the successful detection of breakdown depends on the length of the time series, the magnitude of the perturbation and on the choice of the observable. We find that in order to reliably reject the assumption of linear response for typical observables sufficiently large data sets are needed. Even for simple systems such as the logistic map, one needs of the order of 106 observations to reliably detect the breakdown with a confidence level of 95 %; if less observations are available one may be falsely led to conclude that linear response theory is valid. The amount of data required is larger the smaller the applied perturbation. For judiciously chosen observables the necessary amount of data can be drastically reduced, but requires detailed a priori knowledge about the invariant measure which is typically not available for complex dynamical systems. Furthermore we explore the use of the fluctuation-dissipation theorem (FDT) in cases with limited data length or coarse-graining of observations. The FDT, if applied naively to a system without linear response, is shown to be very sensitive to the details of the sampling method, resulting in erroneous predictions of the response.

Statistical modeling of the reactions Fe(+) + N2O → FeO(+) + N2 and FeO(+) + CO → Fe(+) + CO2.

PubMed

Ushakov, Vladimir G; Troe, Jürgen; Johnson, Ryan S; Guo, Hua; Ard, Shaun G; Melko, Joshua J; Shuman, Nicholas S; Viggiano, Albert A

2015-08-14

The rates of the reactions Fe(+) + N2O → FeO(+) + N2 and FeO(+) + CO → Fe(+) + CO2 are modeled by statistical rate theory accounting for energy- and angular momentum-specific rate constants for formation of the primary and secondary cationic adducts and their backward and forward reactions. The reactions are both suggested to proceed on sextet and quartet potential energy surfaces with efficient, but probably not complete, equilibration by spin-inversion of the populations of the sextet and quartet adducts. The influence of spin-inversion on the overall reaction rate is investigated. The differences of the two reaction rates mostly are due to different numbers of entrance states (atom + linear rotor or linear rotor + linear rotor, respectively). The reaction Fe(+) + N2O was studied either with (6)Fe(+) or with (4)Fe(+) reactants. Differences in the rate constants of (6)Fe(+) and (4)Fe(+) reacting with N2O are attributed to different contributions from electronically excited potential energy surfaces, such as they originate from the open-electronic shell reactants.

Modeling of Acoustic Field Statistics for Deep and Shallow Water Environments and 2015 CANAPE Pilot Study Moored Oceanographic Observations

DTIC Science & Technology

2015-09-30

into acoustic fluctuation calculations. In the Philippine Sea, models of eddies, internal tides, internal waves, and fine structure ( spice ) are...needed, while in the shallow water case a models of the random linear internal waves and spice are lacking. APPROACH The approach to this research is to

Quality of life in breast cancer patients--a quantile regression analysis.

PubMed

Pourhoseingholi, Mohamad Amin; Safaee, Azadeh; Moghimi-Dehkordi, Bijan; Zeighami, Bahram; Faghihzadeh, Soghrat; Tabatabaee, Hamid Reza; Pourhoseingholi, Asma

2008-01-01

Quality of life study has an important role in health care especially in chronic diseases, in clinical judgment and in medical resources supplying. Statistical tools like linear regression are widely used to assess the predictors of quality of life. But when the response is not normal the results are misleading. The aim of this study is to determine the predictors of quality of life in breast cancer patients, using quantile regression model and compare to linear regression. A cross-sectional study conducted on 119 breast cancer patients that admitted and treated in chemotherapy ward of Namazi hospital in Shiraz. We used QLQ-C30 questionnaire to assessment quality of life in these patients. A quantile regression was employed to assess the assocciated factors and the results were compared to linear regression. All analysis carried out using SAS. The mean score for the global health status for breast cancer patients was 64.92+/-11.42. Linear regression showed that only grade of tumor, occupational status, menopausal status, financial difficulties and dyspnea were statistically significant. In spite of linear regression, financial difficulties were not significant in quantile regression analysis and dyspnea was only significant for first quartile. Also emotion functioning and duration of disease statistically predicted the QOL score in the third quartile. The results have demonstrated that using quantile regression leads to better interpretation and richer inference about predictors of the breast cancer patient quality of life.

Drivers willingness to pay progressive rate for street parking.

DOT National Transportation Integrated Search

2015-01-01

This study finds willingness to pay and price elasticity for on-street parking demand using stated : preference data obtained from 238 respondents. Descriptive, statistical and economic analyses including : regression, generalized linear model, and f...

Testing the dose-response specification in epidemiology: public health and policy consequences for lead.

PubMed

Rothenberg, Stephen J; Rothenberg, Jesse C

2005-09-01

Statistical evaluation of the dose-response function in lead epidemiology is rarely attempted. Economic evaluation of health benefits of lead reduction usually assumes a linear dose-response function, regardless of the outcome measure used. We reanalyzed a previously published study, an international pooled data set combining data from seven prospective lead studies examining contemporaneous blood lead effect on IQ (intelligence quotient) of 7-year-old children (n = 1,333). We constructed alternative linear multiple regression models with linear blood lead terms (linear-linear dose response) and natural-log-transformed blood lead terms (log-linear dose response). We tested the two lead specifications for nonlinearity in the models, compared the two lead specifications for significantly better fit to the data, and examined the effects of possible residual confounding on the functional form of the dose-response relationship. We found that a log-linear lead-IQ relationship was a significantly better fit than was a linear-linear relationship for IQ (p = 0.009), with little evidence of residual confounding of included model variables. We substituted the log-linear lead-IQ effect in a previously published health benefits model and found that the economic savings due to U.S. population lead decrease between 1976 and 1999 (from 17.1 microg/dL to 2.0 microg/dL) was 2.2 times (319 billion dollars) that calculated using a linear-linear dose-response function (149 billion dollars). The Centers for Disease Control and Prevention action limit of 10 microg/dL for children fails to protect against most damage and economic cost attributable to lead exposure.

ADME evaluation in drug discovery. 1. Applications of genetic algorithms to the prediction of blood-brain partitioning of a large set of drugs.

PubMed

Hou, Tingjun; Xu, Xiaojie

2002-12-01

In this study, the relationships between the brain-blood concentration ratio of 96 structurally diverse compounds with a large number of structurally derived descriptors were investigated. The linear models were based on molecular descriptors that can be calculated for any compound simply from a knowledge of its molecular structure. The linear correlation coefficients of the models were optimized by genetic algorithms (GAs), and the descriptors used in the linear models were automatically selected from 27 structurally derived descriptors. The GA optimizations resulted in a group of linear models with three or four molecular descriptors with good statistical significance. The change of descriptor use as the evolution proceeds demonstrates that the octane/water partition coefficient and the partial negative solvent-accessible surface area multiplied by the negative charge are crucial to brain-blood barrier permeability. Moreover, we found that the predictions using multiple QSPR models from GA optimization gave quite good results in spite of the diversity of structures, which was better than the predictions using the best single model. The predictions for the two external sets with 37 diverse compounds using multiple QSPR models indicate that the best linear models with four descriptors are sufficiently effective for predictive use. Considering the ease of computation of the descriptors, the linear models may be used as general utilities to screen the blood-brain barrier partitioning of drugs in a high-throughput fashion.

Error Analysis for RADAR Neighbor Matching Localization in Linear Logarithmic Strength Varying Wi-Fi Environment

PubMed Central

Tian, Zengshan; Xu, Kunjie; Yu, Xiang

2014-01-01

This paper studies the statistical errors for the fingerprint-based RADAR neighbor matching localization with the linearly calibrated reference points (RPs) in logarithmic received signal strength (RSS) varying Wi-Fi environment. To the best of our knowledge, little comprehensive analysis work has appeared on the error performance of neighbor matching localization with respect to the deployment of RPs. However, in order to achieve the efficient and reliable location-based services (LBSs) as well as the ubiquitous context-awareness in Wi-Fi environment, much attention has to be paid to the highly accurate and cost-efficient localization systems. To this end, the statistical errors by the widely used neighbor matching localization are significantly discussed in this paper to examine the inherent mathematical relations between the localization errors and the locations of RPs by using a basic linear logarithmic strength varying model. Furthermore, based on the mathematical demonstrations and some testing results, the closed-form solutions to the statistical errors by RADAR neighbor matching localization can be an effective tool to explore alternative deployment of fingerprint-based neighbor matching localization systems in the future. PMID:24683349

Error analysis for RADAR neighbor matching localization in linear logarithmic strength varying Wi-Fi environment.

PubMed

Zhou, Mu; Tian, Zengshan; Xu, Kunjie; Yu, Xiang; Wu, Haibo

2014-01-01

This paper studies the statistical errors for the fingerprint-based RADAR neighbor matching localization with the linearly calibrated reference points (RPs) in logarithmic received signal strength (RSS) varying Wi-Fi environment. To the best of our knowledge, little comprehensive analysis work has appeared on the error performance of neighbor matching localization with respect to the deployment of RPs. However, in order to achieve the efficient and reliable location-based services (LBSs) as well as the ubiquitous context-awareness in Wi-Fi environment, much attention has to be paid to the highly accurate and cost-efficient localization systems. To this end, the statistical errors by the widely used neighbor matching localization are significantly discussed in this paper to examine the inherent mathematical relations between the localization errors and the locations of RPs by using a basic linear logarithmic strength varying model. Furthermore, based on the mathematical demonstrations and some testing results, the closed-form solutions to the statistical errors by RADAR neighbor matching localization can be an effective tool to explore alternative deployment of fingerprint-based neighbor matching localization systems in the future.

AMOVA ["Accumulative Manifold Validation Analysis"]: An Advanced Statistical Methodology Designed to Measure and Test the Validity, Reliability, and Overall Efficacy of Inquiry-Based Psychometric Instruments

ERIC Educational Resources Information Center

Osler, James Edward, II

2015-01-01

This monograph provides an epistemological rational for the Accumulative Manifold Validation Analysis [also referred by the acronym "AMOVA"] statistical methodology designed to test psychometric instruments. This form of inquiry is a form of mathematical optimization in the discipline of linear stochastic modelling. AMOVA is an in-depth…

Climate sensitivity to the lower stratospheric ozone variations

NASA Astrophysics Data System (ADS)

Kilifarska, N. A.

2012-12-01

The strong sensitivity of the Earth's radiation balance to variations in the lower stratospheric ozone—reported previously—is analysed here by the use of non-linear statistical methods. Our non-linear model of the land air temperature (T)—driven by the measured Arosa total ozone (TOZ)—explains 75% of total variability of Earth's T variations during the period 1926-2011. We have analysed also the factors which could influence the TOZ variability and found that the strongest impact belongs to the multi-decadal variations of galactic cosmic rays. Constructing a statistical model of the ozone variability, we have been able to predict the tendency in the land air T evolution till the end of the current decade. Results show that Earth is facing a weak cooling of the surface T by 0.05-0.25 K (depending on the ozone model) until the end of the current solar cycle. A new mechanism for O3 influence on climate is proposed.

Generalized linear mixed models with varying coefficients for longitudinal data.

PubMed

Zhang, Daowen

2004-03-01

The routinely assumed parametric functional form in the linear predictor of a generalized linear mixed model for longitudinal data may be too restrictive to represent true underlying covariate effects. We relax this assumption by representing these covariate effects by smooth but otherwise arbitrary functions of time, with random effects used to model the correlation induced by among-subject and within-subject variation. Due to the usually intractable integration involved in evaluating the quasi-likelihood function, the double penalized quasi-likelihood (DPQL) approach of Lin and Zhang (1999, Journal of the Royal Statistical Society, Series B61, 381-400) is used to estimate the varying coefficients and the variance components simultaneously by representing a nonparametric function by a linear combination of fixed effects and random effects. A scaled chi-squared test based on the mixed model representation of the proposed model is developed to test whether an underlying varying coefficient is a polynomial of certain degree. We evaluate the performance of the procedures through simulation studies and illustrate their application with Indonesian children infectious disease data.

Non-linear learning in online tutorial to enhance students’ knowledge on normal distribution application topic

NASA Astrophysics Data System (ADS)

Kartono; Suryadi, D.; Herman, T.

2018-01-01

This study aimed to analyze the enhancement of non-linear learning (NLL) in the online tutorial (OT) content to students’ knowledge of normal distribution application (KONDA). KONDA is a competence expected to be achieved after students studied the topic of normal distribution application in the course named Education Statistics. The analysis was performed by quasi-experiment study design. The subject of the study was divided into an experimental class that was given OT content in NLL model and a control class which was given OT content in conventional learning (CL) model. Data used in this study were the results of online objective tests to measure students’ statistical prior knowledge (SPK) and students’ pre- and post-test of KONDA. The statistical analysis test of a gain score of KONDA of students who had low and moderate SPK’s scores showed students’ KONDA who learn OT content with NLL model was better than students’ KONDA who learn OT content with CL model. Meanwhile, for students who had high SPK’s scores, the gain score of students who learn OT content with NLL model had relatively similar with the gain score of students who learn OT content with CL model. Based on those findings it could be concluded that the NLL model applied to OT content could enhance KONDA of students in low and moderate SPK’s levels. Extra and more challenging didactical situation was needed for students in high SPK’s level to achieve the significant gain score.

Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

NASA Astrophysics Data System (ADS)

Takabe, Satoshi; Hukushima, Koji

2016-05-01

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.

Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems.

PubMed

Takabe, Satoshi; Hukushima, Koji

2016-05-01

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.

Secular Extragalactic Parallax and Geometric Distances with Gaia Proper Motions

NASA Astrophysics Data System (ADS)

Paine, Jennie; Darling, Jeremiah K.

2018-06-01

The motion of the Solar System with respect to the cosmic microwave background (CMB) rest frame creates a well measured dipole in the CMB, which corresponds to a linear solar velocity of about 78 AU/yr. This motion causes relatively nearby extragalactic objects to appear to move compared to more distant objects, an effect that can be measured in the proper motions of nearby galaxies. An object at 1 Mpc and perpendicular to the CMB apex will exhibit a secular parallax, observed as a proper motion, of 78 µas/yr. The relatively large peculiar motions of galaxies make the detection of secular parallax challenging for individual objects. Instead, a statistical parallax measurement can be made for a sample of objects with proper motions, where the global parallax signal is modeled as an E-mode dipole that diminishes linearly with distance. We present preliminary results of applying this model to a sample of nearby galaxies with Gaia proper motions to detect the statistical secular parallax signal. The statistical measurement can be used to calibrate the canonical cosmological “distance ladder.”

Statistics of Statisticians: Critical Mass of Statistics and Operational Research Groups

NASA Astrophysics Data System (ADS)

Kenna, Ralph; Berche, Bertrand

Using a recently developed model, inspired by mean field theory in statistical physics, and data from the UK's Research Assessment Exercise, we analyse the relationship between the qualities of statistics and operational research groups and the quantities of researchers in them. Similar to other academic disciplines, we provide evidence for a linear dependency of quality on quantity up to an upper critical mass, which is interpreted as the average maximum number of colleagues with whom a researcher can communicate meaningfully within a research group. The model also predicts a lower critical mass, which research groups should strive to achieve to avoid extinction. For statistics and operational research, the lower critical mass is estimated to be 9 ± 3. The upper critical mass, beyond which research quality does not significantly depend on group size, is 17 ± 6.

General Multivariate Linear Modeling of Surface Shapes Using SurfStat

PubMed Central

Chung, Moo K.; Worsley, Keith J.; Nacewicz, Brendon, M.; Dalton, Kim M.; Davidson, Richard J.

2010-01-01

Although there are many imaging studies on traditional ROI-based amygdala volumetry, there are very few studies on modeling amygdala shape variations. This paper present a unified computational and statistical framework for modeling amygdala shape variations in a clinical population. The weighted spherical harmonic representation is used as to parameterize, to smooth out, and to normalize amygdala surfaces. The representation is subsequently used as an input for multivariate linear models accounting for nuisance covariates such as age and brain size difference using SurfStat package that completely avoids the complexity of specifying design matrices. The methodology has been applied for quantifying abnormal local amygdala shape variations in 22 high functioning autistic subjects. PMID:20620211

Dimensional Reduction for the General Markov Model on Phylogenetic Trees.

PubMed

Sumner, Jeremy G

2017-03-01

We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multi-linear dependence in the full space. We discuss potential applications including the computation of split (edge) weights on phylogenetic trees from observed sequence data.

The effect of project-based learning on students' statistical literacy levels for data representation

NASA Astrophysics Data System (ADS)

Koparan, Timur; Güven, Bülent

2015-07-01

The point of this study is to define the effect of project-based learning approach on 8th Grade secondary-school students' statistical literacy levels for data representation. To achieve this goal, a test which consists of 12 open-ended questions in accordance with the views of experts was developed. Seventy 8th grade secondary-school students, 35 in the experimental group and 35 in the control group, took this test twice, one before the application and one after the application. All the raw scores were turned into linear points by using the Winsteps 3.72 modelling program that makes the Rasch analysis and t-tests, and an ANCOVA analysis was carried out with the linear points. Depending on the findings, it was concluded that the project-based learning approach increases students' level of statistical literacy for data representation. Students' levels of statistical literacy before and after the application were shown through the obtained person-item maps.

On statistical independence of a contingency matrix

NASA Astrophysics Data System (ADS)

Tsumoto, Shusaku; Hirano, Shoji

2005-03-01

A contingency table summarizes the conditional frequencies of two attributes and shows how these two attributes are dependent on each other with the information on a partition of universe generated by these attributes. Thus, this table can be viewed as a relation between two attributes with respect to information granularity. This paper focuses on several characteristics of linear and statistical independence in a contingency table from the viewpoint of granular computing, which shows that statistical independence in a contingency table is a special form of linear dependence. The discussions also show that when a contingency table is viewed as a matrix, called a contingency matrix, its rank is equal to 1.0. Thus, the degree of independence, rank plays a very important role in extracting a probabilistic model from a given contingency table. Furthermore, it is found that in some cases, partial rows or columns will satisfy the condition of statistical independence, which can be viewed as a solving process of Diophatine equations.

Statistics of Macroturbulence from Flow Equations

NASA Astrophysics Data System (ADS)

Marston, Brad; Iadecola, Thomas; Qi, Wanming

2012-02-01

Probability distribution functions of stochastically-driven and frictionally-damped fluids are governed by a linear framework that resembles quantum many-body theory. Besides the Fokker-Planck approach, there is a closely related Hopf functional methodfootnotetextOokie Ma and J. B. Marston, J. Stat. Phys. Th. Exp. P10007 (2005).; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we generalize the flow equation approachfootnotetextF. Wegner, Ann. Phys. 3, 77 (1994). (also known as the method of continuous unitary transformationsfootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994).) to find the zero mode. We test the approach using a prototypical model of geophysical and astrophysical flows on a rotating sphere that spontaneously organizes into a coherent jet. Good agreement is found with low-order equal-time statistics accumulated by direct numerical simulation, the traditional method. Different choices for the generators of the continuous transformations, and for closure approximations of the operator algebra, are discussed.

Massive parallelization of serial inference algorithms for a complex generalized linear model

PubMed Central

Suchard, Marc A.; Simpson, Shawn E.; Zorych, Ivan; Ryan, Patrick; Madigan, David

2014-01-01

Following a series of high-profile drug safety disasters in recent years, many countries are redoubling their efforts to ensure the safety of licensed medical products. Large-scale observational databases such as claims databases or electronic health record systems are attracting particular attention in this regard, but present significant methodological and computational concerns. In this paper we show how high-performance statistical computation, including graphics processing units, relatively inexpensive highly parallel computing devices, can enable complex methods in large databases. We focus on optimization and massive parallelization of cyclic coordinate descent approaches to fit a conditioned generalized linear model involving tens of millions of observations and thousands of predictors in a Bayesian context. We find orders-of-magnitude improvement in overall run-time. Coordinate descent approaches are ubiquitous in high-dimensional statistics and the algorithms we propose open up exciting new methodological possibilities with the potential to significantly improve drug safety. PMID:25328363

A theory of fine structure image models with an application to detection and classification of dementia.

PubMed

O'Neill, William; Penn, Richard; Werner, Michael; Thomas, Justin

2015-06-01

Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible.

Prediction of rainfall anomalies during the dry to wet transition season over the Southern Amazonia using machine learning tools

NASA Astrophysics Data System (ADS)

Shan, X.; Zhang, K.; Zhuang, Y.; Fu, R.; Hong, Y.

2017-12-01

Seasonal prediction of rainfall during the dry-to-wet transition season in austral spring (September-November) over southern Amazonia is central for improving planting crops and fire mitigation in that region. Previous studies have identified the key large-scale atmospheric dynamic and thermodynamics pre-conditions during the dry season (June-August) that influence the rainfall anomalies during the dry to wet transition season over Southern Amazonia. Based on these key pre-conditions during dry season, we have evaluated several statistical models and developed a Neural Network based statistical prediction system to predict rainfall during the dry to wet transition for Southern Amazonia (5-15°S, 50-70°W). Multivariate Empirical Orthogonal Function (EOF) Analysis is applied to the following four fields during JJA from the ECMWF Reanalysis (ERA-Interim) spanning from year 1979 to 2015: geopotential height at 200 hPa, surface relative humidity, convective inhibition energy (CIN) index and convective available potential energy (CAPE), to filter out noise and highlight the most coherent spatial and temporal variations. The first 10 EOF modes are retained for inputs to the statistical models, accounting for at least 70% of the total variance in the predictor fields. We have tested several linear and non-linear statistical methods. While the regularized Ridge Regression and Lasso Regression can generally capture the spatial pattern and magnitude of rainfall anomalies, we found that that Neural Network performs best with an accuracy greater than 80%, as expected from the non-linear dependence of the rainfall on the large-scale atmospheric thermodynamic conditions and circulation. Further tests of various prediction skill metrics and hindcasts also suggest this Neural Network prediction approach can significantly improve seasonal prediction skill than the dynamic predictions and regression based statistical predictions. Thus, this statistical prediction system could have shown potential to improve real-time seasonal rainfall predictions in the future.

A Comparison of Conventional Linear Regression Methods and Neural Networks for Forecasting Educational Spending.

ERIC Educational Resources Information Center

Baker, Bruce D.; Richards, Craig E.

1999-01-01

Applies neural network methods for forecasting 1991-95 per-pupil expenditures in U.S. public elementary and secondary schools. Forecasting models included the National Center for Education Statistics' multivariate regression model and three neural architectures. Regarding prediction accuracy, neural network results were comparable or superior to…

Minimizing bias in biomass allometry: Model selection and log transformation of data

Treesearch

Joseph Mascaro; undefined undefined; Flint Hughes; Amanda Uowolo; Stefan A. Schnitzer

2011-01-01

Nonlinear regression is increasingly used to develop allometric equations for forest biomass estimation (i.e., as opposed to the raditional approach of log-transformation followed by linear regression). Most statistical software packages, however, assume additive errors by default, violating a key assumption of allometric theory and possibly producing spurious models....

Assessing risk factors for periodontitis using regression

NASA Astrophysics Data System (ADS)

Lobo Pereira, J. A.; Ferreira, Maria Cristina; Oliveira, Teresa

2013-10-01

Multivariate statistical analysis is indispensable to assess the associations and interactions between different factors and the risk of periodontitis. Among others, regression analysis is a statistical technique widely used in healthcare to investigate and model the relationship between variables. In our work we study the impact of socio-demographic, medical and behavioral factors on periodontal health. Using regression, linear and logistic models, we can assess the relevance, as risk factors for periodontitis disease, of the following independent variables (IVs): Age, Gender, Diabetic Status, Education, Smoking status and Plaque Index. The multiple linear regression analysis model was built to evaluate the influence of IVs on mean Attachment Loss (AL). Thus, the regression coefficients along with respective p-values will be obtained as well as the respective p-values from the significance tests. The classification of a case (individual) adopted in the logistic model was the extent of the destruction of periodontal tissues defined by an Attachment Loss greater than or equal to 4 mm in 25% (AL≥4mm/≥25%) of sites surveyed. The association measures include the Odds Ratios together with the correspondent 95% confidence intervals.

A Model Comparison for Count Data with a Positively Skewed Distribution with an Application to the Number of University Mathematics Courses Completed

ERIC Educational Resources Information Center

Liou, Pey-Yan

2009-01-01

The current study examines three regression models: OLS (ordinary least square) linear regression, Poisson regression, and negative binomial regression for analyzing count data. Simulation results show that the OLS regression model performed better than the others, since it did not produce more false statistically significant relationships than…

Building out a Measurement Model to Incorporate Complexities of Testing in the Language Domain

ERIC Educational Resources Information Center

Wilson, Mark; Moore, Stephen

2011-01-01

This paper provides a summary of a novel and integrated way to think about the item response models (most often used in measurement applications in social science areas such as psychology, education, and especially testing of various kinds) from the viewpoint of the statistical theory of generalized linear and nonlinear mixed models. In addition,…

A comparison of optimal MIMO linear and nonlinear models for brain machine interfaces

NASA Astrophysics Data System (ADS)

Kim, S.-P.; Sanchez, J. C.; Rao, Y. N.; Erdogmus, D.; Carmena, J. M.; Lebedev, M. A.; Nicolelis, M. A. L.; Principe, J. C.

2006-06-01

The field of brain-machine interfaces requires the estimation of a mapping from spike trains collected in motor cortex areas to the hand kinematics of the behaving animal. This paper presents a systematic investigation of several linear (Wiener filter, LMS adaptive filters, gamma filter, subspace Wiener filters) and nonlinear models (time-delay neural network and local linear switching models) applied to datasets from two experiments in monkeys performing motor tasks (reaching for food and target hitting). Ensembles of 100-200 cortical neurons were simultaneously recorded in these experiments, and even larger neuronal samples are anticipated in the future. Due to the large size of the models (thousands of parameters), the major issue studied was the generalization performance. Every parameter of the models (not only the weights) was selected optimally using signal processing and machine learning techniques. The models were also compared statistically with respect to the Wiener filter as the baseline. Each of the optimization procedures produced improvements over that baseline for either one of the two datasets or both.

A comparison of optimal MIMO linear and nonlinear models for brain-machine interfaces.

PubMed

Kim, S-P; Sanchez, J C; Rao, Y N; Erdogmus, D; Carmena, J M; Lebedev, M A; Nicolelis, M A L; Principe, J C

2006-06-01

The field of brain-machine interfaces requires the estimation of a mapping from spike trains collected in motor cortex areas to the hand kinematics of the behaving animal. This paper presents a systematic investigation of several linear (Wiener filter, LMS adaptive filters, gamma filter, subspace Wiener filters) and nonlinear models (time-delay neural network and local linear switching models) applied to datasets from two experiments in monkeys performing motor tasks (reaching for food and target hitting). Ensembles of 100-200 cortical neurons were simultaneously recorded in these experiments, and even larger neuronal samples are anticipated in the future. Due to the large size of the models (thousands of parameters), the major issue studied was the generalization performance. Every parameter of the models (not only the weights) was selected optimally using signal processing and machine learning techniques. The models were also compared statistically with respect to the Wiener filter as the baseline. Each of the optimization procedures produced improvements over that baseline for either one of the two datasets or both.

The Box-Cox power transformation on nursing sensitive indicators: Does it matter if structural effects are omitted during the estimation of the transformation parameter?

PubMed Central

2011-01-01

Background Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The Box-Cox transformation provides a powerful tool for developing a parsimonious model for data representation and interpretation when the distribution of the dependent variable, or outcome measure, of interest deviates from the normal distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings. Methods Simulation data from a 3 × 4 factorial treatments design, along with the Patient Falls and Patient Injury Falls from the National Database of Nursing Quality Indicators (NDNQI®) for the 3rd quarter of 2007 from a convenience sample of over one thousand US hospitals were analyzed. The effect of the nonlinear monotonic transformation was contrasted in two ways: a) estimating the transformation parameter along with factors with potential structural effects, and b) estimating the transformation parameter first and then conducting analysis of variance for the structural effect. Results Linear model ANOVA with Monte Carlo simulation and mixed models with correlated error terms with NDNQI examples showed no substantial differences on statistical tests for structural effects if the factors with structural effects were omitted during the estimation of the transformation parameter. Conclusions The Box-Cox power transformation can still be an effective tool for validating statistical inferences with large observational, cross-sectional, and hierarchical or repeated measure studies under the linear or the mixed model settings without prior knowledge of all the factors with potential structural effects. PMID:21854614

The Box-Cox power transformation on nursing sensitive indicators: does it matter if structural effects are omitted during the estimation of the transformation parameter?

PubMed

Hou, Qingjiang; Mahnken, Jonathan D; Gajewski, Byron J; Dunton, Nancy

2011-08-19

Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The Box-Cox transformation provides a powerful tool for developing a parsimonious model for data representation and interpretation when the distribution of the dependent variable, or outcome measure, of interest deviates from the normal distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings. Simulation data from a 3 × 4 factorial treatments design, along with the Patient Falls and Patient Injury Falls from the National Database of Nursing Quality Indicators (NDNQI® for the 3rd quarter of 2007 from a convenience sample of over one thousand US hospitals were analyzed. The effect of the nonlinear monotonic transformation was contrasted in two ways: a) estimating the transformation parameter along with factors with potential structural effects, and b) estimating the transformation parameter first and then conducting analysis of variance for the structural effect. Linear model ANOVA with Monte Carlo simulation and mixed models with correlated error terms with NDNQI examples showed no substantial differences on statistical tests for structural effects if the factors with structural effects were omitted during the estimation of the transformation parameter. The Box-Cox power transformation can still be an effective tool for validating statistical inferences with large observational, cross-sectional, and hierarchical or repeated measure studies under the linear or the mixed model settings without prior knowledge of all the factors with potential structural effects.

Pattern Recognition Analysis of Age-Related Retinal Ganglion Cell Signatures in the Human Eye

PubMed Central

Yoshioka, Nayuta; Zangerl, Barbara; Nivison-Smith, Lisa; Khuu, Sieu K.; Jones, Bryan W.; Pfeiffer, Rebecca L.; Marc, Robert E.; Kalloniatis, Michael

2017-01-01

Purpose To characterize macular ganglion cell layer (GCL) changes with age and provide a framework to assess changes in ocular disease. This study used data clustering to analyze macular GCL patterns from optical coherence tomography (OCT) in a large cohort of subjects without ocular disease. Methods Single eyes of 201 patients evaluated at the Centre for Eye Health (Sydney, Australia) were retrospectively enrolled (age range, 20–85); 8 × 8 grid locations obtained from Spectralis OCT macular scans were analyzed with unsupervised classification into statistically separable classes sharing common GCL thickness and change with age. The resulting classes and gridwise data were fitted with linear and segmented linear regression curves. Additionally, normalized data were analyzed to determine regression as a percentage. Accuracy of each model was examined through comparison of predicted 50-year-old equivalent macular GCL thickness for the entire cohort to a true 50-year-old reference cohort. Results Pattern recognition clustered GCL thickness across the macula into five to eight spatially concentric classes. F-test demonstrated segmented linear regression to be the most appropriate model for macular GCL change. The pattern recognition–derived and normalized model revealed less difference between the predicted macular GCL thickness and the reference cohort (average ± SD 0.19 ± 0.92 and −0.30 ± 0.61 μm) than a gridwise model (average ± SD 0.62 ± 1.43 μm). Conclusions Pattern recognition successfully identified statistically separable macular areas that undergo a segmented linear reduction with age. This regression model better predicted macular GCL thickness. The various unique spatial patterns revealed by pattern recognition combined with core GCL thickness data provide a framework to analyze GCL loss in ocular disease. PMID:28632847

Effect of correlation on covariate selection in linear and nonlinear mixed effect models.

PubMed

Bonate, Peter L

2017-01-01

The effect of correlation among covariates on covariate selection was examined with linear and nonlinear mixed effect models. Demographic covariates were extracted from the National Health and Nutrition Examination Survey III database. Concentration-time profiles were Monte Carlo simulated where only one covariate affected apparent oral clearance (CL/F). A series of univariate covariate population pharmacokinetic models was fit to the data and compared with the reduced model without covariate. The "best" covariate was identified using either the likelihood ratio test statistic or AIC. Weight and body surface area (calculated using Gehan and George equation, 1970) were highly correlated (r = 0.98). Body surface area was often selected as a better covariate than weight, sometimes as high as 1 in 5 times, when weight was the covariate used in the data generating mechanism. In a second simulation, parent drug concentration and three metabolites were simulated from a thorough QT study and used as covariates in a series of univariate linear mixed effects models of ddQTc interval prolongation. The covariate with the largest significant LRT statistic was deemed the "best" predictor. When the metabolite was formation-rate limited and only parent concentrations affected ddQTc intervals the metabolite was chosen as a better predictor as often as 1 in 5 times depending on the slope of the relationship between parent concentrations and ddQTc intervals. A correlated covariate can be chosen as being a better predictor than another covariate in a linear or nonlinear population analysis by sheer correlation These results explain why for the same drug different covariates may be identified in different analyses. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Groundwater-level prediction using multiple linear regression and artificial neural network techniques: a comparative assessment

NASA Astrophysics Data System (ADS)

Sahoo, Sasmita; Jha, Madan K.

2013-12-01

The potential of multiple linear regression (MLR) and artificial neural network (ANN) techniques in predicting transient water levels over a groundwater basin were compared. MLR and ANN modeling was carried out at 17 sites in Japan, considering all significant inputs: rainfall, ambient temperature, river stage, 11 seasonal dummy variables, and influential lags of rainfall, ambient temperature, river stage and groundwater level. Seventeen site-specific ANN models were developed, using multi-layer feed-forward neural networks trained with Levenberg-Marquardt backpropagation algorithms. The performance of the models was evaluated using statistical and graphical indicators. Comparison of the goodness-of-fit statistics of the MLR models with those of the ANN models indicated that there is better agreement between the ANN-predicted groundwater levels and the observed groundwater levels at all the sites, compared to the MLR. This finding was supported by the graphical indicators and the residual analysis. Thus, it is concluded that the ANN technique is superior to the MLR technique in predicting spatio-temporal distribution of groundwater levels in a basin. However, considering the practical advantages of the MLR technique, it is recommended as an alternative and cost-effective groundwater modeling tool.

A simple linear regression method for quantitative trait loci linkage analysis with censored observations.

PubMed

Anderson, Carl A; McRae, Allan F; Visscher, Peter M

2006-07-01

Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.

Reflexion on linear regression trip production modelling method for ensuring good model quality

NASA Astrophysics Data System (ADS)

Suprayitno, Hitapriya; Ratnasari, Vita

2017-11-01

Transport Modelling is important. For certain cases, the conventional model still has to be used, in which having a good trip production model is capital. A good model can only be obtained from a good sample. Two of the basic principles of a good sampling is having a sample capable to represent the population characteristics and capable to produce an acceptable error at a certain confidence level. It seems that this principle is not yet quite understood and used in trip production modeling. Therefore, investigating the Trip Production Modelling practice in Indonesia and try to formulate a better modeling method for ensuring the Model Quality is necessary. This research result is presented as follows. Statistics knows a method to calculate span of prediction value at a certain confidence level for linear regression, which is called Confidence Interval of Predicted Value. The common modeling practice uses R2 as the principal quality measure, the sampling practice varies and not always conform to the sampling principles. An experiment indicates that small sample is already capable to give excellent R2 value and sample composition can significantly change the model. Hence, good R2 value, in fact, does not always mean good model quality. These lead to three basic ideas for ensuring good model quality, i.e. reformulating quality measure, calculation procedure, and sampling method. A quality measure is defined as having a good R2 value and a good Confidence Interval of Predicted Value. Calculation procedure must incorporate statistical calculation method and appropriate statistical tests needed. A good sampling method must incorporate random well distributed stratified sampling with a certain minimum number of samples. These three ideas need to be more developed and tested.

Weak lensing shear and aperture mass from linear to non-linear scales

NASA Astrophysics Data System (ADS)

Munshi, Dipak; Valageas, Patrick; Barber, Andrew J.

2004-05-01

We describe the predictions for the smoothed weak lensing shear, γs, and aperture mass,Map, of two simple analytical models of the density field: the minimal tree model and the stellar model. Both models give identical results for the statistics of the three-dimensional density contrast smoothed over spherical cells and only differ by the detailed angular dependence of the many-body density correlations. We have shown in previous work that they also yield almost identical results for the probability distribution function (PDF) of the smoothed convergence, κs. We find that the two models give rather close results for both the shear and the positive tail of the aperture mass. However, we note that at small angular scales (θs<~ 2 arcmin) the tail of the PDF, , for negative Map shows a strong variation between the two models, and the stellar model actually breaks down for θs<~ 0.4 arcmin and Map < 0. This shows that the statistics of the aperture mass provides a very precise probe of the detailed structure of the density field, as it is sensitive to both the amplitude and the detailed angular behaviour of the many-body correlations. On the other hand, the minimal tree model shows good agreement with numerical simulations over all the scales and redshifts of interest, while both models provide a good description of the PDF, , of the smoothed shear components. Therefore, the shear and the aperture mass provide robust and complementary tools to measure the cosmological parameters as well as the detailed statistical properties of the density field.

Detecting influential observations in nonlinear regression modeling of groundwater flow

USGS Publications Warehouse

Yager, Richard M.

1998-01-01

Nonlinear regression is used to estimate optimal parameter values in models of groundwater flow to ensure that differences between predicted and observed heads and flows do not result from nonoptimal parameter values. Parameter estimates can be affected, however, by observations that disproportionately influence the regression, such as outliers that exert undue leverage on the objective function. Certain statistics developed for linear regression can be used to detect influential observations in nonlinear regression if the models are approximately linear. This paper discusses the application of Cook's D, which measures the effect of omitting a single observation on a set of estimated parameter values, and the statistical parameter DFBETAS, which quantifies the influence of an observation on each parameter. The influence statistics were used to (1) identify the influential observations in the calibration of a three-dimensional, groundwater flow model of a fractured-rock aquifer through nonlinear regression, and (2) quantify the effect of omitting influential observations on the set of estimated parameter values. Comparison of the spatial distribution of Cook's D with plots of model sensitivity shows that influential observations correspond to areas where the model heads are most sensitive to certain parameters, and where predicted groundwater flow rates are largest. Five of the six discharge observations were identified as influential, indicating that reliable measurements of groundwater flow rates are valuable data in model calibration. DFBETAS are computed and examined for an alternative model of the aquifer system to identify a parameterization error in the model design that resulted in overestimation of the effect of anisotropy on horizontal hydraulic conductivity.

Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

PubMed

Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

2014-04-02

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

Implicit Wiener series analysis of epileptic seizure recordings.

PubMed

Barbero, Alvaro; Franz, Matthias; van Drongelen, Wim; Dorronsoro, José R; Schölkopf, Bernhard; Grosse-Wentrup, Moritz

2009-01-01

Implicit Wiener series are a powerful tool to build Volterra representations of time series with any degree of non-linearity. A natural question is then whether higher order representations yield more useful models. In this work we shall study this question for ECoG data channel relationships in epileptic seizure recordings, considering whether quadratic representations yield more accurate classifiers than linear ones. To do so we first show how to derive statistical information on the Volterra coefficient distribution and how to construct seizure classification patterns over that information. As our results illustrate, a quadratic model seems to provide no advantages over a linear one. Nevertheless, we shall also show that the interpretability of the implicit Wiener series provides insights into the inter-channel relationships of the recordings.

Linear and non-linear bias: predictions versus measurements

NASA Astrophysics Data System (ADS)

Hoffmann, K.; Bel, J.; Gaztañaga, E.

2017-02-01

We study the linear and non-linear bias parameters which determine the mapping between the distributions of galaxies and the full matter density fields, comparing different measurements and predictions. Associating galaxies with dark matter haloes in the Marenostrum Institut de Ciències de l'Espai (MICE) Grand Challenge N-body simulation, we directly measure the bias parameters by comparing the smoothed density fluctuations of haloes and matter in the same region at different positions as a function of smoothing scale. Alternatively, we measure the bias parameters by matching the probability distributions of halo and matter density fluctuations, which can be applied to observations. These direct bias measurements are compared to corresponding measurements from two-point and different third-order correlations, as well as predictions from the peak-background model, which we presented in previous papers using the same data. We find an overall variation of the linear bias measurements and predictions of ˜5 per cent with respect to results from two-point correlations for different halo samples with masses between ˜1012and1015 h-1 M⊙ at the redshifts z = 0.0 and 0.5. Variations between the second- and third-order bias parameters from the different methods show larger variations, but with consistent trends in mass and redshift. The various bias measurements reveal a tight relation between the linear and the quadratic bias parameters, which is consistent with results from the literature based on simulations with different cosmologies. Such a universal relation might improve constraints on cosmological models, derived from second-order clustering statistics at small scales or higher order clustering statistics.

Testing for nonlinearity in time series: The method of surrogate data

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

Theiler, J.; Galdrikian, B.; Longtin, A.

1991-01-01

We describe a statistical approach for identifying nonlinearity in time series; in particular, we want to avoid claims of chaos when simpler models (such as linearly correlated noise) can explain the data. The method requires a careful statement of the null hypothesis which characterizes a candidate linear process, the generation of an ensemble of surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against themore » null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. We present algorithms for generating surrogate data under various null hypotheses, and we show the results of numerical experiments on artificial data using correlation dimension, Lyapunov exponent, and forecasting error as discriminating statistics. Finally, we consider a number of experimental time series -- including sunspots, electroencephalogram (EEG) signals, and fluid convection -- and evaluate the statistical significance of the evidence for nonlinear structure in each case. 56 refs., 8 figs.« less

Effective connectivity between superior temporal gyrus and Heschl's gyrus during white noise listening: linear versus non-linear models.

PubMed

Hamid, Ka; Yusoff, An; Rahman, Mza; Mohamad, M; Hamid, Aia

2012-04-01

This fMRI study is about modelling the effective connectivity between Heschl's gyrus (HG) and the superior temporal gyrus (STG) in human primary auditory cortices. MATERIALS #ENTITYSTARTX00026; Ten healthy male participants were required to listen to white noise stimuli during functional magnetic resonance imaging (fMRI) scans. Statistical parametric mapping (SPM) was used to generate individual and group brain activation maps. For input region determination, two intrinsic connectivity models comprising bilateral HG and STG were constructed using dynamic causal modelling (DCM). The models were estimated and inferred using DCM while Bayesian Model Selection (BMS) for group studies was used for model comparison and selection. Based on the winning model, six linear and six non-linear causal models were derived and were again estimated, inferred, and compared to obtain a model that best represents the effective connectivity between HG and the STG, balancing accuracy and complexity. Group results indicated significant asymmetrical activation (p(uncorr) < 0.001) in bilateral HG and STG. Model comparison results showed strong evidence of STG as the input centre. The winning model is preferred by 6 out of 10 participants. The results were supported by BMS results for group studies with the expected posterior probability, r = 0.7830 and exceedance probability, ϕ = 0.9823. One-sample t-tests performed on connection values obtained from the winning model indicated that the valid connections for the winning model are the unidirectional parallel connections from STG to bilateral HG (p < 0.05). Subsequent model comparison between linear and non-linear models using BMS prefers non-linear connection (r = 0.9160, ϕ = 1.000) from which the connectivity between STG and the ipsi- and contralateral HG is gated by the activity in STG itself. We are able to demonstrate that the effective connectivity between HG and STG while listening to white noise for the respective participants can be explained by a non-linear dynamic causal model with the activity in STG influencing the STG-HG connectivity non-linearly.

Preprocessing Inconsistent Linear System for a Meaningful Least Squares Solution

NASA Technical Reports Server (NTRS)

Sen, Syamal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations. Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

NASA Technical Reports Server (NTRS)

Sen, Symal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Review and statistical analysis of the use of ultrasonic velocity for estimating the porosity fraction in polycrystalline materials

NASA Technical Reports Server (NTRS)

Roth, D. J.; Swickard, S. M.; Stang, D. B.; Deguire, M. R.

1991-01-01

A review and statistical analysis of the ultrasonic velocity method for estimating the porosity fraction in polycrystalline materials is presented. Initially, a semiempirical model is developed showing the origin of the linear relationship between ultrasonic velocity and porosity fraction. Then, from a compilation of data produced by many researchers, scatter plots of velocity versus percent porosity data are shown for Al2O3, MgO, porcelain-based ceramics, PZT, SiC, Si3N4, steel, tungsten, UO2,(U0.30Pu0.70)C, and YBa2Cu3O(7-x). Linear regression analysis produces predicted slope, intercept, correlation coefficient, level of significance, and confidence interval statistics for the data. Velocity values predicted from regression analysis of fully-dense materials are in good agreement with those calculated from elastic properties.

Review and statistical analysis of the ultrasonic velocity method for estimating the porosity fraction in polycrystalline materials

NASA Technical Reports Server (NTRS)

Roth, D. J.; Swickard, S. M.; Stang, D. B.; Deguire, M. R.

1990-01-01

A review and statistical analysis of the ultrasonic velocity method for estimating the porosity fraction in polycrystalline materials is presented. Initially, a semi-empirical model is developed showing the origin of the linear relationship between ultrasonic velocity and porosity fraction. Then, from a compilation of data produced by many researchers, scatter plots of velocity versus percent porosity data are shown for Al2O3, MgO, porcelain-based ceramics, PZT, SiC, Si3N4, steel, tungsten, UO2,(U0.30Pu0.70)C, and YBa2Cu3O(7-x). Linear regression analysis produced predicted slope, intercept, correlation coefficient, level of significance, and confidence interval statistics for the data. Velocity values predicted from regression analysis for fully-dense materials are in good agreement with those calculated from elastic properties.

Classification image analysis: estimation and statistical inference for two-alternative forced-choice experiments

NASA Technical Reports Server (NTRS)

Abbey, Craig K.; Eckstein, Miguel P.

2002-01-01

We consider estimation and statistical hypothesis testing on classification images obtained from the two-alternative forced-choice experimental paradigm. We begin with a probabilistic model of task performance for simple forced-choice detection and discrimination tasks. Particular attention is paid to general linear filter models because these models lead to a direct interpretation of the classification image as an estimate of the filter weights. We then describe an estimation procedure for obtaining classification images from observer data. A number of statistical tests are presented for testing various hypotheses from classification images based on some more compact set of features derived from them. As an example of how the methods we describe can be used, we present a case study investigating detection of a Gaussian bump profile.

Generalized t-statistic for two-group classification.

PubMed

Komori, Osamu; Eguchi, Shinto; Copas, John B

2015-06-01

In the classic discriminant model of two multivariate normal distributions with equal variance matrices, the linear discriminant function is optimal both in terms of the log likelihood ratio and in terms of maximizing the standardized difference (the t-statistic) between the means of the two distributions. In a typical case-control study, normality may be sensible for the control sample but heterogeneity and uncertainty in diagnosis may suggest that a more flexible model is needed for the cases. We generalize the t-statistic approach by finding the linear function which maximizes a standardized difference but with data from one of the groups (the cases) filtered by a possibly nonlinear function U. We study conditions for consistency of the method and find the function U which is optimal in the sense of asymptotic efficiency. Optimality may also extend to other measures of discriminatory efficiency such as the area under the receiver operating characteristic curve. The optimal function U depends on a scalar probability density function which can be estimated non-parametrically using a standard numerical algorithm. A lasso-like version for variable selection is implemented by adding L1-regularization to the generalized t-statistic. Two microarray data sets in the study of asthma and various cancers are used as motivating examples. © 2014, The International Biometric Society.

Valid statistical approaches for analyzing sholl data: Mixed effects versus simple linear models.

PubMed

Wilson, Machelle D; Sethi, Sunjay; Lein, Pamela J; Keil, Kimberly P

2017-03-01

The Sholl technique is widely used to quantify dendritic morphology. Data from such studies, which typically sample multiple neurons per animal, are often analyzed using simple linear models. However, simple linear models fail to account for intra-class correlation that occurs with clustered data, which can lead to faulty inferences. Mixed effects models account for intra-class correlation that occurs with clustered data; thus, these models more accurately estimate the standard deviation of the parameter estimate, which produces more accurate p-values. While mixed models are not new, their use in neuroscience has lagged behind their use in other disciplines. A review of the published literature illustrates common mistakes in analyses of Sholl data. Analysis of Sholl data collected from Golgi-stained pyramidal neurons in the hippocampus of male and female mice using both simple linear and mixed effects models demonstrates that the p-values and standard deviations obtained using the simple linear models are biased downwards and lead to erroneous rejection of the null hypothesis in some analyses. The mixed effects approach more accurately models the true variability in the data set, which leads to correct inference. Mixed effects models avoid faulty inference in Sholl analysis of data sampled from multiple neurons per animal by accounting for intra-class correlation. Given the widespread practice in neuroscience of obtaining multiple measurements per subject, there is a critical need to apply mixed effects models more widely. Copyright © 2017 Elsevier B.V. All rights reserved.

SNDR enhancement in noisy sinusoidal signals by non-linear processing elements

NASA Astrophysics Data System (ADS)

Martorell, Ferran; McDonnell, Mark D.; Abbott, Derek; Rubio, Antonio

2007-06-01

We investigate the possibility of building linear amplifiers capable of enhancing the Signal-to-Noise and Distortion Ratio (SNDR) of sinusoidal input signals using simple non-linear elements. Other works have proven that it is possible to enhance the Signal-to-Noise Ratio (SNR) by using limiters. In this work we study a soft limiter non-linear element with and without hysteresis. We show that the SNDR of sinusoidal signals can be enhanced by 0.94 dB using a wideband soft limiter and up to 9.68 dB using a wideband soft limiter with hysteresis. These results indicate that linear amplifiers could be constructed using non-linear circuits with hysteresis. This paper presents mathematical descriptions for the non-linear elements using statistical parameters. Using these models, the input-output SNDR enhancement is obtained by optimizing the non-linear transfer function parameters to maximize the output SNDR.

Statistical method to compare massive parallel sequencing pipelines.

PubMed

Elsensohn, M H; Leblay, N; Dimassi, S; Campan-Fournier, A; Labalme, A; Roucher-Boulez, F; Sanlaville, D; Lesca, G; Bardel, C; Roy, P

2017-03-01

Today, sequencing is frequently carried out by Massive Parallel Sequencing (MPS) that cuts drastically sequencing time and expenses. Nevertheless, Sanger sequencing remains the main validation method to confirm the presence of variants. The analysis of MPS data involves the development of several bioinformatic tools, academic or commercial. We present here a statistical method to compare MPS pipelines and test it in a comparison between an academic (BWA-GATK) and a commercial pipeline (TMAP-NextGENe®), with and without reference to a gold standard (here, Sanger sequencing), on a panel of 41 genes in 43 epileptic patients. This method used the number of variants to fit log-linear models for pairwise agreements between pipelines. To assess the heterogeneity of the margins and the odds ratios of agreement, four log-linear models were used: a full model, a homogeneous-margin model, a model with single odds ratio for all patients, and a model with single intercept. Then a log-linear mixed model was fitted considering the biological variability as a random effect. Among the 390,339 base-pairs sequenced, TMAP-NextGENe® and BWA-GATK found, on average, 2253.49 and 1857.14 variants (single nucleotide variants and indels), respectively. Against the gold standard, the pipelines had similar sensitivities (63.47% vs. 63.42%) and close but significantly different specificities (99.57% vs. 99.65%; p < 0.001). Same-trend results were obtained when only single nucleotide variants were considered (99.98% specificity and 76.81% sensitivity for both pipelines). The method allows thus pipeline comparison and selection. It is generalizable to all types of MPS data and all pipelines.

Can we detect a nonlinear response to temperature in European plant phenology?

NASA Astrophysics Data System (ADS)

Jochner, Susanne; Sparks, Tim H.; Laube, Julia; Menzel, Annette

2016-10-01

Over a large temperature range, the statistical association between spring phenology and temperature is often regarded and treated as a linear function. There are suggestions that a sigmoidal relationship with definite upper and lower limits to leaf unfolding and flowering onset dates might be more realistic. We utilised European plant phenological records provided by the European phenology database PEP725 and gridded monthly mean temperature data for 1951-2012 calculated from the ENSEMBLES data set E-OBS (version 7.0). We analysed 568,456 observations of ten spring flowering or leafing phenophases derived from 3657 stations in 22 European countries in order to detect possible nonlinear responses to temperature. Linear response rates averaged for all stations ranged between -7.7 (flowering of hazel) and -2.7 days °C-1 (leaf unfolding of beech and oak). A lower sensitivity at the cooler end of the temperature range was detected for most phenophases. However, a similar lower sensitivity at the warmer end was not that evident. For only ˜14 % of the station time series (where a comparison between linear and nonlinear model was possible), nonlinear models described the relationship significantly better than linear models. Although in most cases simple linear models might be still sufficient to predict future changes, this linear relationship between phenology and temperature might not be appropriate when incorporating phenological data of very cold (and possibly very warm) environments. For these cases, extrapolations on the basis of linear models would introduce uncertainty in expected ecosystem changes.

Wavelet-linear genetic programming: A new approach for modeling monthly streamflow

NASA Astrophysics Data System (ADS)

Ravansalar, Masoud; Rajaee, Taher; Kisi, Ozgur

2017-06-01

The streamflows are important and effective factors in stream ecosystems and its accurate prediction is an essential and important issue in water resources and environmental engineering systems. A hybrid wavelet-linear genetic programming (WLGP) model, which includes a discrete wavelet transform (DWT) and a linear genetic programming (LGP) to predict the monthly streamflow (Q) in two gauging stations, Pataveh and Shahmokhtar, on the Beshar River at the Yasuj, Iran were used in this study. In the proposed WLGP model, the wavelet analysis was linked to the LGP model where the original time series of streamflow were decomposed into the sub-time series comprising wavelet coefficients. The results were compared with the single LGP, artificial neural network (ANN), a hybrid wavelet-ANN (WANN) and Multi Linear Regression (MLR) models. The comparisons were done by some of the commonly utilized relevant physical statistics. The Nash coefficients (E) were found as 0.877 and 0.817 for the WLGP model, for the Pataveh and Shahmokhtar stations, respectively. The comparison of the results showed that the WLGP model could significantly increase the streamflow prediction accuracy in both stations. Since, the results demonstrate a closer approximation of the peak streamflow values by the WLGP model, this model could be utilized for the simulation of cumulative streamflow data prediction in one month ahead.

Improvement of PM concentration predictability using WRF-CMAQ-DLM coupled system and its applications

NASA Astrophysics Data System (ADS)

Lee, Soon Hwan; Kim, Ji Sun; Lee, Kang Yeol; Shon, Keon Tae

2017-04-01

Air quality due to increasing Particulate Matter(PM) in Korea in Asia is getting worse. At present, the PM forecast is announced based on the PM concentration predicted from the air quality prediction numerical model. However, forecast accuracy is not as high as expected due to various uncertainties for PM physical and chemical characteristics. The purpose of this study was to develop a numerical-statistically ensemble models to improve the accuracy of prediction of PM10 concentration. Numerical models used in this study are the three dimensional atmospheric model Weather Research and Forecasting(WRF) and the community multiscale air quality model (CMAQ). The target areas for the PM forecast are Seoul, Busan, Daegu, and Daejeon metropolitan areas in Korea. The data used in the model development are PM concentration and CMAQ predictions and the data period is 3 months (March 1 - May 31, 2014). The dynamic-statistical technics for reducing the systematic error of the CMAQ predictions was applied to the dynamic linear model(DLM) based on the Baysian Kalman filter technic. As a result of applying the metrics generated from the dynamic linear model to the forecasting of PM concentrations accuracy was improved. Especially, at the high PM concentration where the damage is relatively large, excellent improvement results are shown.

Skillful prediction of hot temperature extremes over the source region of ancient Silk Road.

PubMed

Zhang, Jingyong; Yang, Zhanmei; Wu, Lingyun

2018-04-27

The source region of ancient Silk Road (SRASR) in China, a region of around 150 million people, faces a rapidly increased risk of extreme heat in summer. In this study, we develop statistical models to predict summer hot temperature extremes over the SRASR based on a timescale decomposition approach. Results show that after removing the linear trends, the inter-annual components of summer hot days and heatwaves over the SRASR are significantly related with those of spring soil temperature over Central Asia and sea surface temperature over Northwest Atlantic while their inter-decadal components are closely linked to those of spring East Pacific/North Pacific pattern and Atlantic Multidecadal Oscillation for 1979-2016. The physical processes involved are also discussed. Leave-one-out cross-validation for detrended 1979-2016 time series indicates that the statistical models based on identified spring predictors can predict 47% and 57% of the total variances of summer hot days and heatwaves averaged over the SRASR, respectively. When the linear trends are put back, the prediction skills increase substantially to 64% and 70%. Hindcast experiments for 2012-2016 show high skills in predicting spatial patterns of hot temperature extremes over the SRASR. The statistical models proposed herein can be easily applied to operational seasonal forecasting.

Uncovering Local Trends in Genetic Effects of Multiple Phenotypes via Functional Linear Models.

PubMed

Vsevolozhskaya, Olga A; Zaykin, Dmitri V; Barondess, David A; Tong, Xiaoren; Jadhav, Sneha; Lu, Qing

2016-04-01

Recent technological advances equipped researchers with capabilities that go beyond traditional genotyping of loci known to be polymorphic in a general population. Genetic sequences of study participants can now be assessed directly. This capability removed technology-driven bias toward scoring predominantly common polymorphisms and let researchers reveal a wealth of rare and sample-specific variants. Although the relative contributions of rare and common polymorphisms to trait variation are being debated, researchers are faced with the need for new statistical tools for simultaneous evaluation of all variants within a region. Several research groups demonstrated flexibility and good statistical power of the functional linear model approach. In this work we extend previous developments to allow inclusion of multiple traits and adjustment for additional covariates. Our functional approach is unique in that it provides a nuanced depiction of effects and interactions for the variables in the model by representing them as curves varying over a genetic region. We demonstrate flexibility and competitive power of our approach by contrasting its performance with commonly used statistical tools and illustrate its potential for discovery and characterization of genetic architecture of complex traits using sequencing data from the Dallas Heart Study. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded.

PubMed

Nakagawa, Shinichi; Johnson, Paul C D; Schielzeth, Holger

2017-09-01

The coefficient of determination R 2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R 2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R 2 that we called [Formula: see text] for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments. © 2017 The Author(s).

An open-access CMIP5 pattern library for temperature and precipitation: Description and methodology

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

Lynch, Cary D.; Hartin, Corinne A.; Bond-Lamberty, Benjamin

Pattern scaling is used to efficiently emulate general circulation models and explore uncertainty in climate projections under multiple forcing scenarios. Pattern scaling methods assume that local climate changes scale with a global mean temperature increase, allowing for spatial patterns to be generated for multiple models for any future emission scenario. For uncertainty quantification and probabilistic statistical analysis, a library of patterns with descriptive statistics for each file would be beneficial, but such a library does not presently exist. Of the possible techniques used to generate patterns, the two most prominent are the delta and least squared regression methods. We exploremore » the differences and statistical significance between patterns generated by each method and assess performance of the generated patterns across methods and scenarios. Differences in patterns across seasons between methods and epochs were largest in high latitudes (60-90°N/S). Bias and mean errors between modeled and pattern predicted output from the linear regression method were smaller than patterns generated by the delta method. Across scenarios, differences in the linear regression method patterns were more statistically significant, especially at high latitudes. We found that pattern generation methodologies were able to approximate the forced signal of change to within ≤ 0.5°C, but choice of pattern generation methodology for pattern scaling purposes should be informed by user goals and criteria. As a result, this paper describes our library of least squared regression patterns from all CMIP5 models for temperature and precipitation on an annual and sub-annual basis, along with the code used to generate these patterns.« less

An open-access CMIP5 pattern library for temperature and precipitation: Description and methodology

DOE PAGES

Lynch, Cary D.; Hartin, Corinne A.; Bond-Lamberty, Benjamin; ...

2017-05-15

Pattern scaling is used to efficiently emulate general circulation models and explore uncertainty in climate projections under multiple forcing scenarios. Pattern scaling methods assume that local climate changes scale with a global mean temperature increase, allowing for spatial patterns to be generated for multiple models for any future emission scenario. For uncertainty quantification and probabilistic statistical analysis, a library of patterns with descriptive statistics for each file would be beneficial, but such a library does not presently exist. Of the possible techniques used to generate patterns, the two most prominent are the delta and least squared regression methods. We exploremore » the differences and statistical significance between patterns generated by each method and assess performance of the generated patterns across methods and scenarios. Differences in patterns across seasons between methods and epochs were largest in high latitudes (60-90°N/S). Bias and mean errors between modeled and pattern predicted output from the linear regression method were smaller than patterns generated by the delta method. Across scenarios, differences in the linear regression method patterns were more statistically significant, especially at high latitudes. We found that pattern generation methodologies were able to approximate the forced signal of change to within ≤ 0.5°C, but choice of pattern generation methodology for pattern scaling purposes should be informed by user goals and criteria. As a result, this paper describes our library of least squared regression patterns from all CMIP5 models for temperature and precipitation on an annual and sub-annual basis, along with the code used to generate these patterns.« less

Genetic Programming Transforms in Linear Regression Situations

NASA Astrophysics Data System (ADS)

Castillo, Flor; Kordon, Arthur; Villa, Carlos

The chapter summarizes the use of Genetic Programming (GP) inMultiple Linear Regression (MLR) to address multicollinearity and Lack of Fit (LOF). The basis of the proposed method is applying appropriate input transforms (model respecification) that deal with these issues while preserving the information content of the original variables. The transforms are selected from symbolic regression models with optimal trade-off between accuracy of prediction and expressional complexity, generated by multiobjective Pareto-front GP. The chapter includes a comparative study of the GP-generated transforms with Ridge Regression, a variant of ordinary Multiple Linear Regression, which has been a useful and commonly employed approach for reducing multicollinearity. The advantages of GP-generated model respecification are clearly defined and demonstrated. Some recommendations for transforms selection are given as well. The application benefits of the proposed approach are illustrated with a real industrial application in one of the broadest empirical modeling areas in manufacturing - robust inferential sensors. The chapter contributes to increasing the awareness of the potential of GP in statistical model building by MLR.

Within crown variation in the relationship between foliage biomass and sapwood area in jack pine.

PubMed

Schneider, Robert; Berninger, Frank; Ung, Chhun-Huor; Mäkelä, Annikki; Swift, D Edwin; Zhang, S Y

2011-01-01

The relationship between sapwood area and foliage biomass is the basis for a lot of research on eco-phyisology. In this paper, foliage biomass change between two consecutive whorls is studied, using different variations in the pipe model theory. Linear and non-linear mixed-effect models relating foliage differences to sapwood area increments were tested to take into account whorl location, with the best fit statistics supporting the non-linear formulation. The estimated value of the exponent is 0.5130, which is significantly different from 1, the expected value given by the pipe model theory. When applied to crown stem sapwood taper, the model indicates that foliage biomass distribution influences the foliage biomass to sapwood area at crown base ratio. This result is interpreted as being the consequence of differences in the turnover rates of sapwood and foliage. More importantly, the model explains previously reported trends in jack pine sapwood area at crown base to tree foliage biomass ratio.

Estimation of the limit of detection in semiconductor gas sensors through linearized calibration models.

PubMed

Burgués, Javier; Jiménez-Soto, Juan Manuel; Marco, Santiago

2018-07-12

The limit of detection (LOD) is a key figure of merit in chemical sensing. However, the estimation of this figure of merit is hindered by the non-linear calibration curve characteristic of semiconductor gas sensor technologies such as, metal oxide (MOX), gasFETs or thermoelectric sensors. Additionally, chemical sensors suffer from cross-sensitivities and temporal stability problems. The application of the International Union of Pure and Applied Chemistry (IUPAC) recommendations for univariate LOD estimation in non-linear semiconductor gas sensors is not straightforward due to the strong statistical requirements of the IUPAC methodology (linearity, homoscedasticity, normality). Here, we propose a methodological approach to LOD estimation through linearized calibration models. As an example, the methodology is applied to the detection of low concentrations of carbon monoxide using MOX gas sensors in a scenario where the main source of error is the presence of uncontrolled levels of humidity. Copyright © 2018 Elsevier B.V. All rights reserved.

Coronary artery calcium distributions in older persons in the AGES-Reykjavik study

PubMed Central

Gudmundsson, Elias Freyr; Gudnason, Vilmundur; Sigurdsson, Sigurdur; Launer, Lenore J.; Harris, Tamara B.; Aspelund, Thor

2013-01-01

Coronary Artery Calcium (CAC) is a sign of advanced atherosclerosis and an independent risk factor for cardiac events. Here, we describe CAC-distributions in an unselected aged population and compare modelling methods to characterize CAC-distribution. CAC is difficult to model because it has a skewed and zero inflated distribution with over-dispersion. Data are from the AGES-Reykjavik sample, a large population based study [2002-2006] in Iceland of 5,764 persons aged 66-96 years. Linear regressions using logarithmic- and Box-Cox transformations on CAC+1, quantile regression and a Zero-Inflated Negative Binomial model (ZINB) were applied. Methods were compared visually and with the PRESS-statistic, R2 and number of detected associations with concurrently measured variables. There were pronounced differences in CAC according to sex, age, history of coronary events and presence of plaque in the carotid artery. Associations with conventional coronary artery disease (CAD) risk factors varied between the sexes. The ZINB model provided the best results with respect to the PRESS-statistic, R2, and predicted proportion of zero scores. The ZINB model detected similar numbers of associations as the linear regression on ln(CAC+1) and usually with the same risk factors. PMID:22990371

Removing an intersubject variance component in a general linear model improves multiway factoring of event-related spectral perturbations in group EEG studies.

PubMed

Spence, Jeffrey S; Brier, Matthew R; Hart, John; Ferree, Thomas C

2013-03-01

Linear statistical models are used very effectively to assess task-related differences in EEG power spectral analyses. Mixed models, in particular, accommodate more than one variance component in a multisubject study, where many trials of each condition of interest are measured on each subject. Generally, intra- and intersubject variances are both important to determine correct standard errors for inference on functions of model parameters, but it is often assumed that intersubject variance is the most important consideration in a group study. In this article, we show that, under common assumptions, estimates of some functions of model parameters, including estimates of task-related differences, are properly tested relative to the intrasubject variance component only. A substantial gain in statistical power can arise from the proper separation of variance components when there is more than one source of variability. We first develop this result analytically, then show how it benefits a multiway factoring of spectral, spatial, and temporal components from EEG data acquired in a group of healthy subjects performing a well-studied response inhibition task. Copyright © 2011 Wiley Periodicals, Inc.

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

NASA Astrophysics Data System (ADS)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

The microcomputer scientific software series 3: general linear model--analysis of variance.

Treesearch

Harold M. Rauscher

1985-01-01

A BASIC language set of programs, designed for use on microcomputers, is presented. This set of programs will perform the analysis of variance for any statistical model describing either balanced or unbalanced designs. The program computes and displays the degrees of freedom, Type I sum of squares, and the mean square for the overall model, the error, and each factor...

Statistics and Machine Learning based Outlier Detection Techniques for Exoplanets

NASA Astrophysics Data System (ADS)

Goel, Amit; Montgomery, Michele

2015-08-01

Architectures of planetary systems are observable snapshots in time that can indicate formation and dynamic evolution of planets. The observable key parameters that we consider are planetary mass and orbital period. If planet masses are significantly less than their host star masses, then Keplerian Motion is defined as P^2 = a^3 where P is the orbital period in units of years and a is the orbital period in units of Astronomical Units (AU). Keplerian motion works on small scales such as the size of the Solar System but not on large scales such as the size of the Milky Way Galaxy. In this work, for confirmed exoplanets of known stellar mass, planetary mass, orbital period, and stellar age, we analyze Keplerian motion of systems based on stellar age to seek if Keplerian motion has an age dependency and to identify outliers. For detecting outliers, we apply several techniques based on statistical and machine learning methods such as probabilistic, linear, and proximity based models. In probabilistic and statistical models of outliers, the parameters of a closed form probability distributions are learned in order to detect the outliers. Linear models use regression analysis based techniques for detecting outliers. Proximity based models use distance based algorithms such as k-nearest neighbour, clustering algorithms such as k-means, or density based algorithms such as kernel density estimation. In this work, we will use unsupervised learning algorithms with only the proximity based models. In addition, we explore the relative strengths and weaknesses of the various techniques by validating the outliers. The validation criteria for the outliers is if the ratio of planetary mass to stellar mass is less than 0.001. In this work, we present our statistical analysis of the outliers thus detected.

Modeling Outcomes with Floor or Ceiling Effects: An Introduction to the Tobit Model

ERIC Educational Resources Information Center

McBee, Matthew

2010-01-01

In gifted education research, it is common for outcome variables to exhibit strong floor or ceiling effects due to insufficient range of measurement of many instruments when used with gifted populations. Common statistical methods (e.g., analysis of variance, linear regression) produce biased estimates when such effects are present. In practice,…

Quantifying and Testing Indirect Effects in Simple Mediation Models when the Constituent Paths Are Nonlinear

ERIC Educational Resources Information Center

Hayes, Andrew F.; Preacher, Kristopher J.

2010-01-01

Most treatments of indirect effects and mediation in the statistical methods literature and the corresponding methods used by behavioral scientists have assumed linear relationships between variables in the causal system. Here we describe and extend a method first introduced by Stolzenberg (1980) for estimating indirect effects in models of…

Helping Students Assess the Relative Importance of Different Intermolecular Interactions

ERIC Educational Resources Information Center

Jasien, Paul G.

2008-01-01

A semi-quantitative model has been developed to estimate the relative effects of dispersion, dipole-dipole interactions, and H-bonding on the normal boiling points ("T[subscript b]") for a subset of simple organic systems. The model is based upon a statistical analysis using multiple linear regression on a series of straight-chain organic…

QSAR study of curcumine derivatives as HIV-1 integrase inhibitors.

PubMed

Gupta, Pawan; Sharma, Anju; Garg, Prabha; Roy, Nilanjan

2013-03-01

A QSAR study was performed on curcumine derivatives as HIV-1 integrase inhibitors using multiple linear regression. The statistically significant model was developed with squared correlation coefficients (r(2)) 0.891 and cross validated r(2) (r(2) cv) 0.825. The developed model revealed that electronic, shape, size, geometry, substitution's information and hydrophilicity were important atomic properties for determining the inhibitory activity of these molecules. The model was also tested successfully for external validation (r(2) pred = 0.849) as well as Tropsha's test for model predictability. Furthermore, the domain analysis was carried out to evaluate the prediction reliability of external set molecules. The model was statistically robust and had good predictive power which can be successfully utilized for screening of new molecules.

Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model

NASA Astrophysics Data System (ADS)

Sandfeld, Stefan; Budrikis, Zoe; Zapperi, Stefano; Fernandez Castellanos, David

2015-02-01

Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand—where the concept of linear lattice defects is not applicable—still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena.

Log-normal frailty models fitted as Poisson generalized linear mixed models.

PubMed

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

A quasi-likelihood approach to non-negative matrix factorization

PubMed Central

Devarajan, Karthik; Cheung, Vincent C.K.

2017-01-01

A unified approach to non-negative matrix factorization based on the theory of generalized linear models is proposed. This approach embeds a variety of statistical models, including the exponential family, within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi-likelihood. Using this framework, a family of algorithms for handling signal-dependent noise is developed and its convergence proven using the Expectation-Maximization algorithm. In addition, a measure to evaluate the goodness-of-fit of the resulting factorization is described. The proposed methods allow modeling of non-linear effects via appropriate link functions and are illustrated using an application in biomedical signal processing. PMID:27348511

Improving UWB-Based Localization in IoT Scenarios with Statistical Models of Distance Error.

PubMed

Monica, Stefania; Ferrari, Gianluigi

2018-05-17

Interest in the Internet of Things (IoT) is rapidly increasing, as the number of connected devices is exponentially growing. One of the application scenarios envisaged for IoT technologies involves indoor localization and context awareness. In this paper, we focus on a localization approach that relies on a particular type of communication technology, namely Ultra Wide Band (UWB). UWB technology is an attractive choice for indoor localization, owing to its high accuracy. Since localization algorithms typically rely on estimated inter-node distances, the goal of this paper is to evaluate the improvement brought by a simple (linear) statistical model of the distance error. On the basis of an extensive experimental measurement campaign, we propose a general analytical framework, based on a Least Square (LS) method, to derive a novel statistical model for the range estimation error between a pair of UWB nodes. The proposed statistical model is then applied to improve the performance of a few illustrative localization algorithms in various realistic scenarios. The obtained experimental results show that the use of the proposed statistical model improves the accuracy of the considered localization algorithms with a reduction of the localization error up to 66%.

Hybrid Reynolds-Averaged/Large Eddy Simulation of a Cavity Flameholder; Assessment of Modeling Sensitivities

NASA Technical Reports Server (NTRS)

Baurle, R. A.

2015-01-01

Steady-state and scale-resolving simulations have been performed for flow in and around a model scramjet combustor flameholder. The cases simulated corresponded to those used to examine this flowfield experimentally using particle image velocimetry. A variety of turbulence models were used for the steady-state Reynolds-averaged simulations which included both linear and non-linear eddy viscosity models. The scale-resolving simulations used a hybrid Reynolds-averaged / large eddy simulation strategy that is designed to be a large eddy simulation everywhere except in the inner portion (log layer and below) of the boundary layer. Hence, this formulation can be regarded as a wall-modeled large eddy simulation. This effort was undertaken to formally assess the performance of the hybrid Reynolds-averaged / large eddy simulation modeling approach in a flowfield of interest to the scramjet research community. The numerical errors were quantified for both the steady-state and scale-resolving simulations prior to making any claims of predictive accuracy relative to the measurements. The steady-state Reynolds-averaged results showed a high degree of variability when comparing the predictions obtained from each turbulence model, with the non-linear eddy viscosity model (an explicit algebraic stress model) providing the most accurate prediction of the measured values. The hybrid Reynolds-averaged/large eddy simulation results were carefully scrutinized to ensure that even the coarsest grid had an acceptable level of resolution for large eddy simulation, and that the time-averaged statistics were acceptably accurate. The autocorrelation and its Fourier transform were the primary tools used for this assessment. The statistics extracted from the hybrid simulation strategy proved to be more accurate than the Reynolds-averaged results obtained using the linear eddy viscosity models. However, there was no predictive improvement noted over the results obtained from the explicit Reynolds stress model. Fortunately, the numerical error assessment at most of the axial stations used to compare with measurements clearly indicated that the scale-resolving simulations were improving (i.e. approaching the measured values) as the grid was refined. Hence, unlike a Reynolds-averaged simulation, the hybrid approach provides a mechanism to the end-user for reducing model-form errors.

The seasonal response of the Held-Suarez climate model to prescribed ocean temperature anomalies. II - Dynamical analysis

NASA Technical Reports Server (NTRS)

Phillips, T. J.

1984-01-01

The heating associated with equatorial, subtropical, and midlatitude ocean temperature anamolies in the Held-Suarez climate model is analyzed. The local and downstream response to the anomalies is analyzed, first by examining the seasonal variation in heating associated with each ocean temperature anomaly, and then by combining knowledge of the heating with linear dynamical theory in order to develop a more comprehensive explanation of the seasonal variation in local and downstream atmospheric response to each anomaly. The extent to which the linear theory of propagating waves can assist the interpretation of the remote cross-latitudinal response of the model to the ocean temperature anomalies is considered. Alternative hypotheses that attempt to avoid the contradictions inherent in a strict application of linear theory are investigated, and the impact of sampling errors on the assessment of statistical significance is also examined.

Assembly of Ultra-Dense Nanowire-Based Computing Systems

DTIC Science & Technology

2006-06-30

34* characterized basic device element properties and statistics "* demonstrated product of sums (POS) validating assembled 2-bit adder structures " Demonstrated...linear region (Vds= 10 mV) from the peak g = 3 jiS at IVg -VTI= 0.13 V using the charge control model, representsmore than a factor of 10 improvement over...disrupted by ionizing particles or thermal fluctuation. Further, when working with such small charges, it is statistically possible that logic

Statistical Models for the Analysis and Design of Digital Polymerase Chain Reaction (dPCR) Experiments.

PubMed

Dorazio, Robert M; Hunter, Margaret E

2015-11-03

Statistical methods for the analysis and design of experiments using digital PCR (dPCR) have received only limited attention and have been misused in many instances. To address this issue and to provide a more general approach to the analysis of dPCR data, we describe a class of statistical models for the analysis and design of experiments that require quantification of nucleic acids. These models are mathematically equivalent to generalized linear models of binomial responses that include a complementary, log-log link function and an offset that is dependent on the dPCR partition volume. These models are both versatile and easy to fit using conventional statistical software. Covariates can be used to specify different sources of variation in nucleic acid concentration, and a model's parameters can be used to quantify the effects of these covariates. For purposes of illustration, we analyzed dPCR data from different types of experiments, including serial dilution, evaluation of copy number variation, and quantification of gene expression. We also showed how these models can be used to help design dPCR experiments, as in selection of sample sizes needed to achieve desired levels of precision in estimates of nucleic acid concentration or to detect differences in concentration among treatments with prescribed levels of statistical power.

Unbiased split variable selection for random survival forests using maximally selected rank statistics.

PubMed

Wright, Marvin N; Dankowski, Theresa; Ziegler, Andreas

2017-04-15

The most popular approach for analyzing survival data is the Cox regression model. The Cox model may, however, be misspecified, and its proportionality assumption may not always be fulfilled. An alternative approach for survival prediction is random forests for survival outcomes. The standard split criterion for random survival forests is the log-rank test statistic, which favors splitting variables with many possible split points. Conditional inference forests avoid this split variable selection bias. However, linear rank statistics are utilized by default in conditional inference forests to select the optimal splitting variable, which cannot detect non-linear effects in the independent variables. An alternative is to use maximally selected rank statistics for the split point selection. As in conditional inference forests, splitting variables are compared on the p-value scale. However, instead of the conditional Monte-Carlo approach used in conditional inference forests, p-value approximations are employed. We describe several p-value approximations and the implementation of the proposed random forest approach. A simulation study demonstrates that unbiased split variable selection is possible. However, there is a trade-off between unbiased split variable selection and runtime. In benchmark studies of prediction performance on simulated and real datasets, the new method performs better than random survival forests if informative dichotomous variables are combined with uninformative variables with more categories and better than conditional inference forests if non-linear covariate effects are included. In a runtime comparison, the method proves to be computationally faster than both alternatives, if a simple p-value approximation is used. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Characterizations of linear sufficient statistics

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Reoner, R.; Decell, H. P., Jr.

1977-01-01

A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic.

Statistical and Biophysical Models for Predicting Total and Outdoor Water Use in Los Angeles

NASA Astrophysics Data System (ADS)

Mini, C.; Hogue, T. S.; Pincetl, S.

2012-04-01

Modeling water demand is a complex exercise in the choice of the functional form, techniques and variables to integrate in the model. The goal of the current research is to identify the determinants that control total and outdoor residential water use in semi-arid cities and to utilize that information in the development of statistical and biophysical models that can forecast spatial and temporal urban water use. The City of Los Angeles is unique in its highly diverse socio-demographic, economic and cultural characteristics across neighborhoods, which introduces significant challenges in modeling water use. Increasing climate variability also contributes to uncertainties in water use predictions in urban areas. Monthly individual water use records were acquired from the Los Angeles Department of Water and Power (LADWP) for the 2000 to 2010 period. Study predictors of residential water use include socio-demographic, economic, climate and landscaping variables at the zip code level collected from US Census database. Climate variables are estimated from ground-based observations and calculated at the centroid of each zip code by inverse-distance weighting method. Remotely-sensed products of vegetation biomass and landscape land cover are also utilized. Two linear regression models were developed based on the panel data and variables described: a pooled-OLS regression model and a linear mixed effects model. Both models show income per capita and the percentage of landscape areas in each zip code as being statistically significant predictors. The pooled-OLS model tends to over-estimate higher water use zip codes and both models provide similar RMSE values.Outdoor water use was estimated at the census tract level as the residual between total water use and indoor use. This residual is being compared with the output from a biophysical model including tree and grass cover areas, climate variables and estimates of evapotranspiration at very high spatial resolution. A genetic algorithm based model (Shuffled Complex Evolution-UA; SCE-UA) is also being developed to provide estimates of the predictions and parameters uncertainties and to compare against the linear regression models. Ultimately, models will be selected to undertake predictions for a range of climate change and landscape scenarios. Finally, project results will contribute to a better understanding of water demand to help predict future water use and implement targeted landscaping conservation programs to maintain sustainable water needs for a growing population under uncertain climate variability.

Visual aftereffects and sensory nonlinearities from a single statistical framework

PubMed Central

Laparra, Valero; Malo, Jesús

2015-01-01

When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture, and motion may tell us where these visual illusions come from. However, such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner. Current normative explanations of aftereffects based on scene statistics derive gain changes by (1) invoking decorrelation and linear manifold matching/equalization, or (2) using nonlinear divisive normalization obtained from parametric scene models. These principled approaches have different drawbacks: the first is not compatible with the known saturation nonlinearities in the sensors and it cannot fully accomplish information maximization due to its linear nature. In the second, gain change is almost determined a priori by the assumed parametric image model linked to divisive normalization. In this study we show that both the response changes that lead to aftereffects and the nonlinear behavior can be simultaneously derived from a single statistical framework: the Sequential Principal Curves Analysis (SPCA). As opposed to mechanistic models, SPCA is not intended to describe how physiological sensors work, but it is focused on explaining why they behave as they do. Nonparametric SPCA has two key advantages as a normative model of adaptation: (i) it is better than linear techniques as it is a flexible equalization that can be tuned for more sensible criteria other than plain decorrelation (either full information maximization or error minimization); and (ii) it makes no a priori functional assumption regarding the nonlinearity, so the saturations emerge directly from the scene data and the goal (and not from the assumed function). It turns out that the optimal responses derived from these more sensible criteria and SPCA are consistent with dysfunctional behaviors such as aftereffects. PMID:26528165

Novel forecasting approaches using combination of machine learning and statistical models for flood susceptibility mapping.

PubMed

Shafizadeh-Moghadam, Hossein; Valavi, Roozbeh; Shahabi, Himan; Chapi, Kamran; Shirzadi, Ataollah

2018-07-01

In this research, eight individual machine learning and statistical models are implemented and compared, and based on their results, seven ensemble models for flood susceptibility assessment are introduced. The individual models included artificial neural networks, classification and regression trees, flexible discriminant analysis, generalized linear model, generalized additive model, boosted regression trees, multivariate adaptive regression splines, and maximum entropy, and the ensemble models were Ensemble Model committee averaging (EMca), Ensemble Model confidence interval Inferior (EMciInf), Ensemble Model confidence interval Superior (EMciSup), Ensemble Model to estimate the coefficient of variation (EMcv), Ensemble Model to estimate the mean (EMmean), Ensemble Model to estimate the median (EMmedian), and Ensemble Model based on weighted mean (EMwmean). The data set covered 201 flood events in the Haraz watershed (Mazandaran province in Iran) and 10,000 randomly selected non-occurrence points. Among the individual models, the Area Under the Receiver Operating Characteristic (AUROC), which showed the highest value, belonged to boosted regression trees (0.975) and the lowest value was recorded for generalized linear model (0.642). On the other hand, the proposed EMmedian resulted in the highest accuracy (0.976) among all models. In spite of the outstanding performance of some models, nevertheless, variability among the prediction of individual models was considerable. Therefore, to reduce uncertainty, creating more generalizable, more stable, and less sensitive models, ensemble forecasting approaches and in particular the EMmedian is recommended for flood susceptibility assessment. Copyright © 2018 Elsevier Ltd. All rights reserved.

Regression modeling of ground-water flow

USGS Publications Warehouse

Cooley, R.L.; Naff, R.L.

1985-01-01

Nonlinear multiple regression methods are developed to model and analyze groundwater flow systems. Complete descriptions of regression methodology as applied to groundwater flow models allow scientists and engineers engaged in flow modeling to apply the methods to a wide range of problems. Organization of the text proceeds from an introduction that discusses the general topic of groundwater flow modeling, to a review of basic statistics necessary to properly apply regression techniques, and then to the main topic: exposition and use of linear and nonlinear regression to model groundwater flow. Statistical procedures are given to analyze and use the regression models. A number of exercises and answers are included to exercise the student on nearly all the methods that are presented for modeling and statistical analysis. Three computer programs implement the more complex methods. These three are a general two-dimensional, steady-state regression model for flow in an anisotropic, heterogeneous porous medium, a program to calculate a measure of model nonlinearity with respect to the regression parameters, and a program to analyze model errors in computed dependent variables such as hydraulic head. (USGS)

The Relationship Between Surface Curvature and Abdominal Aortic Aneurysm Wall Stress.

PubMed

de Galarreta, Sergio Ruiz; Cazón, Aitor; Antón, Raúl; Finol, Ender A

2017-08-01

The maximum diameter (MD) criterion is the most important factor when predicting risk of rupture of abdominal aortic aneurysms (AAAs). An elevated wall stress has also been linked to a high risk of aneurysm rupture, yet is an uncommon clinical practice to compute AAA wall stress. The purpose of this study is to assess whether other characteristics of the AAA geometry are statistically correlated with wall stress. Using in-house segmentation and meshing algorithms, 30 patient-specific AAA models were generated for finite element analysis (FEA). These models were subsequently used to estimate wall stress and maximum diameter and to evaluate the spatial distributions of wall thickness, cross-sectional diameter, mean curvature, and Gaussian curvature. Data analysis consisted of statistical correlations of the aforementioned geometry metrics with wall stress for the 30 AAA inner and outer wall surfaces. In addition, a linear regression analysis was performed with all the AAA wall surfaces to quantify the relationship of the geometric indices with wall stress. These analyses indicated that while all the geometry metrics have statistically significant correlations with wall stress, the local mean curvature (LMC) exhibits the highest average Pearson's correlation coefficient for both inner and outer wall surfaces. The linear regression analysis revealed coefficients of determination for the outer and inner wall surfaces of 0.712 and 0.516, respectively, with LMC having the largest effect on the linear regression equation with wall stress. This work underscores the importance of evaluating AAA mean wall curvature as a potential surrogate for wall stress.

Three-Dimensional City Determinants of the Urban Heat Island: A Statistical Approach

NASA Astrophysics Data System (ADS)

Chun, Bum Seok

There is no doubt that the Urban Heat Island (UHI) is a mounting problem in built-up environments, due to the energy retention by the surface materials of dense buildings, leading to increased temperatures, air pollution, and energy consumption. Much of the earlier research on the UHI has used two-dimensional (2-D) information, such as land uses and the distribution of vegetation. In the case of homogeneous land uses, it is possible to predict surface temperatures with reasonable accuracy with 2-D information. However, three-dimensional (3-D) information is necessary to analyze more complex sites, including dense building clusters. Recent research on the UHI has started to consider multi-dimensional models. The purpose of this research is to explore the urban determinants of the UHI, using 2-D/3-D urban information with statistical modeling. The research includes the following stages: (a) estimating urban temperature, using satellite images, (b) developing a 3-D city model by LiDAR data, (c) generating geometric parameters with regard to 2-/3-D geospatial information, and (d) conducting different statistical analyses: OLS and spatial regressions. The research area is part of the City of Columbus, Ohio. To effectively and systematically analyze the UHI, hierarchical grid scales (480m, 240m, 120m, 60m, and 30m) are proposed, together with linear and the log-linear regression models. The non-linear OLS models with Log(AST) as dependent variable have the highest R2 among all the OLS-estimated models. However, both SAR and GSM models are estimated for the 480m, 240m, 120m, and 60m grids to reduce their spatial dependency. Most GSM models have R2s higher than 0.9, except for the 240m grid. Overall, the urban characteristics having high impacts in all grids are embodied in solar radiation, 3-D open space, greenery, and water streams. These results demonstrate that it is possible to mitigate the UHI, providing guidelines for policies aiming to reduce the UHI.

Conditional statistical inference with multistage testing designs.

PubMed

Zwitser, Robert J; Maris, Gunter

2015-03-01

In this paper it is demonstrated how statistical inference from multistage test designs can be made based on the conditional likelihood. Special attention is given to parameter estimation, as well as the evaluation of model fit. Two reasons are provided why the fit of simple measurement models is expected to be better in adaptive designs, compared to linear designs: more parameters are available for the same number of observations; and undesirable response behavior, like slipping and guessing, might be avoided owing to a better match between item difficulty and examinee proficiency. The results are illustrated with simulated data, as well as with real data.

Stochastic or statistic? Comparing flow duration curve models in ungauged basins and changing climates

NASA Astrophysics Data System (ADS)

Müller, M. F.; Thompson, S. E.

2015-09-01

The prediction of flow duration curves (FDCs) in ungauged basins remains an important task for hydrologists given the practical relevance of FDCs for water management and infrastructure design. Predicting FDCs in ungauged basins typically requires spatial interpolation of statistical or model parameters. This task is complicated if climate becomes non-stationary, as the prediction challenge now also requires extrapolation through time. In this context, process-based models for FDCs that mechanistically link the streamflow distribution to climate and landscape factors may have an advantage over purely statistical methods to predict FDCs. This study compares a stochastic (process-based) and statistical method for FDC prediction in both stationary and non-stationary contexts, using Nepal as a case study. Under contemporary conditions, both models perform well in predicting FDCs, with Nash-Sutcliffe coefficients above 0.80 in 75 % of the tested catchments. The main drives of uncertainty differ between the models: parameter interpolation was the main source of error for the statistical model, while violations of the assumptions of the process-based model represented the main source of its error. The process-based approach performed better than the statistical approach in numerical simulations with non-stationary climate drivers. The predictions of the statistical method under non-stationary rainfall conditions were poor if (i) local runoff coefficients were not accurately determined from the gauge network, or (ii) streamflow variability was strongly affected by changes in rainfall. A Monte Carlo analysis shows that the streamflow regimes in catchments characterized by a strong wet-season runoff and a rapid, strongly non-linear hydrologic response are particularly sensitive to changes in rainfall statistics. In these cases, process-based prediction approaches are strongly favored over statistical models.

Comparing statistical and process-based flow duration curve models in ungauged basins and changing rain regimes

NASA Astrophysics Data System (ADS)

Müller, M. F.; Thompson, S. E.

2016-02-01

The prediction of flow duration curves (FDCs) in ungauged basins remains an important task for hydrologists given the practical relevance of FDCs for water management and infrastructure design. Predicting FDCs in ungauged basins typically requires spatial interpolation of statistical or model parameters. This task is complicated if climate becomes non-stationary, as the prediction challenge now also requires extrapolation through time. In this context, process-based models for FDCs that mechanistically link the streamflow distribution to climate and landscape factors may have an advantage over purely statistical methods to predict FDCs. This study compares a stochastic (process-based) and statistical method for FDC prediction in both stationary and non-stationary contexts, using Nepal as a case study. Under contemporary conditions, both models perform well in predicting FDCs, with Nash-Sutcliffe coefficients above 0.80 in 75 % of the tested catchments. The main drivers of uncertainty differ between the models: parameter interpolation was the main source of error for the statistical model, while violations of the assumptions of the process-based model represented the main source of its error. The process-based approach performed better than the statistical approach in numerical simulations with non-stationary climate drivers. The predictions of the statistical method under non-stationary rainfall conditions were poor if (i) local runoff coefficients were not accurately determined from the gauge network, or (ii) streamflow variability was strongly affected by changes in rainfall. A Monte Carlo analysis shows that the streamflow regimes in catchments characterized by frequent wet-season runoff and a rapid, strongly non-linear hydrologic response are particularly sensitive to changes in rainfall statistics. In these cases, process-based prediction approaches are favored over statistical models.

Development of statistical linear regression model for metals from transportation land uses.

PubMed

Maniquiz, Marla C; Lee, Soyoung; Lee, Eunju; Kim, Lee-Hyung

2009-01-01

The transportation landuses possessing impervious surfaces such as highways, parking lots, roads, and bridges were recognized as the highly polluted non-point sources (NPSs) in the urban areas. Lots of pollutants from urban transportation are accumulating on the paved surfaces during dry periods and are washed-off during a storm. In Korea, the identification and monitoring of NPSs still represent a great challenge. Since 2004, the Ministry of Environment (MOE) has been engaged in several researches and monitoring to develop stormwater management policies and treatment systems for future implementation. The data over 131 storm events during May 2004 to September 2008 at eleven sites were analyzed to identify correlation relationships between particulates and metals, and to develop simple linear regression (SLR) model to estimate event mean concentration (EMC). Results indicate that there was no significant relationship between metals and TSS EMC. However, the SLR estimation models although not providing useful results are valuable indicators of high uncertainties that NPS pollution possess. Therefore, long term monitoring employing proper methods and precise statistical analysis of the data should be undertaken to eliminate these uncertainties.

Impact of isotropic constitutive descriptions on the predicted peak wall stress in abdominal aortic aneurysms.

PubMed

Man, V; Polzer, S; Gasser, T C; Novotny, T; Bursa, J

2018-03-01

Biomechanics-based assessment of Abdominal Aortic Aneurysm (AAA) rupture risk has gained considerable scientific and clinical momentum. However, computation of peak wall stress (PWS) using state-of-the-art finite element models is time demanding. This study investigates which features of the constitutive description of AAA wall are decisive for achieving acceptable stress predictions in it. Influence of five different isotropic constitutive descriptions of AAA wall is tested; models reflect realistic non-linear, artificially stiff non-linear, or artificially stiff pseudo-linear constitutive descriptions of AAA wall. Influence of the AAA wall model is tested on idealized (n=4) and patient-specific (n=16) AAA geometries. Wall stress computations consider a (hypothetical) load-free configuration and include residual stresses homogenizing the stresses across the wall. Wall stress differences amongst the different descriptions were statistically analyzed. When the qualitatively similar non-linear response of the AAA wall with low initial stiffness and subsequent strain stiffening was taken into consideration, wall stress (and PWS) predictions did not change significantly. Keeping this non-linear feature when using an artificially stiff wall can save up to 30% of the computational time, without significant change in PWS. In contrast, a stiff pseudo-linear elastic model may underestimate the PWS and is not reliable for AAA wall stress computations. Copyright © 2018 IPEM. Published by Elsevier Ltd. All rights reserved.

Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

Subcellular localization for Gram positive and Gram negative bacterial proteins using linear interpolation smoothing model.

PubMed

Saini, Harsh; Raicar, Gaurav; Dehzangi, Abdollah; Lal, Sunil; Sharma, Alok

2015-12-07

Protein subcellular localization is an important topic in proteomics since it is related to a protein׳s overall function, helps in the understanding of metabolic pathways, and in drug design and discovery. In this paper, a basic approximation technique from natural language processing called the linear interpolation smoothing model is applied for predicting protein subcellular localizations. The proposed approach extracts features from syntactical information in protein sequences to build probabilistic profiles using dependency models, which are used in linear interpolation to determine how likely is a sequence to belong to a particular subcellular location. This technique builds a statistical model based on maximum likelihood. It is able to deal effectively with high dimensionality that hinders other traditional classifiers such as Support Vector Machines or k-Nearest Neighbours without sacrificing performance. This approach has been evaluated by predicting subcellular localizations of Gram positive and Gram negative bacterial proteins. Copyright © 2015 Elsevier Ltd. All rights reserved.

Comparative study of sea ice dynamics simulations with a Maxwell elasto-brittle rheology and the elastic-viscous-plastic rheology in NEMO-LIM3

NASA Astrophysics Data System (ADS)

Raulier, Jonathan; Dansereau, Véronique; Fichefet, Thierry; Legat, Vincent; Weiss, Jérôme

2017-04-01

Sea ice is a highly dynamical environment characterized by a dense mesh of fractures or leads, constantly opening and closing over short time scales. This characteristic geomorphology is linked to the existence of linear kinematic features, which consist of quasi-linear patterns emerging from the observed strain rate field of sea ice. Standard rheologies used in most state-of-the-art sea ice models, like the well-known elastic-viscous-plastic rheology, are thought to misrepresent those linear kinematic features and the observed statistical distribution of deformation rates. Dedicated rheologies built to catch the processes known to be at the origin of the formation of leads are developed but still need evaluations on the global scale. One of them, based on a Maxwell elasto-brittle formulation, is being integrated in the NEMO-LIM3 global ocean-sea ice model (www.nemo-ocean.eu; www.elic.ucl.ac.be/lim). In the present study, we compare the results of the sea ice model LIM3 obtained with two different rheologies: the elastic-viscous-plastic rheology commonly used in LIM3 and a Maxwell elasto-brittle rheology. This comparison is focused on the statistical characteristics of the simulated deformation rate and on the ability of the model to reproduce the existence of leads within the ice pack. The impact of the lead representation on fluxes between ice, atmosphere and ocean is also assessed.

Statistical analysis of dendritic spine distributions in rat hippocampal cultures

PubMed Central

2013-01-01

Background Dendritic spines serve as key computational structures in brain plasticity. Much remains to be learned about their spatial and temporal distribution among neurons. Our aim in this study was to perform exploratory analyses based on the population distributions of dendritic spines with regard to their morphological characteristics and period of growth in dissociated hippocampal neurons. We fit a log-linear model to the contingency table of spine features such as spine type and distance from the soma to first determine which features were important in modeling the spines, as well as the relationships between such features. A multinomial logistic regression was then used to predict the spine types using the features suggested by the log-linear model, along with neighboring spine information. Finally, an important variant of Ripley’s K-function applicable to linear networks was used to study the spatial distribution of spines along dendrites. Results Our study indicated that in the culture system, (i) dendritic spine densities were "completely spatially random", (ii) spine type and distance from the soma were independent quantities, and most importantly, (iii) spines had a tendency to cluster with other spines of the same type. Conclusions Although these results may vary with other systems, our primary contribution is the set of statistical tools for morphological modeling of spines which can be used to assess neuronal cultures following gene manipulation such as RNAi, and to study induced pluripotent stem cells differentiated to neurons. PMID:24088199

Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering.

PubMed

Rigatos, Gerasimos G; Rigatou, Efthymia G; Djida, Jean Daniel

2015-10-01

A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of x2 change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies).

BOOK REVIEW: Statistical Mechanics of Turbulent Flows

NASA Astrophysics Data System (ADS)

Cambon, C.

2004-10-01

This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their counterparts at the molecular level. In addition, equations are given for multicomponent reacting systems. The chapter ends with miscellaneous topics, including DNS, (idea of) the energy cascade, and RANS. Chapter 5 is devoted to stochastic models for the large scales of turbulence. Langevin-type models for velocity (and particle position) are presented, and their various consequences for second-order single-point corelations (Reynolds stress components, Kolmogorov constant) are discussed. These models are then presented for the scalar. The chapter ends with compressible high-speed flows and various models, ranging from k-epsilon to hybrid RANS-pdf. Stochastic models for small-scale turbulence are addressed in chapter 6. These models are based on the concept of a filter density function (FDF) for the scalar, and a more conventional SGS (sub-grid-scale model) for the velocity in LES. The final chapter, chapter 7, is entitled `The unification of turbulence models' and aims at reconciling large-scale and small-scale modelling. This book offers a timely survey of techniques in modern computational fluid mechanics for turbulent flows with reacting scalars. It should be of interest to engineers, while the discussion of the underlying tools, namely pdfs, stochastic and statistical equations should also be attractive to applied mathematicians and physicists. The book's emphasis on local pdfs and stochastic Langevin models gives a consistent structure to the book and allows the author to cover almost the whole spectrum of practical modelling in turbulent CFD. On the other hand, one might regret that non-local issues are not mentioned explicitly, or even briefly. These problems range from the presence of pressure-strain correlations in the Reynolds stress transport equations to the presence of two-point pdfs in the single-point pdf equation derived from the Navier--Stokes equations. (One may recall that, even without scalar transport, a general closure problem for turbulence statistics results from both non-linearity and non-locality of Navier-Stokes equations, the latter coming from, e.g., the nonlocal relationship of velocity and pressure in the quasi-incompressible case. These two aspects are often intricately linked. It is well known that non-linearity alone is not responsible for the `problem', as evidenced by 1D turbulence without pressure (`Burgulence' from the Burgers equation) and probably 3D (cosmological gas). A local description in terms of pdf for the velocity can resolve the `non-linear' problem, which instead yields an infinite hierarchy of equations in terms of moments. On the other hand, non-locality yields a hierarchy of unclosed equations, with the single-point pdf equation for velocity derived from NS incompressible equations involving a two-point pdf, and so on. The general relationship was given by Lundgren (1967, Phys. Fluids 10 (5), 969-975), with the equation for pdf at n points involving the pdf at n+1 points. The nonlocal problem appears in various statistical models which are not discussed in the book. The simplest example is full RST or ASM models, in which the closure of pressure-strain correlations is pivotal (their counterpart ought to be identified and discussed in equations (5-21) and the following ones). The book does not address more sophisticated non-local approaches, such as two-point (or spectral) non-linear closure theories and models, `rapid distortion theory' for linear regimes, not to mention scaling and intermittency based on two-point structure functions, etc. The book sometimes mixes theoretical modelling and pure empirical relationships, the empirical character coming from the lack of a nonlocal (two-point) approach.) In short, the book is orientated more towards applications than towards turbulence theory; it is written clearly and concisely and should be useful to a large community, interested either in the underlying stochastic formalism or in CFD applications.

Application of the Hyper-Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes.

PubMed

Khazraee, S Hadi; Sáez-Castillo, Antonio Jose; Geedipally, Srinivas Reddy; Lord, Dominique

2015-05-01

The hyper-Poisson distribution can handle both over- and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation-specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper-Poisson distribution in analyzing motor vehicle crash count data. The hyper-Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway-highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness-of-fit measures indicated that the hyper-Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper-Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway-Maxwell-Poisson model previously developed for the same data set. The advantages of the hyper-Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper-Poisson model can handle both over- and underdispersed crash data. Although not a major issue for the Conway-Maxwell-Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model. © 2014 Society for Risk Analysis.

Can we detect a nonlinear response to temperature in European plant phenology?

PubMed

Jochner, Susanne; Sparks, Tim H; Laube, Julia; Menzel, Annette

2016-10-01

Over a large temperature range, the statistical association between spring phenology and temperature is often regarded and treated as a linear function. There are suggestions that a sigmoidal relationship with definite upper and lower limits to leaf unfolding and flowering onset dates might be more realistic. We utilised European plant phenological records provided by the European phenology database PEP725 and gridded monthly mean temperature data for 1951-2012 calculated from the ENSEMBLES data set E-OBS (version 7.0). We analysed 568,456 observations of ten spring flowering or leafing phenophases derived from 3657 stations in 22 European countries in order to detect possible nonlinear responses to temperature. Linear response rates averaged for all stations ranged between -7.7 (flowering of hazel) and -2.7 days °C -1 (leaf unfolding of beech and oak). A lower sensitivity at the cooler end of the temperature range was detected for most phenophases. However, a similar lower sensitivity at the warmer end was not that evident. For only ∼14 % of the station time series (where a comparison between linear and nonlinear model was possible), nonlinear models described the relationship significantly better than linear models. Although in most cases simple linear models might be still sufficient to predict future changes, this linear relationship between phenology and temperature might not be appropriate when incorporating phenological data of very cold (and possibly very warm) environments. For these cases, extrapolations on the basis of linear models would introduce uncertainty in expected ecosystem changes.

Statistical models for the analysis and design of digital polymerase chain (dPCR) experiments

USGS Publications Warehouse

Dorazio, Robert; Hunter, Margaret

2015-01-01

Statistical methods for the analysis and design of experiments using digital PCR (dPCR) have received only limited attention and have been misused in many instances. To address this issue and to provide a more general approach to the analysis of dPCR data, we describe a class of statistical models for the analysis and design of experiments that require quantification of nucleic acids. These models are mathematically equivalent to generalized linear models of binomial responses that include a complementary, log–log link function and an offset that is dependent on the dPCR partition volume. These models are both versatile and easy to fit using conventional statistical software. Covariates can be used to specify different sources of variation in nucleic acid concentration, and a model’s parameters can be used to quantify the effects of these covariates. For purposes of illustration, we analyzed dPCR data from different types of experiments, including serial dilution, evaluation of copy number variation, and quantification of gene expression. We also showed how these models can be used to help design dPCR experiments, as in selection of sample sizes needed to achieve desired levels of precision in estimates of nucleic acid concentration or to detect differences in concentration among treatments with prescribed levels of statistical power.

Perturbative Gaussianizing transforms for cosmological fields

NASA Astrophysics Data System (ADS)

Hall, Alex; Mead, Alexander

2018-01-01

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

Examining the predictive accuracy of the novel 3D N-linear algebraic molecular codifications on benchmark datasets.

PubMed

García-Jacas, César R; Contreras-Torres, Ernesto; Marrero-Ponce, Yovani; Pupo-Meriño, Mario; Barigye, Stephen J; Cabrera-Leyva, Lisset

2016-01-01

Recently, novel 3D alignment-free molecular descriptors (also known as QuBiLS-MIDAS) based on two-linear, three-linear and four-linear algebraic forms have been introduced. These descriptors codify chemical information for relations between two, three and four atoms by using several (dis-)similarity metrics and multi-metrics. Several studies aimed at assessing the quality of these novel descriptors have been performed. However, a deeper analysis of their performance is necessary. Therefore, in the present manuscript an assessment and statistical validation of the performance of these novel descriptors in QSAR studies is performed. To this end, eight molecular datasets (angiotensin converting enzyme, acetylcholinesterase inhibitors, benzodiazepine receptor, cyclooxygenase-2 inhibitors, dihydrofolate reductase inhibitors, glycogen phosphorylase b, thermolysin inhibitors, thrombin inhibitors) widely used as benchmarks in the evaluation of several procedures are utilized. Three to nine variable QSAR models based on Multiple Linear Regression are built for each chemical dataset according to the original division into training/test sets. Comparisons with respect to leave-one-out cross-validation correlation coefficients[Formula: see text] reveal that the models based on QuBiLS-MIDAS indices possess superior predictive ability in 7 of the 8 datasets analyzed, outperforming methodologies based on similar or more complex techniques such as: Partial Least Square, Neural Networks, Support Vector Machine and others. On the other hand, superior external correlation coefficients[Formula: see text] are attained in 6 of the 8 test sets considered, confirming the good predictive power of the obtained models. For the [Formula: see text] values non-parametric statistic tests were performed, which demonstrated that the models based on QuBiLS-MIDAS indices have the best global performance and yield significantly better predictions in 11 of the 12 QSAR procedures used in the comparison. Lastly, a study concerning to the performance of the indices according to several conformer generation methods was performed. This demonstrated that the quality of predictions of the QSAR models based on QuBiLS-MIDAS indices depend on 3D structure generation method considered, although in this preliminary study the results achieved do not present significant statistical differences among them. As conclusions it can be stated that the QuBiLS-MIDAS indices are suitable for extracting structural information of the molecules and thus, constitute a promissory alternative to build models that contribute to the prediction of pharmacokinetic, pharmacodynamics and toxicological properties on novel compounds.Graphical abstractComparative graphical representation of the performance of the novel QuBiLS-MIDAS 3D-MDs with respect to other methodologies in QSAR modeling of eight chemical datasets.

Educational Leadership as Best Practice in Highly Effective Schools in the Autonomous Region of the Basque County (Spain)

ERIC Educational Resources Information Center

Intxausti, Nahia; Joaristi, Luis; Lizasoain, Luis

2016-01-01

This study presents part of a research project currently underway which aims to characterise the best practices of highly effective schools in the Autonomous Region of the Basque Country (Spain). Multilevel statistical modelling and hierarchical linear models were used to select 32 highly effective schools, with highly effective being taken to…

A statistical model of brittle fracture by transgranular cleavage

NASA Astrophysics Data System (ADS)

Lin, Tsann; Evans, A. G.; Ritchie, R. O.

A MODEL for brittle fracture by transgranular cleavage cracking is presented based on the application of weakest link statistics to the critical microstructural fracture mechanisms. The model permits prediction of the macroscopic fracture toughness, KI c, in single phase microstructures containing a known distribution of particles, and defines the critical distance from the crack tip at which the initial cracking event is most probable. The model is developed for unstable fracture ahead of a sharp crack considering both linear elastic and nonlinear elastic ("elastic/plastic") crack tip stress fields. Predictions are evaluated by comparison with experimental results on the low temperature flow and fracture behavior of a low carbon mild steel with a simple ferrite/grain boundary carbide microstructure.

An Interactive Tool For Semi-automated Statistical Prediction Using Earth Observations and Models

NASA Astrophysics Data System (ADS)

Zaitchik, B. F.; Berhane, F.; Tadesse, T.

2015-12-01

We developed a semi-automated statistical prediction tool applicable to concurrent analysis or seasonal prediction of any time series variable in any geographic location. The tool was developed using Shiny, JavaScript, HTML and CSS. A user can extract a predictand by drawing a polygon over a region of interest on the provided user interface (global map). The user can select the Climatic Research Unit (CRU) precipitation or Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS) as predictand. They can also upload their own predictand time series. Predictors can be extracted from sea surface temperature, sea level pressure, winds at different pressure levels, air temperature at various pressure levels, and geopotential height at different pressure levels. By default, reanalysis fields are applied as predictors, but the user can also upload their own predictors, including a wide range of compatible satellite-derived datasets. The package generates correlations of the variables selected with the predictand. The user also has the option to generate composites of the variables based on the predictand. Next, the user can extract predictors by drawing polygons over the regions that show strong correlations (composites). Then, the user can select some or all of the statistical prediction models provided. Provided models include Linear Regression models (GLM, SGLM), Tree-based models (bagging, random forest, boosting), Artificial Neural Network, and other non-linear models such as Generalized Additive Model (GAM) and Multivariate Adaptive Regression Splines (MARS). Finally, the user can download the analysis steps they used, such as the region they selected, the time period they specified, the predictand and predictors they chose and preprocessing options they used, and the model results in PDF or HTML format. Key words: Semi-automated prediction, Shiny, R, GLM, ANN, RF, GAM, MARS

Generalized functional linear models for gene-based case-control association studies.

PubMed

Fan, Ruzong; Wang, Yifan; Mills, James L; Carter, Tonia C; Lobach, Iryna; Wilson, Alexander F; Bailey-Wilson, Joan E; Weeks, Daniel E; Xiong, Momiao

2014-11-01

By using functional data analysis techniques, we developed generalized functional linear models for testing association between a dichotomous trait and multiple genetic variants in a genetic region while adjusting for covariates. Both fixed and mixed effect models are developed and compared. Extensive simulations show that Rao's efficient score tests of the fixed effect models are very conservative since they generate lower type I errors than nominal levels, and global tests of the mixed effect models generate accurate type I errors. Furthermore, we found that the Rao's efficient score test statistics of the fixed effect models have higher power than the sequence kernel association test (SKAT) and its optimal unified version (SKAT-O) in most cases when the causal variants are both rare and common. When the causal variants are all rare (i.e., minor allele frequencies less than 0.03), the Rao's efficient score test statistics and the global tests have similar or slightly lower power than SKAT and SKAT-O. In practice, it is not known whether rare variants or common variants in a gene region are disease related. All we can assume is that a combination of rare and common variants influences disease susceptibility. Thus, the improved performance of our models when the causal variants are both rare and common shows that the proposed models can be very useful in dissecting complex traits. We compare the performance of our methods with SKAT and SKAT-O on real neural tube defects and Hirschsprung's disease datasets. The Rao's efficient score test statistics and the global tests are more sensitive than SKAT and SKAT-O in the real data analysis. Our methods can be used in either gene-disease genome-wide/exome-wide association studies or candidate gene analyses. © 2014 WILEY PERIODICALS, INC.

Generalized Functional Linear Models for Gene-based Case-Control Association Studies

PubMed Central

Mills, James L.; Carter, Tonia C.; Lobach, Iryna; Wilson, Alexander F.; Bailey-Wilson, Joan E.; Weeks, Daniel E.; Xiong, Momiao

2014-01-01

By using functional data analysis techniques, we developed generalized functional linear models for testing association between a dichotomous trait and multiple genetic variants in a genetic region while adjusting for covariates. Both fixed and mixed effect models are developed and compared. Extensive simulations show that Rao's efficient score tests of the fixed effect models are very conservative since they generate lower type I errors than nominal levels, and global tests of the mixed effect models generate accurate type I errors. Furthermore, we found that the Rao's efficient score test statistics of the fixed effect models have higher power than the sequence kernel association test (SKAT) and its optimal unified version (SKAT-O) in most cases when the causal variants are both rare and common. When the causal variants are all rare (i.e., minor allele frequencies less than 0.03), the Rao's efficient score test statistics and the global tests have similar or slightly lower power than SKAT and SKAT-O. In practice, it is not known whether rare variants or common variants in a gene are disease-related. All we can assume is that a combination of rare and common variants influences disease susceptibility. Thus, the improved performance of our models when the causal variants are both rare and common shows that the proposed models can be very useful in dissecting complex traits. We compare the performance of our methods with SKAT and SKAT-O on real neural tube defects and Hirschsprung's disease data sets. The Rao's efficient score test statistics and the global tests are more sensitive than SKAT and SKAT-O in the real data analysis. Our methods can be used in either gene-disease genome-wide/exome-wide association studies or candidate gene analyses. PMID:25203683

Potential pitfalls when denoising resting state fMRI data using nuisance regression.

PubMed

Bright, Molly G; Tench, Christopher R; Murphy, Kevin

2017-07-01

In resting state fMRI, it is necessary to remove signal variance associated with noise sources, leaving cleaned fMRI time-series that more accurately reflect the underlying intrinsic brain fluctuations of interest. This is commonly achieved through nuisance regression, in which the fit is calculated of a noise model of head motion and physiological processes to the fMRI data in a General Linear Model, and the "cleaned" residuals of this fit are used in further analysis. We examine the statistical assumptions and requirements of the General Linear Model, and whether these are met during nuisance regression of resting state fMRI data. Using toy examples and real data we show how pre-whitening, temporal filtering and temporal shifting of regressors impact model fit. Based on our own observations, existing literature, and statistical theory, we make the following recommendations when employing nuisance regression: pre-whitening should be applied to achieve valid statistical inference of the noise model fit parameters; temporal filtering should be incorporated into the noise model to best account for changes in degrees of freedom; temporal shifting of regressors, although merited, should be achieved via optimisation and validation of a single temporal shift. We encourage all readers to make simple, practical changes to their fMRI denoising pipeline, and to regularly assess the appropriateness of the noise model used. By negotiating the potential pitfalls described in this paper, and by clearly reporting the details of nuisance regression in future manuscripts, we hope that the field will achieve more accurate and precise noise models for cleaning the resting state fMRI time-series. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

[Comparison of application of Cochran-Armitage trend test and linear regression analysis for rate trend analysis in epidemiology study].

PubMed

Wang, D Z; Wang, C; Shen, C F; Zhang, Y; Zhang, H; Song, G D; Xue, X D; Xu, Z L; Zhang, S; Jiang, G H

2017-05-10

We described the time trend of acute myocardial infarction (AMI) from 1999 to 2013 in Tianjin incidence rate with Cochran-Armitage trend (CAT) test and linear regression analysis, and the results were compared. Based on actual population, CAT test had much stronger statistical power than linear regression analysis for both overall incidence trend and age specific incidence trend (Cochran-Armitage trend P value

Light propagation and the distance-redshift relation in a realistic inhomogeneous universe

NASA Technical Reports Server (NTRS)

Futamase, Toshifumi; Sasaki, Misao

1989-01-01

The propagation of light rays in a clumpy universe constructed by cosmological version of the post-Newtonian approximation was investigated. It is shown that linear approximation to the propagation equations is valid in the region where zeta is approximately less than 1 even if the density contrast is much larger than unity. Based on a gerneral order-of-magnitude statistical consideration, it is argued that the linear approximation is still valid where zeta is approximately greater than 1. A general formula for the distance-redshift relation in a clumpy universe is given. An explicit expression is derived for a simplified situation in which the effect of the gravitational potential of inhomogeneities dominates. In the light of the derived relation, the validity of the Dyer-Roeder distance is discussed. Also, statistical properties of light rays are investigated for a simple model of an inhomogeneous universe. The result of this example supports the validity of the linear approximation.

Linear regression analysis: part 14 of a series on evaluation of scientific publications.

PubMed

Schneider, Astrid; Hommel, Gerhard; Blettner, Maria

2010-11-01

Regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication. This article is based on selected textbooks of statistics, a selective review of the literature, and our own experience. After a brief introduction of the uni- and multivariable regression models, illustrative examples are given to explain what the important considerations are before a regression analysis is performed, and how the results should be interpreted. The reader should then be able to judge whether the method has been used correctly and interpret the results appropriately. The performance and interpretation of linear regression analysis are subject to a variety of pitfalls, which are discussed here in detail. The reader is made aware of common errors of interpretation through practical examples. Both the opportunities for applying linear regression analysis and its limitations are presented.

The Impact of New Technology on Accounting Education.

ERIC Educational Resources Information Center

Shaoul, Jean

The introduction of computers in the Department of Accounting and Finance at Manchester University is described. General background outlining the increasing need for microcomputers in the accounting curriculum (including financial modelling tools and decision support systems such as linear programming, statistical packages, and simulation) is…

How Universal Is the Relationship Between Remotely Sensed Vegetation Indices (VI) and Crop Leaf Area Index (LAI)?

NASA Technical Reports Server (NTRS)

Kang, Yanghui; Ozdogan, Mutlu; Zipper, Samuel C.; Roman, Miguel

2016-01-01

Global LAI-VI relationships are statistically significant, crop-specific, and mostly non-linear. This research enables the operationalization of large-area crop modeling and, by extension, has relevance to both fundamental and applied agroecosystem research.

On the linearity of tracer bias around voids

NASA Astrophysics Data System (ADS)

Pollina, Giorgia; Hamaus, Nico; Dolag, Klaus; Weller, Jochen; Baldi, Marco; Moscardini, Lauro

2017-07-01

The large-scale structure of the Universe can be observed only via luminous tracers of the dark matter. However, the clustering statistics of tracers are biased and depend on various properties, such as their host-halo mass and assembly history. On very large scales, this tracer bias results in a constant offset in the clustering amplitude, known as linear bias. Towards smaller non-linear scales, this is no longer the case and tracer bias becomes a complicated function of scale and time. We focus on tracer bias centred on cosmic voids, I.e. depressions of the density field that spatially dominate the Universe. We consider three types of tracers: galaxies, galaxy clusters and active galactic nuclei, extracted from the hydrodynamical simulation Magneticum Pathfinder. In contrast to common clustering statistics that focus on auto-correlations of tracers, we find that void-tracer cross-correlations are successfully described by a linear bias relation. The tracer-density profile of voids can thus be related to their matter-density profile by a single number. We show that it coincides with the linear tracer bias extracted from the large-scale auto-correlation function and expectations from theory, if sufficiently large voids are considered. For smaller voids we observe a shift towards higher values. This has important consequences on cosmological parameter inference, as the problem of unknown tracer bias is alleviated up to a constant number. The smallest scales in existing data sets become accessible to simpler models, providing numerous modes of the density field that have been disregarded so far, but may help to further reduce statistical errors in constraining cosmology.

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

DOE PAGES

Del-Castillo-Negrete, Diego B.; Moradi, Sara; Anderson, Johan

2016-09-01

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of -stable Levy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Levy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Levy fluctuations. The absolute value ofmore » the power law decay exponents are linearly proportional to the Levy index. Furthermore, the observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Levy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.« less

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

NASA Astrophysics Data System (ADS)

Moradi, Sara; del-Castillo-Negrete, Diego; Anderson, Johan

2016-09-01

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of α-stable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents is linearly proportional to the Lévy index α. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Lévy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.

Analysis and generation of groundwater concentration time series

NASA Astrophysics Data System (ADS)

Crăciun, Maria; Vamoş, Călin; Suciu, Nicolae

2018-01-01

Concentration time series are provided by simulated concentrations of a nonreactive solute transported in groundwater, integrated over the transverse direction of a two-dimensional computational domain and recorded at the plume center of mass. The analysis of a statistical ensemble of time series reveals subtle features that are not captured by the first two moments which characterize the approximate Gaussian distribution of the two-dimensional concentration fields. The concentration time series exhibit a complex preasymptotic behavior driven by a nonstationary trend and correlated fluctuations with time-variable amplitude. Time series with almost the same statistics are generated by successively adding to a time-dependent trend a sum of linear regression terms, accounting for correlations between fluctuations around the trend and their increments in time, and terms of an amplitude modulated autoregressive noise of order one with time-varying parameter. The algorithm generalizes mixing models used in probability density function approaches. The well-known interaction by exchange with the mean mixing model is a special case consisting of a linear regression with constant coefficients.

Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.

PubMed

Chaubert-Pereira, Florence; Guédon, Yann; Lavergne, Christian; Trottier, Catherine

2010-09-01

Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates. © 2009, The International Biometric Society.

Modeling Count Outcomes from HIV Risk Reduction Interventions: A Comparison of Competing Statistical Models for Count Responses

PubMed Central

Xia, Yinglin; Morrison-Beedy, Dianne; Ma, Jingming; Feng, Changyong; Cross, Wendi; Tu, Xin

2012-01-01

Modeling count data from sexual behavioral outcomes involves many challenges, especially when the data exhibit a preponderance of zeros and overdispersion. In particular, the popular Poisson log-linear model is not appropriate for modeling such outcomes. Although alternatives exist for addressing both issues, they are not widely and effectively used in sex health research, especially in HIV prevention intervention and related studies. In this paper, we discuss how to analyze count outcomes distributed with excess of zeros and overdispersion and introduce appropriate model-fit indices for comparing the performance of competing models, using data from a real study on HIV prevention intervention. The in-depth look at these common issues arising from studies involving behavioral outcomes will promote sound statistical analyses and facilitate research in this and other related areas. PMID:22536496

An open-access CMIP5 pattern library for temperature and precipitation: description and methodology

NASA Astrophysics Data System (ADS)

Lynch, Cary; Hartin, Corinne; Bond-Lamberty, Ben; Kravitz, Ben

2017-05-01

Pattern scaling is used to efficiently emulate general circulation models and explore uncertainty in climate projections under multiple forcing scenarios. Pattern scaling methods assume that local climate changes scale with a global mean temperature increase, allowing for spatial patterns to be generated for multiple models for any future emission scenario. For uncertainty quantification and probabilistic statistical analysis, a library of patterns with descriptive statistics for each file would be beneficial, but such a library does not presently exist. Of the possible techniques used to generate patterns, the two most prominent are the delta and least squares regression methods. We explore the differences and statistical significance between patterns generated by each method and assess performance of the generated patterns across methods and scenarios. Differences in patterns across seasons between methods and epochs were largest in high latitudes (60-90° N/S). Bias and mean errors between modeled and pattern-predicted output from the linear regression method were smaller than patterns generated by the delta method. Across scenarios, differences in the linear regression method patterns were more statistically significant, especially at high latitudes. We found that pattern generation methodologies were able to approximate the forced signal of change to within ≤ 0.5 °C, but the choice of pattern generation methodology for pattern scaling purposes should be informed by user goals and criteria. This paper describes our library of least squares regression patterns from all CMIP5 models for temperature and precipitation on an annual and sub-annual basis, along with the code used to generate these patterns. The dataset and netCDF data generation code are available at doi:10.5281/zenodo.495632.

An evaluation of three statistical estimation methods for assessing health policy effects on prescription drug claims.

PubMed

Mittal, Manish; Harrison, Donald L; Thompson, David M; Miller, Michael J; Farmer, Kevin C; Ng, Yu-Tze

2016-01-01

While the choice of analytical approach affects study results and their interpretation, there is no consensus to guide the choice of statistical approaches to evaluate public health policy change. This study compared and contrasted three statistical estimation procedures in the assessment of a U.S. Food and Drug Administration (FDA) suicidality warning, communicated in January 2008 and implemented in May 2009, on antiepileptic drug (AED) prescription claims. Longitudinal designs were utilized to evaluate Oklahoma (U.S. State) Medicaid claim data from January 2006 through December 2009. The study included 9289 continuously eligible individuals with prevalent diagnoses of epilepsy and/or psychiatric disorder. Segmented regression models using three estimation procedures [i.e., generalized linear models (GLM), generalized estimation equations (GEE), and generalized linear mixed models (GLMM)] were used to estimate trends of AED prescription claims across three time periods: before (January 2006-January 2008); during (February 2008-May 2009); and after (June 2009-December 2009) the FDA warning. All three statistical procedures estimated an increasing trend (P < 0.0001) in AED prescription claims before the FDA warning period. No procedures detected a significant change in trend during (GLM: -30.0%, 99% CI: -60.0% to 10.0%; GEE: -20.0%, 99% CI: -70.0% to 30.0%; GLMM: -23.5%, 99% CI: -58.8% to 1.2%) and after (GLM: 50.0%, 99% CI: -70.0% to 160.0%; GEE: 80.0%, 99% CI: -20.0% to 200.0%; GLMM: 47.1%, 99% CI: -41.2% to 135.3%) the FDA warning when compared to pre-warning period. Although the three procedures provided consistent inferences, the GEE and GLMM approaches accounted appropriately for correlation. Further, marginal models estimated using GEE produced more robust and valid population-level estimations. Copyright © 2016 Elsevier Inc. All rights reserved.

Hybrid regulatory models: a statistically tractable approach to model regulatory network dynamics.

PubMed

Ocone, Andrea; Millar, Andrew J; Sanguinetti, Guido

2013-04-01

Computational modelling of the dynamics of gene regulatory networks is a central task of systems biology. For networks of small/medium scale, the dominant paradigm is represented by systems of coupled non-linear ordinary differential equations (ODEs). ODEs afford great mechanistic detail and flexibility, but calibrating these models to data is often an extremely difficult statistical problem. Here, we develop a general statistical inference framework for stochastic transcription-translation networks. We use a coarse-grained approach, which represents the system as a network of stochastic (binary) promoter and (continuous) protein variables. We derive an exact inference algorithm and an efficient variational approximation that allows scalable inference and learning of the model parameters. We demonstrate the power of the approach on two biological case studies, showing that the method allows a high degree of flexibility and is capable of testable novel biological predictions. http://homepages.inf.ed.ac.uk/gsanguin/software.html. Supplementary data are available at Bioinformatics online.

Estimation and Selection via Absolute Penalized Convex Minimization And Its Multistage Adaptive Applications

PubMed Central

Huang, Jian; Zhang, Cun-Hui

2013-01-01

The ℓ1-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of high-dimensional statistical problems. In this article, we consider a class of weighted ℓ1-penalized estimators for convex loss functions of a general form, including the generalized linear models. We study the estimation, prediction, selection and sparsity properties of the weighted ℓ1-penalized estimator in sparse, high-dimensional settings where the number of predictors p can be much larger than the sample size n. Adaptive Lasso is considered as a special case. A multistage method is developed to approximate concave regularized estimation by applying an adaptive Lasso recursively. We provide prediction and estimation oracle inequalities for single- and multi-stage estimators, a general selection consistency theorem, and an upper bound for the dimension of the Lasso estimator. Important models including the linear regression, logistic regression and log-linear models are used throughout to illustrate the applications of the general results. PMID:24348100

Statistical quality assessment criteria for a linear mixing model with elliptical t-distribution errors

NASA Astrophysics Data System (ADS)

Manolakis, Dimitris G.

2004-10-01

The linear mixing model is widely used in hyperspectral imaging applications to model the reflectance spectra of mixed pixels in the SWIR atmospheric window or the radiance spectra of plume gases in the LWIR atmospheric window. In both cases it is important to detect the presence of materials or gases and then estimate their amount, if they are present. The detection and estimation algorithms available for these tasks are related but they are not identical. The objective of this paper is to theoretically investigate how the heavy tails observed in hyperspectral background data affect the quality of abundance estimates and how the F-test, used for endmember selection, is robust to the presence of heavy tails when the model fits the data.

Stochastic Lanchester-type Combat Models I.

DTIC Science & Technology

1979-10-01

necessarily hold when the attrition rates become non- linear in b and/or r. 13 iL 4. OTHER COMBAT MODELS In this section we briefly describe how other...AD-A092 898 FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS F/6 12/2 STOCHASTIC LANCHESTER-TYPE COMBAT MODELS I.(U) OCT 79 L BILLARD N62271-79-M...COMBAT MODELS I by L. BILLARD October 1979 Approved for public release; distribution unlimited. Prepared for: Naval Postgraduate School Monterey, CA 93940

Convergent evolution and mimicry of protein linear motifs in host-pathogen interactions.

PubMed

Chemes, Lucía Beatriz; de Prat-Gay, Gonzalo; Sánchez, Ignacio Enrique

2015-06-01

Pathogen linear motif mimics are highly evolvable elements that facilitate rewiring of host protein interaction networks. Host linear motifs and pathogen mimics differ in sequence, leading to thermodynamic and structural differences in the resulting protein-protein interactions. Moreover, the functional output of a mimic depends on the motif and domain repertoire of the pathogen protein. Regulatory evolution mediated by linear motifs can be understood by measuring evolutionary rates, quantifying positive and negative selection and performing phylogenetic reconstructions of linear motif natural history. Convergent evolution of linear motif mimics is widespread among unrelated proteins from viral, prokaryotic and eukaryotic pathogens and can also take place within individual protein phylogenies. Statistics, biochemistry and laboratory models of infection link pathogen linear motifs to phenotypic traits such as tropism, virulence and oncogenicity. In vitro evolution experiments and analysis of natural sequences suggest that changes in linear motif composition underlie pathogen adaptation to a changing environment. Copyright © 2015 Elsevier Ltd. All rights reserved.

Estimating linear effects in ANOVA designs: the easy way.

PubMed

Pinhas, Michal; Tzelgov, Joseph; Ganor-Stern, Dana

2012-09-01

Research in cognitive science has documented numerous phenomena that are approximated by linear relationships. In the domain of numerical cognition, the use of linear regression for estimating linear effects (e.g., distance and SNARC effects) became common following Fias, Brysbaert, Geypens, and d'Ydewalle's (1996) study on the SNARC effect. While their work has become the model for analyzing linear effects in the field, it requires statistical analysis of individual participants and does not provide measures of the proportions of variability accounted for (cf. Lorch & Myers, 1990). In the present methodological note, using both the distance and SNARC effects as examples, we demonstrate how linear effects can be estimated in a simple way within the framework of repeated measures analysis of variance. This method allows for estimating effect sizes in terms of both slope and proportions of variability accounted for. Finally, we show that our method can easily be extended to estimate linear interaction effects, not just linear effects calculated as main effects.

Comparison of Linear and Non-linear Regression Analysis to Determine Pulmonary Pressure in Hyperthyroidism.

PubMed

Scarneciu, Camelia C; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D; Varciu, Mihai S; Andreescu, Oana; Scarneciu, Ioan

2017-01-01

This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second degree where the parabola is its graphical representation.

Testing the Dose–Response Specification in Epidemiology: Public Health and Policy Consequences for Lead

PubMed Central

Rothenberg, Stephen J.; Rothenberg, Jesse C.

2005-01-01

Statistical evaluation of the dose–response function in lead epidemiology is rarely attempted. Economic evaluation of health benefits of lead reduction usually assumes a linear dose–response function, regardless of the outcome measure used. We reanalyzed a previously published study, an international pooled data set combining data from seven prospective lead studies examining contemporaneous blood lead effect on IQ (intelligence quotient) of 7-year-old children (n = 1,333). We constructed alternative linear multiple regression models with linear blood lead terms (linear–linear dose response) and natural-log–transformed blood lead terms (log-linear dose response). We tested the two lead specifications for nonlinearity in the models, compared the two lead specifications for significantly better fit to the data, and examined the effects of possible residual confounding on the functional form of the dose–response relationship. We found that a log-linear lead–IQ relationship was a significantly better fit than was a linear–linear relationship for IQ (p = 0.009), with little evidence of residual confounding of included model variables. We substituted the log-linear lead–IQ effect in a previously published health benefits model and found that the economic savings due to U.S. population lead decrease between 1976 and 1999 (from 17.1 μg/dL to 2.0 μg/dL) was 2.2 times ($319 billion) that calculated using a linear–linear dose–response function ($149 billion). The Centers for Disease Control and Prevention action limit of 10 μg/dL for children fails to protect against most damage and economic cost attributable to lead exposure. PMID:16140626

Statistical emulators of maize, rice, soybean and wheat yields from global gridded crop models

DOE PAGES

Blanc, Élodie

2017-01-26

This study provides statistical emulators of crop yields based on global gridded crop model simulations from the Inter-Sectoral Impact Model Intercomparison Project Fast Track project. The ensemble of simulations is used to build a panel of annual crop yields from five crop models and corresponding monthly summer weather variables for over a century at the grid cell level globally. This dataset is then used to estimate, for each crop and gridded crop model, the statistical relationship between yields, temperature, precipitation and carbon dioxide. This study considers a new functional form to better capture the non-linear response of yields to weather,more » especially for extreme temperature and precipitation events, and now accounts for the effect of soil type. In- and out-of-sample validations show that the statistical emulators are able to replicate spatial patterns of yields crop levels and changes overtime projected by crop models reasonably well, although the accuracy of the emulators varies by model and by region. This study therefore provides a reliable and accessible alternative to global gridded crop yield models. By emulating crop yields for several models using parsimonious equations, the tools provide a computationally efficient method to account for uncertainty in climate change impact assessments.« less

Statistical emulators of maize, rice, soybean and wheat yields from global gridded crop models

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

Blanc, Élodie

This study provides statistical emulators of crop yields based on global gridded crop model simulations from the Inter-Sectoral Impact Model Intercomparison Project Fast Track project. The ensemble of simulations is used to build a panel of annual crop yields from five crop models and corresponding monthly summer weather variables for over a century at the grid cell level globally. This dataset is then used to estimate, for each crop and gridded crop model, the statistical relationship between yields, temperature, precipitation and carbon dioxide. This study considers a new functional form to better capture the non-linear response of yields to weather,more » especially for extreme temperature and precipitation events, and now accounts for the effect of soil type. In- and out-of-sample validations show that the statistical emulators are able to replicate spatial patterns of yields crop levels and changes overtime projected by crop models reasonably well, although the accuracy of the emulators varies by model and by region. This study therefore provides a reliable and accessible alternative to global gridded crop yield models. By emulating crop yields for several models using parsimonious equations, the tools provide a computationally efficient method to account for uncertainty in climate change impact assessments.« less

Variable Selection with Prior Information for Generalized Linear Models via the Prior LASSO Method.

PubMed

Jiang, Yuan; He, Yunxiao; Zhang, Heping

LASSO is a popular statistical tool often used in conjunction with generalized linear models that can simultaneously select variables and estimate parameters. When there are many variables of interest, as in current biological and biomedical studies, the power of LASSO can be limited. Fortunately, so much biological and biomedical data have been collected and they may contain useful information about the importance of certain variables. This paper proposes an extension of LASSO, namely, prior LASSO (pLASSO), to incorporate that prior information into penalized generalized linear models. The goal is achieved by adding in the LASSO criterion function an additional measure of the discrepancy between the prior information and the model. For linear regression, the whole solution path of the pLASSO estimator can be found with a procedure similar to the Least Angle Regression (LARS). Asymptotic theories and simulation results show that pLASSO provides significant improvement over LASSO when the prior information is relatively accurate. When the prior information is less reliable, pLASSO shows great robustness to the misspecification. We illustrate the application of pLASSO using a real data set from a genome-wide association study.

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Influence of the nucleus area distribution on the survival fraction after charged particles broad beam irradiation.

PubMed

Wéra, A-C; Barazzuol, L; Jeynes, J C G; Merchant, M J; Suzuki, M; Kirkby, K J

2014-08-07

It is well known that broad beam irradiation with heavy ions leads to variation in the number of hit(s) received by each cell as the distribution of particles follows the Poisson statistics. Although the nucleus area will determine the number of hit(s) received for a given dose, variation amongst its irradiated cell population is generally not considered. In this work, we investigate the effect of the nucleus area's distribution on the survival fraction. More specifically, this work aims to explain the deviation, or tail, which might be observed in the survival fraction at high irradiation doses. For this purpose, the nucleus area distribution was added to the beam Poisson statistics and the Linear-Quadratic model in order to fit the experimental data. As shown in this study, nucleus size variation, and the associated Poisson statistics, can lead to an upward survival trend after broad beam irradiation. The influence of the distribution parameters (mean area and standard deviation) was studied using a normal distribution, along with the Linear-Quadratic model parameters (α and β). Finally, the model proposed here was successfully tested to the survival fraction of LN18 cells irradiated with a 85 keV µm(- 1) carbon ion broad beam for which the distribution in the area of the nucleus had been determined.

Estimating labile particulate iron concentrations in coastal waters from remote sensing data

NASA Astrophysics Data System (ADS)

McGaraghan, Anna R.; Kudela, Raphael M.

2012-02-01

Owing to the difficulties inherent in measuring trace metals and the importance of iron as a limiting nutrient for biological systems, the ability to monitor particulate iron concentration remotely is desirable. This study examines the relationship between labile particulate iron, described here as weak acid leachable particulate iron or total dissolvable iron, and easily obtained bio-optical measurements. We develop a bio-optical proxy that can be used to estimate large-scale patterns of labile iron concentrations in surface waters, and we extend this by including other environmental variables in a multiple linear regression statistical model. By utilizing a ratio of optical backscatter and fluorescence obtained by satellite, we identify patterns in iron concentrations confirmed by traditional shipboard sampling. This basic relationship is improved with the addition of other environmental parameters in the statistical linear regression model. The optical proxy detects known temporal and spatial trends in average surface iron concentrations in Monterey Bay. The proxy is robust in that similar performance was obtained using two independent particulate iron data sets, but it exhibits weaker correlations than the full statistical model. This proxy will be a valuable tool for oceanographers seeking to monitor iron concentrations in coastal regions and allows for better understanding of the variability of labile particulate iron in surface waters to complement direct measurement of leachable particulate or total dissolvable iron.

2-Point microstructure archetypes for improved elastic properties

NASA Astrophysics Data System (ADS)

Adams, Brent L.; Gao, Xiang

2004-01-01

Rectangular models of material microstructure are described by their 1- and 2-point (spatial) correlation statistics of placement of local state. In the procedure described here the local state space is described in discrete form; and the focus is on placement of local state within a finite number of cells comprising rectangular models. It is illustrated that effective elastic properties (generalized Hashin Shtrikman bounds) can be obtained that are linear in components of the correlation statistics. Within this framework the concept of an eigen-microstructure within the microstructure hull is useful. Given the practical innumerability of the microstructure hull, however, we introduce a method for generating a sequence of archetypes of eigen-microstructure, from the 2-point correlation statistics of local state, assuming that the 1-point statistics are stationary. The method is illustrated by obtaining an archetype for an imaginary two-phase material where the objective is to maximize the combination C_{xxxx}^{*} + C_{xyxy}^{*}

Monthly reservoir inflow forecasting using a new hybrid SARIMA genetic programming approach

NASA Astrophysics Data System (ADS)

Moeeni, Hamid; Bonakdari, Hossein; Ebtehaj, Isa

2017-03-01

Forecasting reservoir inflow is one of the most important components of water resources and hydroelectric systems operation management. Seasonal autoregressive integrated moving average (SARIMA) models have been frequently used for predicting river flow. SARIMA models are linear and do not consider the random component of statistical data. To overcome this shortcoming, monthly inflow is predicted in this study based on a combination of seasonal autoregressive integrated moving average (SARIMA) and gene expression programming (GEP) models, which is a new hybrid method (SARIMA-GEP). To this end, a four-step process is employed. First, the monthly inflow datasets are pre-processed. Second, the datasets are modelled linearly with SARIMA and in the third stage, the non-linearity of residual series caused by linear modelling is evaluated. After confirming the non-linearity, the residuals are modelled in the fourth step using a gene expression programming (GEP) method. The proposed hybrid model is employed to predict the monthly inflow to the Jamishan Dam in west Iran. Thirty years' worth of site measurements of monthly reservoir dam inflow with extreme seasonal variations are used. The results of this hybrid model (SARIMA-GEP) are compared with SARIMA, GEP, artificial neural network (ANN) and SARIMA-ANN models. The results indicate that the SARIMA-GEP model ( R 2=78.8, VAF =78.8, RMSE =0.89, MAPE =43.4, CRM =0.053) outperforms SARIMA and GEP and SARIMA-ANN ( R 2=68.3, VAF =66.4, RMSE =1.12, MAPE =56.6, CRM =0.032) displays better performance than the SARIMA and ANN models. A comparison of the two hybrid models indicates the superiority of SARIMA-GEP over the SARIMA-ANN model.

Can upstaging of ductal carcinoma in situ be predicted at biopsy by histologic and mammographic features?

NASA Astrophysics Data System (ADS)

Shi, Bibo; Grimm, Lars J.; Mazurowski, Maciej A.; Marks, Jeffrey R.; King, Lorraine M.; Maley, Carlo C.; Hwang, E. Shelley; Lo, Joseph Y.

2017-03-01

Reducing the overdiagnosis and overtreatment associated with ductal carcinoma in situ (DCIS) requires accurate prediction of the invasive potential at cancer screening. In this work, we investigated the utility of pre-operative histologic and mammographic features to predict upstaging of DCIS. The goal was to provide intentionally conservative baseline performance using readily available data from radiologists and pathologists and only linear models. We conducted a retrospective analysis on 99 patients with DCIS. Of those 25 were upstaged to invasive cancer at the time of definitive surgery. Pre-operative factors including both the histologic features extracted from stereotactic core needle biopsy (SCNB) reports and the mammographic features annotated by an expert breast radiologist were investigated with statistical analysis. Furthermore, we built classification models based on those features in an attempt to predict the presence of an occult invasive component in DCIS, with generalization performance assessed by receiver operating characteristic (ROC) curve analysis. Histologic features including nuclear grade and DCIS subtype did not show statistically significant differences between cases with pure DCIS and with DCIS plus invasive disease. However, three mammographic features, i.e., the major axis length of DCIS lesion, the BI-RADS level of suspicion, and radiologist's assessment did achieve the statistical significance. Using those three statistically significant features as input, a linear discriminant model was able to distinguish patients with DCIS plus invasive disease from those with pure DCIS, with AUC-ROC equal to 0.62. Overall, mammograms used for breast screening contain useful information that can be perceived by radiologists and help predict occult invasive components in DCIS.

A theory of fine structure image models with an application to detection and classification of dementia

PubMed Central

Penn, Richard; Werner, Michael; Thomas, Justin

2015-01-01

Background Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. Methods In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. Results We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Conclusions Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible. PMID:26029638

Functional Relationships and Regression Analysis.

ERIC Educational Resources Information Center

Preece, Peter F. W.

1978-01-01

Using a degenerate multivariate normal model for the distribution of organismic variables, the form of least-squares regression analysis required to estimate a linear functional relationship between variables is derived. It is suggested that the two conventional regression lines may be considered to describe functional, not merely statistical,…

The ultrasound-enhanced bioscouring performance of four polygalacturonase enzymes obtained from rhizopus oryzae

USDA-ARS?s Scientific Manuscript database

An analytical and statistical method has been developed to measure the ultrasound-enhanced bioscouring performance of milligram quantities of endo- and exo-polygalacturonase enzymes obtained from Rhizopus oryzae fungi. UV-Vis spectrophotometric data and a general linear mixed models procedure indic...

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

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

Application of Linear Mixed-Effects Models in Human Neuroscience Research: A Comparison with Pearson Correlation in Two Auditory Electrophysiology Studies.

PubMed

Koerner, Tess K; Zhang, Yang

2017-02-27

Neurophysiological studies are often designed to examine relationships between measures from different testing conditions, time points, or analysis techniques within the same group of participants. Appropriate statistical techniques that can take into account repeated measures and multivariate predictor variables are integral and essential to successful data analysis and interpretation. This work implements and compares conventional Pearson correlations and linear mixed-effects (LME) regression models using data from two recently published auditory electrophysiology studies. For the specific research questions in both studies, the Pearson correlation test is inappropriate for determining strengths between the behavioral responses for speech-in-noise recognition and the multiple neurophysiological measures as the neural responses across listening conditions were simply treated as independent measures. In contrast, the LME models allow a systematic approach to incorporate both fixed-effect and random-effect terms to deal with the categorical grouping factor of listening conditions, between-subject baseline differences in the multiple measures, and the correlational structure among the predictor variables. Together, the comparative data demonstrate the advantages as well as the necessity to apply mixed-effects models to properly account for the built-in relationships among the multiple predictor variables, which has important implications for proper statistical modeling and interpretation of human behavior in terms of neural correlates and biomarkers.

Inferring gene regression networks with model trees

PubMed Central

2010-01-01

Background Novel strategies are required in order to handle the huge amount of data produced by microarray technologies. To infer gene regulatory networks, the first step is to find direct regulatory relationships between genes building the so-called gene co-expression networks. They are typically generated using correlation statistics as pairwise similarity measures. Correlation-based methods are very useful in order to determine whether two genes have a strong global similarity but do not detect local similarities. Results We propose model trees as a method to identify gene interaction networks. While correlation-based methods analyze each pair of genes, in our approach we generate a single regression tree for each gene from the remaining genes. Finally, a graph from all the relationships among output and input genes is built taking into account whether the pair of genes is statistically significant. For this reason we apply a statistical procedure to control the false discovery rate. The performance of our approach, named REGNET, is experimentally tested on two well-known data sets: Saccharomyces Cerevisiae and E.coli data set. First, the biological coherence of the results are tested. Second the E.coli transcriptional network (in the Regulon database) is used as control to compare the results to that of a correlation-based method. This experiment shows that REGNET performs more accurately at detecting true gene associations than the Pearson and Spearman zeroth and first-order correlation-based methods. Conclusions REGNET generates gene association networks from gene expression data, and differs from correlation-based methods in that the relationship between one gene and others is calculated simultaneously. Model trees are very useful techniques to estimate the numerical values for the target genes by linear regression functions. They are very often more precise than linear regression models because they can add just different linear regressions to separate areas of the search space favoring to infer localized similarities over a more global similarity. Furthermore, experimental results show the good performance of REGNET. PMID:20950452

Accelerated Testing and Modeling of Potential-Induced Degradation as a Function of Temperature and Relative Humidity

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

Hacke, Peter; Spataru, Sergiu; Terwilliger, Kent

2015-06-14

An acceleration model based on the Peck equation was applied to power performance of crystalline silicon cell modules as a function of time and of temperature and humidity, the two main environmental stress factors that promote potential-induced degradation. This model was derived from module power degradation data obtained semi-continuously and statistically by in-situ dark current-voltage measurements in an environmental chamber. The modeling enables prediction of degradation rates and times as functions of temperature and humidity. Power degradation could be modeled linearly as a function of time to the second power; additionally, we found that coulombs transferred from the active cellmore » circuit to ground during the stress test is approximately linear with time. Therefore, the power loss could be linearized as a function of coulombs squared. With this result, we observed that when the module face was completely grounded with a condensed phase conductor, leakage current exceeded the anticipated corresponding degradation rate relative to the other tests performed in damp heat.« less

Guidelines and Procedures for Computing Time-Series Suspended-Sediment Concentrations and Loads from In-Stream Turbidity-Sensor and Streamflow Data

USGS Publications Warehouse

Rasmussen, Patrick P.; Gray, John R.; Glysson, G. Douglas; Ziegler, Andrew C.

2009-01-01

In-stream continuous turbidity and streamflow data, calibrated with measured suspended-sediment concentration data, can be used to compute a time series of suspended-sediment concentration and load at a stream site. Development of a simple linear (ordinary least squares) regression model for computing suspended-sediment concentrations from instantaneous turbidity data is the first step in the computation process. If the model standard percentage error (MSPE) of the simple linear regression model meets a minimum criterion, this model should be used to compute a time series of suspended-sediment concentrations. Otherwise, a multiple linear regression model using paired instantaneous turbidity and streamflow data is developed and compared to the simple regression model. If the inclusion of the streamflow variable proves to be statistically significant and the uncertainty associated with the multiple regression model results in an improvement over that for the simple linear model, the turbidity-streamflow multiple linear regression model should be used to compute a suspended-sediment concentration time series. The computed concentration time series is subsequently used with its paired streamflow time series to compute suspended-sediment loads by standard U.S. Geological Survey techniques. Once an acceptable regression model is developed, it can be used to compute suspended-sediment concentration beyond the period of record used in model development with proper ongoing collection and analysis of calibration samples. Regression models to compute suspended-sediment concentrations are generally site specific and should never be considered static, but they represent a set period in a continually dynamic system in which additional data will help verify any change in sediment load, type, and source.

VizieR Online Data Catalog: Supernova matter EOS (Buyukcizmeci+, 2014)

NASA Astrophysics Data System (ADS)

Buyukcizmeci, N.; Botvina, A. S.; Mishustin, I. N.

2017-03-01

The Statistical Model for Supernova Matter (SMSM) was developed in Botvina & Mishustin (2004, PhLB, 584, 233 ; 2010, NuPhA, 843, 98) as a direct generalization of the Statistical Multifragmentation Model (SMM; Bondorf et al. 1995, PhR, 257, 133). We treat supernova matter as a mixture of nuclear species, electrons, and photons in statistical equilibrium. The SMSM EOS tables cover the following ranges of control parameters: 1. Temperature: T = 0.2-25 MeV; for 35 T values. 2. Electron fraction Ye: 0.02-0.56; linear mesh of Ye = 0.02, giving 28 Ye values. It is equal to the total proton fraction Xp, due to charge neutrality. 3. Baryon number density fraction {rho}/{rho}0 = (10-8-0.32), giving 31 {rho}/{rho}0 values. (2 data files).

Evaluating and implementing temporal, spatial, and spatio-temporal methods for outbreak detection in a local syndromic surveillance system

PubMed Central

Lall, Ramona; Levin-Rector, Alison; Sell, Jessica; Paladini, Marc; Konty, Kevin J.; Olson, Don; Weiss, Don

2017-01-01

The New York City Department of Health and Mental Hygiene has operated an emergency department syndromic surveillance system since 2001, using temporal and spatial scan statistics run on a daily basis for cluster detection. Since the system was originally implemented, a number of new methods have been proposed for use in cluster detection. We evaluated six temporal and four spatial/spatio-temporal detection methods using syndromic surveillance data spiked with simulated injections. The algorithms were compared on several metrics, including sensitivity, specificity, positive predictive value, coherence, and timeliness. We also evaluated each method’s implementation, programming time, run time, and the ease of use. Among the temporal methods, at a set specificity of 95%, a Holt-Winters exponential smoother performed the best, detecting 19% of the simulated injects across all shapes and sizes, followed by an autoregressive moving average model (16%), a generalized linear model (15%), a modified version of the Early Aberration Reporting System’s C2 algorithm (13%), a temporal scan statistic (11%), and a cumulative sum control chart (<2%). Of the spatial/spatio-temporal methods we tested, a spatial scan statistic detected 3% of all injects, a Bayes regression found 2%, and a generalized linear mixed model and a space-time permutation scan statistic detected none at a specificity of 95%. Positive predictive value was low (<7%) for all methods. Overall, the detection methods we tested did not perform well in identifying the temporal and spatial clusters of cases in the inject dataset. The spatial scan statistic, our current method for spatial cluster detection, performed slightly better than the other tested methods across different inject magnitudes and types. Furthermore, we found the scan statistics, as applied in the SaTScan software package, to be the easiest to program and implement for daily data analysis. PMID:28886112

Evaluating and implementing temporal, spatial, and spatio-temporal methods for outbreak detection in a local syndromic surveillance system.

PubMed

Mathes, Robert W; Lall, Ramona; Levin-Rector, Alison; Sell, Jessica; Paladini, Marc; Konty, Kevin J; Olson, Don; Weiss, Don

2017-01-01

The New York City Department of Health and Mental Hygiene has operated an emergency department syndromic surveillance system since 2001, using temporal and spatial scan statistics run on a daily basis for cluster detection. Since the system was originally implemented, a number of new methods have been proposed for use in cluster detection. We evaluated six temporal and four spatial/spatio-temporal detection methods using syndromic surveillance data spiked with simulated injections. The algorithms were compared on several metrics, including sensitivity, specificity, positive predictive value, coherence, and timeliness. We also evaluated each method's implementation, programming time, run time, and the ease of use. Among the temporal methods, at a set specificity of 95%, a Holt-Winters exponential smoother performed the best, detecting 19% of the simulated injects across all shapes and sizes, followed by an autoregressive moving average model (16%), a generalized linear model (15%), a modified version of the Early Aberration Reporting System's C2 algorithm (13%), a temporal scan statistic (11%), and a cumulative sum control chart (<2%). Of the spatial/spatio-temporal methods we tested, a spatial scan statistic detected 3% of all injects, a Bayes regression found 2%, and a generalized linear mixed model and a space-time permutation scan statistic detected none at a specificity of 95%. Positive predictive value was low (<7%) for all methods. Overall, the detection methods we tested did not perform well in identifying the temporal and spatial clusters of cases in the inject dataset. The spatial scan statistic, our current method for spatial cluster detection, performed slightly better than the other tested methods across different inject magnitudes and types. Furthermore, we found the scan statistics, as applied in the SaTScan software package, to be the easiest to program and implement for daily data analysis.

Statistical methods for launch vehicle guidance, navigation, and control (GN&C) system design and analysis

NASA Astrophysics Data System (ADS)

Rose, Michael Benjamin

A novel trajectory and attitude control and navigation analysis tool for powered ascent is developed. The tool is capable of rapid trade-space analysis and is designed to ultimately reduce turnaround time for launch vehicle design, mission planning, and redesign work. It is streamlined to quickly determine trajectory and attitude control dispersions, propellant dispersions, orbit insertion dispersions, and navigation errors and their sensitivities to sensor errors, actuator execution uncertainties, and random disturbances. The tool is developed by applying both Monte Carlo and linear covariance analysis techniques to a closed-loop, launch vehicle guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight GN&C software models of a closed-loop, six-degree-of-freedom (6-DOF), Monte Carlo simulation are formulated and developed. The nominal reference trajectory (NRT) for the proposed lunar ascent trajectory is defined and generated. The Monte Carlo truth models and GN&C algorithms are linearized about the NRT, the linear covariance equations are formulated, and the linear covariance simulation is developed. The performance of the launch vehicle GN&C system is evaluated using both Monte Carlo and linear covariance techniques and their trajectory and attitude control dispersion, propellant dispersion, orbit insertion dispersion, and navigation error results are validated and compared. Statistical results from linear covariance analysis are generally within 10% of Monte Carlo results, and in most cases the differences are less than 5%. This is an excellent result given the many complex nonlinearities that are embedded in the ascent GN&C problem. Moreover, the real value of this tool lies in its speed, where the linear covariance simulation is 1036.62 times faster than the Monte Carlo simulation. Although the application and results presented are for a lunar, single-stage-to-orbit (SSTO), ascent vehicle, the tools, techniques, and mathematical formulations that are discussed are applicable to ascent on Earth or other planets as well as other rocket-powered systems such as sounding rockets and ballistic missiles.

Regression Models and Fuzzy Logic Prediction of TBM Penetration Rate

NASA Astrophysics Data System (ADS)

Minh, Vu Trieu; Katushin, Dmitri; Antonov, Maksim; Veinthal, Renno

2017-03-01

This paper presents statistical analyses of rock engineering properties and the measured penetration rate of tunnel boring machine (TBM) based on the data of an actual project. The aim of this study is to analyze the influence of rock engineering properties including uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), rock brittleness index (BI), the distance between planes of weakness (DPW), and the alpha angle (Alpha) between the tunnel axis and the planes of weakness on the TBM rate of penetration (ROP). Four (4) statistical regression models (two linear and two nonlinear) are built to predict the ROP of TBM. Finally a fuzzy logic model is developed as an alternative method and compared to the four statistical regression models. Results show that the fuzzy logic model provides better estimations and can be applied to predict the TBM performance. The R-squared value (R2) of the fuzzy logic model scores the highest value of 0.714 over the second runner-up of 0.667 from the multiple variables nonlinear regression model.

Nonlinear Extraction of Independent Components of Natural Images Using Radial Gaussianization

PubMed Central

Lyu, Siwei; Simoncelli, Eero P.

2011-01-01

We consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent. A widely studied linear solution, known as independent component analysis (ICA), exists for the case when the signal is generated as a linear transformation of independent nongaussian sources. Here, we examine a complementary case, in which the source is nongaussian and elliptically symmetric. In this case, no invertible linear transform suffices to decompose the signal into independent components, but we show that a simple nonlinear transformation, which we call radial gaussianization (RG), is able to remove all dependencies. We then examine this methodology in the context of natural image statistics. We first show that distributions of spatially proximal bandpass filter responses are better described as elliptical than as linearly transformed independent sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either nearby pairs or blocks of bandpass filter responses is significantly greater than that achieved by ICA. Finally, we show that the RG transformation may be closely approximated by divisive normalization, which has been used to model the nonlinear response properties of visual neurons. PMID:19191599

The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions

ERIC Educational Resources Information Center

Molenaar, Dylan; Dolan, Conor V.; de Boeck, Paul

2012-01-01

The Graded Response Model (GRM; Samejima, "Estimation of ability using a response pattern of graded scores," Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, [theta], to underlie the ordinal item scores (Takane & de Leeuw in…

Proceedings: USACERL/ASCE First Joint Conference on Expert Systems, 29-30 June 1988

DTIC Science & Technology

1989-01-01

Wong KOWLEDGE -BASED GRAPHIC DIALOGUES . o ...................... .... 80 D. L Mw 4 CONTENTS (Cont’d) ABSTRACTS ACCEPTED FOR PUBLICATION MAD, AN EXPERT...methodology of inductive shallow modeling was developed. Inductive systems may become powerful shallow modeling tools applicable to a large class of...analysis was conducted using a statistical package, Trajectories. Four different types of relationships were analyzed: linear, logarithmic, power , and

Modelling of binary logistic regression for obesity among secondary students in a rural area of Kedah

NASA Astrophysics Data System (ADS)

Kamaruddin, Ainur Amira; Ali, Zalila; Noor, Norlida Mohd.; Baharum, Adam; Ahmad, Wan Muhamad Amir W.

2014-07-01

Logistic regression analysis examines the influence of various factors on a dichotomous outcome by estimating the probability of the event's occurrence. Logistic regression, also called a logit model, is a statistical procedure used to model dichotomous outcomes. In the logit model the log odds of the dichotomous outcome is modeled as a linear combination of the predictor variables. The log odds ratio in logistic regression provides a description of the probabilistic relationship of the variables and the outcome. In conducting logistic regression, selection procedures are used in selecting important predictor variables, diagnostics are used to check that assumptions are valid which include independence of errors, linearity in the logit for continuous variables, absence of multicollinearity, and lack of strongly influential outliers and a test statistic is calculated to determine the aptness of the model. This study used the binary logistic regression model to investigate overweight and obesity among rural secondary school students on the basis of their demographics profile, medical history, diet and lifestyle. The results indicate that overweight and obesity of students are influenced by obesity in family and the interaction between a student's ethnicity and routine meals intake. The odds of a student being overweight and obese are higher for a student having a family history of obesity and for a non-Malay student who frequently takes routine meals as compared to a Malay student.

Performance of an Axisymmetric Rocket Based Combined Cycle Engine During Rocket Only Operation Using Linear Regression Analysis

NASA Technical Reports Server (NTRS)

Smith, Timothy D.; Steffen, Christopher J., Jr.; Yungster, Shaye; Keller, Dennis J.

1998-01-01

The all rocket mode of operation is shown to be a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. An axisymmetric RBCC engine was used to determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and multiple linear regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inlet diameter ratio. A perfect gas computational fluid dynamics analysis, using both the Spalart-Allmaras and k-omega turbulence models, was performed with the NPARC code to obtain values of vacuum specific impulse. Results from the multiple linear regression analysis showed that for both the full flow and gas generator configurations increasing mixer-ejector area ratio and rocket area ratio increase performance, while increasing mixer-ejector inlet area ratio and mixer-ejector length-to-diameter ratio decrease performance. Increasing injected secondary flow increased performance for the gas generator analysis, but was not statistically significant for the full flow analysis. Chamber pressure was found to be not statistically significant.

kruX: matrix-based non-parametric eQTL discovery.

PubMed

Qi, Jianlong; Asl, Hassan Foroughi; Björkegren, Johan; Michoel, Tom

2014-01-14

The Kruskal-Wallis test is a popular non-parametric statistical test for identifying expression quantitative trait loci (eQTLs) from genome-wide data due to its robustness against variations in the underlying genetic model and expression trait distribution, but testing billions of marker-trait combinations one-by-one can become computationally prohibitive. We developed kruX, an algorithm implemented in Matlab, Python and R that uses matrix multiplications to simultaneously calculate the Kruskal-Wallis test statistic for several millions of marker-trait combinations at once. KruX is more than ten thousand times faster than computing associations one-by-one on a typical human dataset. We used kruX and a dataset of more than 500k SNPs and 20k expression traits measured in 102 human blood samples to compare eQTLs detected by the Kruskal-Wallis test to eQTLs detected by the parametric ANOVA and linear model methods. We found that the Kruskal-Wallis test is more robust against data outliers and heterogeneous genotype group sizes and detects a higher proportion of non-linear associations, but is more conservative for calling additive linear associations. kruX enables the use of robust non-parametric methods for massive eQTL mapping without the need for a high-performance computing infrastructure and is freely available from http://krux.googlecode.com.

MWASTools: an R/bioconductor package for metabolome-wide association studies.

PubMed

Rodriguez-Martinez, Andrea; Posma, Joram M; Ayala, Rafael; Neves, Ana L; Anwar, Maryam; Petretto, Enrico; Emanueli, Costanza; Gauguier, Dominique; Nicholson, Jeremy K; Dumas, Marc-Emmanuel

2018-03-01

MWASTools is an R package designed to provide an integrated pipeline to analyse metabonomic data in large-scale epidemiological studies. Key functionalities of our package include: quality control analysis; metabolome-wide association analysis using various models (partial correlations, generalized linear models); visualization of statistical outcomes; metabolite assignment using statistical total correlation spectroscopy (STOCSY); and biological interpretation of metabolome-wide association studies results. The MWASTools R package is implemented in R (version  > =3.4) and is available from Bioconductor: https://bioconductor.org/packages/MWASTools/. m.dumas@imperial.ac.uk. Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.

A new statistical method for transfer coefficient calculations in the framework of the general multiple-compartment model of transport for radionuclides in biological systems.

PubMed

Garcia, F; Arruda-Neto, J D; Manso, M V; Helene, O M; Vanin, V R; Rodriguez, O; Mesa, J; Likhachev, V P; Filho, J W; Deppman, A; Perez, G; Guzman, F; de Camargo, S P

1999-10-01

A new and simple statistical procedure (STATFLUX) for the calculation of transfer coefficients of radionuclide transport to animals and plants is proposed. The method is based on the general multiple-compartment model, which uses a system of linear equations involving geometrical volume considerations. By using experimentally available curves of radionuclide concentrations versus time, for each animal compartment (organs), flow parameters were estimated by employing a least-squares procedure, whose consistency is tested. Some numerical results are presented in order to compare the STATFLUX transfer coefficients with those from other works and experimental data.

Catalytic conversion reactions in nanoporous systems with concentration-dependent selectivity: Statistical mechanical modeling

DOE PAGES

Garcia, Andres; Wang, Jing; Windus, Theresa L.; ...

2016-05-20

Statistical mechanical modeling is developed to describe a catalytic conversion reaction A → B c or B t with concentration-dependent selectivity of the products, B c or B t, where reaction occurs inside catalytic particles traversed by narrow linear nanopores. The associated restricted diffusive transport, which in the extreme case is described by single-file diffusion, naturally induces strong concentration gradients. Hence, by comparing kinetic Monte Carlo simulation results with analytic treatments, selectivity is shown to be impacted by strong spatial correlations induced by restricted diffusivity in the presence of reaction and also by a subtle clustering of reactants, A.

Chaos as an intermittently forced linear system.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

Strategies for Reduced-Order Models in Uncertainty Quantification of Complex Turbulent Dynamical Systems

NASA Astrophysics Data System (ADS)

Qi, Di

Turbulent dynamical systems are ubiquitous in science and engineering. Uncertainty quantification (UQ) in turbulent dynamical systems is a grand challenge where the goal is to obtain statistical estimates for key physical quantities. In the development of a proper UQ scheme for systems characterized by both a high-dimensional phase space and a large number of instabilities, significant model errors compared with the true natural signal are always unavoidable due to both the imperfect understanding of the underlying physical processes and the limited computational resources available. One central issue in contemporary research is the development of a systematic methodology for reduced order models that can recover the crucial features both with model fidelity in statistical equilibrium and with model sensitivity in response to perturbations. In the first part, we discuss a general mathematical framework to construct statistically accurate reduced-order models that have skill in capturing the statistical variability in the principal directions of a general class of complex systems with quadratic nonlinearity. A systematic hierarchy of simple statistical closure schemes, which are built through new global statistical energy conservation principles combined with statistical equilibrium fidelity, are designed and tested for UQ of these problems. Second, the capacity of imperfect low-order stochastic approximations to model extreme events in a passive scalar field advected by turbulent flows is investigated. The effects in complicated flow systems are considered including strong nonlinear and non-Gaussian interactions, and much simpler and cheaper imperfect models with model error are constructed to capture the crucial statistical features in the stationary tracer field. Several mathematical ideas are introduced to improve the prediction skill of the imperfect reduced-order models. Most importantly, empirical information theory and statistical linear response theory are applied in the training phase for calibrating model errors to achieve optimal imperfect model parameters; and total statistical energy dynamics are introduced to improve the model sensitivity in the prediction phase especially when strong external perturbations are exerted. The validity of reduced-order models for predicting statistical responses and intermittency is demonstrated on a series of instructive models with increasing complexity, including the stochastic triad model, the Lorenz '96 model, and models for barotropic and baroclinic turbulence. The skillful low-order modeling methods developed here should also be useful for other applications such as efficient algorithms for data assimilation.

Linear and non-linear quantitative structure-activity relationship models on indole substitution patterns as inhibitors of HIV-1 attachment.

PubMed

Nirouei, Mahyar; Ghasemi, Ghasem; Abdolmaleki, Parviz; Tavakoli, Abdolreza; Shariati, Shahab

2012-06-01

The antiviral drugs that inhibit human immunodeficiency virus (HIV) entry to the target cells are already in different phases of clinical trials. They prevent viral entry and have a highly specific mechanism of action with a low toxicity profile. Few QSAR studies have been performed on this group of inhibitors. This study was performed to develop a quantitative structure-activity relationship (QSAR) model of the biological activity of indole glyoxamide derivatives as inhibitors of the interaction between HIV glycoprotein gp120 and host cell CD4 receptors. Forty different indole glyoxamide derivatives were selected as a sample set and geometrically optimized using Gaussian 98W. Different combinations of multiple linear regression (MLR), genetic algorithms (GA) and artificial neural networks (ANN) were then utilized to construct the QSAR models. These models were also utilized to select the most efficient subsets of descriptors in a cross-validation procedure for non-linear log (1/EC50) prediction. The results that were obtained using GA-ANN were compared with MLR-MLR and MLR-ANN models. A high predictive ability was observed for the MLR, MLR-ANN and GA-ANN models, with root mean sum square errors (RMSE) of 0.99, 0.91 and 0.67, respectively (N = 40). In summary, machine learning methods were highly effective in designing QSAR models when compared to statistical method.

Machine Learning-based discovery of closures for reduced models of dynamical systems

NASA Astrophysics Data System (ADS)

Pan, Shaowu; Duraisamy, Karthik

2017-11-01

Despite the successful application of machine learning (ML) in fields such as image processing and speech recognition, only a few attempts has been made toward employing ML to represent the dynamics of complex physical systems. Previous attempts mostly focus on parameter calibration or data-driven augmentation of existing models. In this work we present a ML framework to discover closure terms in reduced models of dynamical systems and provide insights into potential problems associated with data-driven modeling. Based on exact closure models for linear system, we propose a general linear closure framework from viewpoint of optimization. The framework is based on trapezoidal approximation of convolution term. Hyperparameters that need to be determined include temporal length of memory effect, number of sampling points, and dimensions of hidden states. To circumvent the explicit specification of memory effect, a general framework inspired from neural networks is also proposed. We conduct both a priori and posteriori evaluations of the resulting model on a number of non-linear dynamical systems. This work was supported in part by AFOSR under the project ``LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

COMPARISON OF CANCER SLOPE FACTORS FOR USING DIFFERENT STATISTICAL APPROACHES

EPA Science Inventory

In the past, the cancer slope factor has been calculated as the upper 95% confidence limit on the coefficient (q1*) of the linear term of the multistage model for the extra cancer risk over background. The U.S. EPA's draft final cancer guidelines, released in 2003, however, pres...

Social Inequality and Labor Force Participation.

ERIC Educational Resources Information Center

King, Jonathan

The labor force participation rates of whites, blacks, and Spanish-Americans, grouped by sex, are explained in a linear regression model fitted with 1970 U. S. Census data on Standard Metropolitan Statistical Area (SMSA). The explanatory variables are: average age, average years of education, vocational training rate, disabled rate, unemployment…

Inferring Action Structure and Causal Relationships in Continuous Sequences of Human Action

DTIC Science & Technology

2014-01-01

language processing literature (e.g., Brent, 1999; Venkataraman , 2001), and which were also used by Goldwater et al. (2009). Precision (P) is the...trees in oriented linear graphs. Simon Stevin: Wis-en Natuurkundig Tijdschrift, 28 , 203. Venkataraman , A. (2001). A statistical model for word discovery

Regression Commonality Analysis: A Technique for Quantitative Theory Building

ERIC Educational Resources Information Center

Nimon, Kim; Reio, Thomas G., Jr.

2011-01-01

When it comes to multiple linear regression analysis (MLR), it is common for social and behavioral science researchers to rely predominately on beta weights when evaluating how predictors contribute to a regression model. Presenting an underutilized statistical technique, this article describes how organizational researchers can use commonality…

Neuroimaging Research: from Null-Hypothesis Falsification to Out-Of-Sample Generalization

ERIC Educational Resources Information Center

Bzdok, Danilo; Varoquaux, Gaël; Thirion, Bertrand

2017-01-01

Brain-imaging technology has boosted the quantification of neurobiological phenomena underlying human mental operations and their disturbances. Since its inception, drawing inference on neurophysiological effects hinged on classical statistical methods, especially, the general linear model. The tens of thousands of variables per brain scan were…

Spatially resolved regression analysis of pre-treatment FDG, FLT and Cu-ATSM PET from post-treatment FDG PET: an exploratory study

PubMed Central

Bowen, Stephen R; Chappell, Richard J; Bentzen, Søren M; Deveau, Michael A; Forrest, Lisa J; Jeraj, Robert

2012-01-01

Purpose To quantify associations between pre-radiotherapy and post-radiotherapy PET parameters via spatially resolved regression. Materials and methods Ten canine sinonasal cancer patients underwent PET/CT scans of [18F]FDG (FDGpre), [18F]FLT (FLTpre), and [61Cu]Cu-ATSM (Cu-ATSMpre). Following radiotherapy regimens of 50 Gy in 10 fractions, veterinary patients underwent FDG PET/CT scans at three months (FDGpost). Regression of standardized uptake values in baseline FDGpre, FLTpre and Cu-ATSMpre tumour voxels to those in FDGpost images was performed for linear, log-linear, generalized-linear and mixed-fit linear models. Goodness-of-fit in regression coefficients was assessed by R2. Hypothesis testing of coefficients over the patient population was performed. Results Multivariate linear model fits of FDGpre to FDGpost were significantly positive over the population (FDGpost~0.17 FDGpre, p=0.03), and classified slopes of RECIST non-responders and responders to be different (0.37 vs. 0.07, p=0.01). Generalized-linear model fits related FDGpre to FDGpost by a linear power law (FDGpost~FDGpre0.93, p<0.001). Univariate mixture model fits of FDGpre improved R2 from 0.17 to 0.52. Neither baseline FLT PET nor Cu-ATSM PET uptake contributed statistically significant multivariate regression coefficients. Conclusions Spatially resolved regression analysis indicates that pre-treatment FDG PET uptake is most strongly associated with three-month post-treatment FDG PET uptake in this patient population, though associations are histopathology-dependent. PMID:22682748

Fragment size distribution statistics in dynamic fragmentation of laser shock-loaded tin

NASA Astrophysics Data System (ADS)

He, Weihua; Xin, Jianting; Zhao, Yongqiang; Chu, Genbai; Xi, Tao; Shui, Min; Lu, Feng; Gu, Yuqiu

2017-06-01

This work investigates the geometric statistics method to characterize the size distribution of tin fragments produced in the laser shock-loaded dynamic fragmentation process. In the shock experiments, the ejection of the tin sample with etched V-shape groove in the free surface are collected by the soft recovery technique. Subsequently, the produced fragments are automatically detected with the fine post-shot analysis techniques including the X-ray micro-tomography and the improved watershed method. To characterize the size distributions of the fragments, a theoretical random geometric statistics model based on Poisson mixtures is derived for dynamic heterogeneous fragmentation problem, which reveals linear combinational exponential distribution. The experimental data related to fragment size distributions of the laser shock-loaded tin sample are examined with the proposed theoretical model, and its fitting performance is compared with that of other state-of-the-art fragment size distribution models. The comparison results prove that our proposed model can provide far more reasonable fitting result for the laser shock-loaded tin.

Are well functioning civil registration and vital statistics systems associated with better health outcomes?

PubMed

Phillips, David E; AbouZahr, Carla; Lopez, Alan D; Mikkelsen, Lene; de Savigny, Don; Lozano, Rafael; Wilmoth, John; Setel, Philip W

2015-10-03

In this Series paper, we examine whether well functioning civil registration and vital statistics (CRVS) systems are associated with improved population health outcomes. We present a conceptual model connecting CRVS to wellbeing, and describe an ecological association between CRVS and health outcomes. The conceptual model posits that the legal identity that civil registration provides to individuals is key to access entitlements and services. Vital statistics produced by CRVS systems provide essential information for public health policy and prevention. These outcomes benefit individuals and societies, including improved health. We use marginal linear models and lag-lead analysis to measure ecological associations between a composite metric of CRVS performance and three health outcomes. Results are consistent with the conceptual model: improved CRVS performance coincides with improved health outcomes worldwide in a temporally consistent manner. Investment to strengthen CRVS systems is not only an important goal for individuals and societies, but also a development imperative that is good for health. Copyright © 2015 Elsevier Ltd. All rights reserved.

Separate-channel analysis of two-channel microarrays: recovering inter-spot information.

PubMed

Smyth, Gordon K; Altman, Naomi S

2013-05-26

Two-channel (or two-color) microarrays are cost-effective platforms for comparative analysis of gene expression. They are traditionally analysed in terms of the log-ratios (M-values) of the two channel intensities at each spot, but this analysis does not use all the information available in the separate channel observations. Mixed models have been proposed to analyse intensities from the two channels as separate observations, but such models can be complex to use and the gain in efficiency over the log-ratio analysis is difficult to quantify. Mixed models yield test statistics for the null distributions can be specified only approximately, and some approaches do not borrow strength between genes. This article reformulates the mixed model to clarify the relationship with the traditional log-ratio analysis, to facilitate information borrowing between genes, and to obtain an exact distributional theory for the resulting test statistics. The mixed model is transformed to operate on the M-values and A-values (average log-expression for each spot) instead of on the log-expression values. The log-ratio analysis is shown to ignore information contained in the A-values. The relative efficiency of the log-ratio analysis is shown to depend on the size of the intraspot correlation. A new separate channel analysis method is proposed that assumes a constant intra-spot correlation coefficient across all genes. This approach permits the mixed model to be transformed into an ordinary linear model, allowing the data analysis to use a well-understood empirical Bayes analysis pipeline for linear modeling of microarray data. This yields statistically powerful test statistics that have an exact distributional theory. The log-ratio, mixed model and common correlation methods are compared using three case studies. The results show that separate channel analyses that borrow strength between genes are more powerful than log-ratio analyses. The common correlation analysis is the most powerful of all. The common correlation method proposed in this article for separate-channel analysis of two-channel microarray data is no more difficult to apply in practice than the traditional log-ratio analysis. It provides an intuitive and powerful means to conduct analyses and make comparisons that might otherwise not be possible.

Landslide susceptibility mapping using GIS-based statistical models and Remote sensing data in tropical environment

PubMed Central

Hashim, Mazlan

2015-01-01

This research presents the results of the GIS-based statistical models for generation of landslide susceptibility mapping using geographic information system (GIS) and remote-sensing data for Cameron Highlands area in Malaysia. Ten factors including slope, aspect, soil, lithology, NDVI, land cover, distance to drainage, precipitation, distance to fault, and distance to road were extracted from SAR data, SPOT 5 and WorldView-1 images. The relationships between the detected landslide locations and these ten related factors were identified by using GIS-based statistical models including analytical hierarchy process (AHP), weighted linear combination (WLC) and spatial multi-criteria evaluation (SMCE) models. The landslide inventory map which has a total of 92 landslide locations was created based on numerous resources such as digital aerial photographs, AIRSAR data, WorldView-1 images, and field surveys. Then, 80% of the landslide inventory was used for training the statistical models and the remaining 20% was used for validation purpose. The validation results using the Relative landslide density index (R-index) and Receiver operating characteristic (ROC) demonstrated that the SMCE model (accuracy is 96%) is better in prediction than AHP (accuracy is 91%) and WLC (accuracy is 89%) models. These landslide susceptibility maps would be useful for hazard mitigation purpose and regional planning. PMID:25898919

Landslide susceptibility mapping using GIS-based statistical models and Remote sensing data in tropical environment.

PubMed

Shahabi, Himan; Hashim, Mazlan

2015-04-22

This research presents the results of the GIS-based statistical models for generation of landslide susceptibility mapping using geographic information system (GIS) and remote-sensing data for Cameron Highlands area in Malaysia. Ten factors including slope, aspect, soil, lithology, NDVI, land cover, distance to drainage, precipitation, distance to fault, and distance to road were extracted from SAR data, SPOT 5 and WorldView-1 images. The relationships between the detected landslide locations and these ten related factors were identified by using GIS-based statistical models including analytical hierarchy process (AHP), weighted linear combination (WLC) and spatial multi-criteria evaluation (SMCE) models. The landslide inventory map which has a total of 92 landslide locations was created based on numerous resources such as digital aerial photographs, AIRSAR data, WorldView-1 images, and field surveys. Then, 80% of the landslide inventory was used for training the statistical models and the remaining 20% was used for validation purpose. The validation results using the Relative landslide density index (R-index) and Receiver operating characteristic (ROC) demonstrated that the SMCE model (accuracy is 96%) is better in prediction than AHP (accuracy is 91%) and WLC (accuracy is 89%) models. These landslide susceptibility maps would be useful for hazard mitigation purpose and regional planning.

Walking through the statistical black boxes of plant breeding.

PubMed

Xavier, Alencar; Muir, William M; Craig, Bruce; Rainey, Katy Martin

2016-10-01

The main statistical procedures in plant breeding are based on Gaussian process and can be computed through mixed linear models. Intelligent decision making relies on our ability to extract useful information from data to help us achieve our goals more efficiently. Many plant breeders and geneticists perform statistical analyses without understanding the underlying assumptions of the methods or their strengths and pitfalls. In other words, they treat these statistical methods (software and programs) like black boxes. Black boxes represent complex pieces of machinery with contents that are not fully understood by the user. The user sees the inputs and outputs without knowing how the outputs are generated. By providing a general background on statistical methodologies, this review aims (1) to introduce basic concepts of machine learning and its applications to plant breeding; (2) to link classical selection theory to current statistical approaches; (3) to show how to solve mixed models and extend their application to pedigree-based and genomic-based prediction; and (4) to clarify how the algorithms of genome-wide association studies work, including their assumptions and limitations.

Statistical mechanics of competitive resource allocation using agent-based models

NASA Astrophysics Data System (ADS)

Chakraborti, Anirban; Challet, Damien; Chatterjee, Arnab; Marsili, Matteo; Zhang, Yi-Cheng; Chakrabarti, Bikas K.

2015-01-01

Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition (El Farol Bar problem, Minority Game, Kolkata Paise Restaurant problem, Stable marriage problem, Parking space problem and others) and the methods used to understand them analytically. We emphasize the power of concepts and tools from statistical mechanics to understand and explain fully collective phenomena such as phase transitions and long memory, and the mapping between agent heterogeneity and physical disorder. As these methods can be applied to any large-scale model of competitive resource allocation made up of heterogeneous adaptive agent with non-linear interaction, they provide a prospective unifying paradigm for many scientific disciplines.

Nonlinear Schrödinger approach to European option pricing

NASA Astrophysics Data System (ADS)

Wróblewski, Marcin

2017-05-01

This paper deals with numerical option pricing methods based on a Schrödinger model rather than the Black-Scholes model. Nonlinear Schrödinger boundary value problems seem to be alternatives to linear models which better reflect the complexity and behavior of real markets. Therefore, based on the nonlinear Schrödinger option pricing model proposed in the literature, in this paper a model augmented by external atomic potentials is proposed and numerically tested. In terms of statistical physics the developed model describes the option in analogy to a pair of two identical quantum particles occupying the same state. The proposed model is used to price European call options on a stock index. the model is calibrated using the Levenberg-Marquardt algorithm based on market data. A Runge-Kutta method is used to solve the discretized boundary value problem numerically. Numerical results are provided and discussed. It seems that our proposal more accurately models phenomena observed in the real market than do linear models.

Mueller-matrix mapping of biological tissues in differential diagnosis of optical anisotropy mechanisms of protein networks

NASA Astrophysics Data System (ADS)

Ushenko, V. A.; Sidor, M. I.; Marchuk, Yu F.; Pashkovskaya, N. V.; Andreichuk, D. R.

2015-03-01

We report a model of Mueller-matrix description of optical anisotropy of protein networks in biological tissues with allowance for the linear birefringence and dichroism. The model is used to construct the reconstruction algorithms of coordinate distributions of phase shifts and the linear dichroism coefficient. In the statistical analysis of such distributions, we have found the objective criteria of differentiation between benign and malignant tissues of the female reproductive system. From the standpoint of evidence-based medicine, we have determined the operating characteristics (sensitivity, specificity and accuracy) of the Mueller-matrix reconstruction method of optical anisotropy parameters and demonstrated its effectiveness in the differentiation of benign and malignant tumours.

A simple white noise analysis of neuronal light responses.

PubMed

Chichilnisky, E J

2001-05-01

A white noise technique is presented for estimating the response properties of spiking visual system neurons. The technique is simple, robust, efficient and well suited to simultaneous recordings from multiple neurons. It provides a complete and easily interpretable model of light responses even for neurons that display a common form of response nonlinearity that precludes classical linear systems analysis. A theoretical justification of the technique is presented that relies only on elementary linear algebra and statistics. Implementation is described with examples. The technique and the underlying model of neural responses are validated using recordings from retinal ganglion cells, and in principle are applicable to other neurons. Advantages and disadvantages of the technique relative to classical approaches are discussed.

Overcoming bias in estimating the volume-outcome relationship.

PubMed

Tsai, Alexander C; Votruba, Mark; Bridges, John F P; Cebul, Randall D

2006-02-01

To examine the effect of hospital volume on 30-day mortality for patients with congestive heart failure (CHF) using administrative and clinical data in conventional regression and instrumental variables (IV) estimation models. The primary data consisted of longitudinal information on comorbid conditions, vital signs, clinical status, and laboratory test results for 21,555 Medicare-insured patients aged 65 years and older hospitalized for CHF in northeast Ohio in 1991-1997. The patient was the primary unit of analysis. We fit a linear probability model to the data to assess the effects of hospital volume on patient mortality within 30 days of admission. Both administrative and clinical data elements were included for risk adjustment. Linear distances between patients and hospitals were used to construct the instrument, which was then used to assess the endogeneity of hospital volume. When only administrative data elements were included in the risk adjustment model, the estimated volume-outcome effect was statistically significant (p=.029) but small in magnitude. The estimate was markedly attenuated in magnitude and statistical significance when clinical data were added to the model as risk adjusters (p=.39). IV estimation shifted the estimate in a direction consistent with selective referral, but we were unable to reject the consistency of the linear probability estimates. Use of only administrative data for volume-outcomes research may generate spurious findings. The IV analysis further suggests that conventional estimates of the volume-outcome relationship may be contaminated by selective referral effects. Taken together, our results suggest that efforts to concentrate hospital-based CHF care in high-volume hospitals may not reduce mortality among elderly patients.

Evaluating the statistical performance of less applied algorithms in classification of worldview-3 imagery data in an urbanized landscape

NASA Astrophysics Data System (ADS)

Ranaie, Mehrdad; Soffianian, Alireza; Pourmanafi, Saeid; Mirghaffari, Noorollah; Tarkesh, Mostafa

2018-03-01

In recent decade, analyzing the remotely sensed imagery is considered as one of the most common and widely used procedures in the environmental studies. In this case, supervised image classification techniques play a central role. Hence, taking a high resolution Worldview-3 over a mixed urbanized landscape in Iran, three less applied image classification methods including Bagged CART, Stochastic gradient boosting model and Neural network with feature extraction were tested and compared with two prevalent methods: random forest and support vector machine with linear kernel. To do so, each method was run ten time and three validation techniques was used to estimate the accuracy statistics consist of cross validation, independent validation and validation with total of train data. Moreover, using ANOVA and Tukey test, statistical difference significance between the classification methods was significantly surveyed. In general, the results showed that random forest with marginal difference compared to Bagged CART and stochastic gradient boosting model is the best performing method whilst based on independent validation there was no significant difference between the performances of classification methods. It should be finally noted that neural network with feature extraction and linear support vector machine had better processing speed than other.

Development of a design space and predictive statistical model for capsule filling of low-fill-weight inhalation products.

PubMed

Faulhammer, E; Llusa, M; Wahl, P R; Paudel, A; Lawrence, S; Biserni, S; Calzolari, V; Khinast, J G

2016-01-01

The objectives of this study were to develop a predictive statistical model for low-fill-weight capsule filling of inhalation products with dosator nozzles via the quality by design (QbD) approach and based on that to create refined models that include quadratic terms for significant parameters. Various controllable process parameters and uncontrolled material attributes of 12 powders were initially screened using a linear model with partial least square (PLS) regression to determine their effect on the critical quality attributes (CQA; fill weight and weight variability). After identifying critical material attributes (CMAs) and critical process parameters (CPPs) that influenced the CQA, model refinement was performed to study if interactions or quadratic terms influence the model. Based on the assessment of the effects of the CPPs and CMAs on fill weight and weight variability for low-fill-weight inhalation products, we developed an excellent linear predictive model for fill weight (R(2 )= 0.96, Q(2 )= 0.96 for powders with good flow properties and R(2 )= 0.94, Q(2 )= 0.93 for cohesive powders) and a model that provides a good approximation of the fill weight variability for each powder group. We validated the model, established a design space for the performance of different types of inhalation grade lactose on low-fill weight capsule filling and successfully used the CMAs and CPPs to predict fill weight of powders that were not included in the development set.

Climate patterns as predictors of amphibians species richness and indicators of potential stress

USGS Publications Warehouse

Battaglin, W.; Hay, L.; McCabe, G.; Nanjappa, P.; Gallant, Alisa L.

2005-01-01

Amphibians occupy a range of habitats throughout the world, but species richness is greatest in regions with moist, warm climates. We modeled the statistical relations of anuran and urodele species richness with mean annual climate for the conterminous United States, and compared the strength of these relations at national and regional levels. Model variables were calculated for county and subcounty mapping units, and included 40-year (1960-1999) annual mean and mean annual climate statistics, mapping unit average elevation, mapping unit land area, and estimates of anuran and urodele species richness. Climate data were derived from more than 7,500 first-order and cooperative meteorological stations and were interpolated to the mapping units using multiple linear regression models. Anuran and urodele species richness were calculated from the United States Geological Survey's Amphibian Research and Monitoring Initiative (ARMI) National Atlas for Amphibian Distributions. The national multivariate linear regression (MLR) model of anuran species richness had an adjusted coefficient of determination (R2) value of 0.64 and the national MLR model for urodele species richness had an R2 value of 0.45. Stratifying the United States by coarse-resolution ecological regions provided models for anUrans that ranged in R2 values from 0.15 to 0.78. Regional models for urodeles had R2 values. ranging from 0.27 to 0.74. In general, regional models for anurans were more strongly influenced by temperature variables, whereas precipitation variables had a larger influence on urodele models.

Log-Linear Models for Gene Association

PubMed Central

Hu, Jianhua; Joshi, Adarsh; Johnson, Valen E.

2009-01-01

We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data that have been reduced to contingency tables using ranks of observations within subjects, and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on Ewens’ sampling distribution is used to restrict the number of interacting components assigned high posterior probability, and the calculation of posterior model probabilities is expedited by approximations based on the likelihood ratio statistic. Simulation studies are used to evaluate the efficiency of the resulting algorithm for known interaction structures. Finally, the algorithm is validated in a microarray study for which it was possible to obtain biological confirmation of detected interactions. PMID:19655032

Modelling Dominance Hierarchies Under Winner and Loser Effects.

PubMed

Kura, Klodeta; Broom, Mark; Kandler, Anne

2015-06-01

Animals that live in groups commonly form themselves into dominance hierarchies which are used to allocate important resources such as access to mating opportunities and food. In this paper, we develop a model of dominance hierarchy formation based upon the concept of winner and loser effects using a simulation-based model and consider the linearity of our hierarchy using existing and new statistical measures. Two models are analysed: when each individual in a group does not know the real ability of their opponents to win a fight and when they can estimate their opponents' ability every time they fight. This estimation may be accurate or fall within an error bound. For both models, we investigate if we can achieve hierarchy linearity, and if so, when it is established. We are particularly interested in the question of how many fights are necessary to establish a dominance hierarchy.

Identifying fMRI Model Violations with Lagrange Multiplier Tests

PubMed Central

Cassidy, Ben; Long, Christopher J; Rae, Caroline; Solo, Victor

2013-01-01

The standard modeling framework in Functional Magnetic Resonance Imaging (fMRI) is predicated on assumptions of linearity, time invariance and stationarity. These assumptions are rarely checked because doing so requires specialised software, although failure to do so can lead to bias and mistaken inference. Identifying model violations is an essential but largely neglected step in standard fMRI data analysis. Using Lagrange Multiplier testing methods we have developed simple and efficient procedures for detecting model violations such as non-linearity, non-stationarity and validity of the common Double Gamma specification for hemodynamic response. These procedures are computationally cheap and can easily be added to a conventional analysis. The test statistic is calculated at each voxel and displayed as a spatial anomaly map which shows regions where a model is violated. The methodology is illustrated with a large number of real data examples. PMID:22542665

Interval Timing Accuracy and Scalar Timing in C57BL/6 Mice

PubMed Central

Buhusi, Catalin V.; Aziz, Dyana; Winslow, David; Carter, Rickey E.; Swearingen, Joshua E.; Buhusi, Mona C.

2010-01-01

In many species, interval timing behavior is accurate—appropriate estimated durations—and scalar—errors vary linearly with estimated durations. While accuracy has been previously examined, scalar timing has not been yet clearly demonstrated in house mice (Mus musculus), raising concerns about mouse models of human disease. We estimated timing accuracy and precision in C57BL/6 mice, the most used background strain for genetic models of human disease, in a peak-interval procedure with multiple intervals. Both when timing two intervals (Experiment 1) or three intervals (Experiment 2), C57BL/6 mice demonstrated varying degrees of timing accuracy. Importantly, both at individual and group level, their precision varied linearly with the subjective estimated duration. Further evidence for scalar timing was obtained using an intraclass correlation statistic. This is the first report of consistent, reliable scalar timing in a sizable sample of house mice, thus validating the PI procedure as a valuable technique, the intraclass correlation statistic as a powerful test of the scalar property, and the C57BL/6 strain as a suitable background for behavioral investigations of genetically engineered mice modeling disorders of interval timing. PMID:19824777

Estimation of Quasi-Stiffness of the Human Hip in the Stance Phase of Walking

PubMed Central

Shamaei, Kamran; Sawicki, Gregory S.; Dollar, Aaron M.

2013-01-01

This work presents a framework for selection of subject-specific quasi-stiffness of hip orthoses and exoskeletons, and other devices that are intended to emulate the biological performance of this joint during walking. The hip joint exhibits linear moment-angular excursion behavior in both the extension and flexion stages of the resilient loading-unloading phase that consists of terminal stance and initial swing phases. Here, we establish statistical models that can closely estimate the slope of linear fits to the moment-angle graph of the hip in this phase, termed as the quasi-stiffness of the hip. Employing an inverse dynamics analysis, we identify a series of parameters that can capture the nearly linear hip quasi-stiffnesses in the resilient loading phase. We then employ regression analysis on experimental moment-angle data of 216 gait trials across 26 human adults walking over a wide range of gait speeds (0.75–2.63 m/s) to obtain a set of general-form statistical models that estimate the hip quasi-stiffnesses using body weight and height, gait speed, and hip excursion. We show that the general-form models can closely estimate the hip quasi-stiffness in the extension (R2 = 92%) and flexion portions (R2 = 89%) of the resilient loading phase of the gait. We further simplify the general-form models and present a set of stature-based models that can estimate the hip quasi-stiffness for the preferred gait speed using only body weight and height with an average error of 27% for the extension stage and 37% for the flexion stage. PMID:24349136

A complete sample of double-lobed radio quasars for VLBI tests of source models - Definition and statistics

NASA Technical Reports Server (NTRS)

Hough, D. H.; Readhead, A. C. S.

1989-01-01

A complete, flux-density-limited sample of double-lobed radio quasars is defined, with nuclei bright enough to be mapped with the Mark III VLBI system. It is shown that the statistics of linear size, nuclear strength, and curvature are consistent with the assumption of random source orientations and simple relativistic beaming in the nuclei. However, these statistics are also consistent with the effects of interaction between the beams and the surrounding medium. The distribution of jet velocities in the nuclei, as measured with VLBI, will provide a powerful test of physical theories of extragalactic radio sources.

Numerical modelling of instantaneous plate tectonics

NASA Technical Reports Server (NTRS)

Minster, J. B.; Haines, E.; Jordan, T. H.; Molnar, P.

1974-01-01

Assuming lithospheric plates to be rigid, 68 spreading rates, 62 fracture zones trends, and 106 earthquake slip vectors are systematically inverted to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum-likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set. The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable.

Linear score tests for variance components in linear mixed models and applications to genetic association studies.

PubMed

Qu, Long; Guennel, Tobias; Marshall, Scott L

2013-12-01

Following the rapid development of genome-scale genotyping technologies, genetic association mapping has become a popular tool to detect genomic regions responsible for certain (disease) phenotypes, especially in early-phase pharmacogenomic studies with limited sample size. In response to such applications, a good association test needs to be (1) applicable to a wide range of possible genetic models, including, but not limited to, the presence of gene-by-environment or gene-by-gene interactions and non-linearity of a group of marker effects, (2) accurate in small samples, fast to compute on the genomic scale, and amenable to large scale multiple testing corrections, and (3) reasonably powerful to locate causal genomic regions. The kernel machine method represented in linear mixed models provides a viable solution by transforming the problem into testing the nullity of variance components. In this study, we consider score-based tests by choosing a statistic linear in the score function. When the model under the null hypothesis has only one error variance parameter, our test is exact in finite samples. When the null model has more than one variance parameter, we develop a new moment-based approximation that performs well in simulations. Through simulations and analysis of real data, we demonstrate that the new test possesses most of the aforementioned characteristics, especially when compared to existing quadratic score tests or restricted likelihood ratio tests. © 2013, The International Biometric Society.

A land use regression model for ambient ultrafine particles in Montreal, Canada: A comparison of linear regression and a machine learning approach.

PubMed

Weichenthal, Scott; Ryswyk, Keith Van; Goldstein, Alon; Bagg, Scott; Shekkarizfard, Maryam; Hatzopoulou, Marianne

2016-04-01

Existing evidence suggests that ambient ultrafine particles (UFPs) (<0.1µm) may contribute to acute cardiorespiratory morbidity. However, few studies have examined the long-term health effects of these pollutants owing in part to a need for exposure surfaces that can be applied in large population-based studies. To address this need, we developed a land use regression model for UFPs in Montreal, Canada using mobile monitoring data collected from 414 road segments during the summer and winter months between 2011 and 2012. Two different approaches were examined for model development including standard multivariable linear regression and a machine learning approach (kernel-based regularized least squares (KRLS)) that learns the functional form of covariate impacts on ambient UFP concentrations from the data. The final models included parameters for population density, ambient temperature and wind speed, land use parameters (park space and open space), length of local roads and rail, and estimated annual average NOx emissions from traffic. The final multivariable linear regression model explained 62% of the spatial variation in ambient UFP concentrations whereas the KRLS model explained 79% of the variance. The KRLS model performed slightly better than the linear regression model when evaluated using an external dataset (R(2)=0.58 vs. 0.55) or a cross-validation procedure (R(2)=0.67 vs. 0.60). In general, our findings suggest that the KRLS approach may offer modest improvements in predictive performance compared to standard multivariable linear regression models used to estimate spatial variations in ambient UFPs. However, differences in predictive performance were not statistically significant when evaluated using the cross-validation procedure. Crown Copyright © 2015. Published by Elsevier Inc. All rights reserved.

Entropy Conservation of Linear Dilaton Black Holes in Quantum Corrected Hawking Radiation

NASA Astrophysics Data System (ADS)

Sakalli, I.; Halilsoy, M.; Pasaoglu, H.

2011-10-01

It has been shown recently that information is lost in the Hawking radiation of the linear dilaton black holes in various theories when applying the tunneling formalism of Parikh and Wilczek without considering quantum gravity effects. In this paper, we recalculate the emission probability by taking into account the log-area correction to the Bekenstein-Hawking entropy and the statistical correlation between quanta emitted. The crucial role of the quantum gravity effects on the information leakage and black hole remnant is highlighted. The entropy conservation of the linear dilaton black holes is discussed in detail. We also model the remnant as an extreme linear dilaton black hole with a pointlike horizon in order to show that such a remnant cannot radiate and its temperature becomes zero. In summary, we show that the information can also leak out of the linear dilaton black holes together with preserving unitarity in quantum mechanics.

Redshift-space distortions with the halo occupation distribution - II. Analytic model

NASA Astrophysics Data System (ADS)

Tinker, Jeremy L.

2007-01-01

We present an analytic model for the galaxy two-point correlation function in redshift space. The cosmological parameters of the model are the matter density Ωm, power spectrum normalization σ8, and velocity bias of galaxies αv, circumventing the linear theory distortion parameter β and eliminating nuisance parameters for non-linearities. The model is constructed within the framework of the halo occupation distribution (HOD), which quantifies galaxy bias on linear and non-linear scales. We model one-halo pairwise velocities by assuming that satellite galaxy velocities follow a Gaussian distribution with dispersion proportional to the virial dispersion of the host halo. Two-halo velocity statistics are a combination of virial motions and host halo motions. The velocity distribution function (DF) of halo pairs is a complex function with skewness and kurtosis that vary substantially with scale. Using a series of collisionless N-body simulations, we demonstrate that the shape of the velocity DF is determined primarily by the distribution of local densities around a halo pair, and at fixed density the velocity DF is close to Gaussian and nearly independent of halo mass. We calibrate a model for the conditional probability function of densities around halo pairs on these simulations. With this model, the full shape of the halo velocity DF can be accurately calculated as a function of halo mass, radial separation, angle and cosmology. The HOD approach to redshift-space distortions utilizes clustering data from linear to non-linear scales to break the standard degeneracies inherent in previous models of redshift-space clustering. The parameters of the occupation function are well constrained by real-space clustering alone, separating constraints on bias and cosmology. We demonstrate the ability of the model to separately constrain Ωm,σ8 and αv in models that are constructed to have the same value of β at large scales as well as the same finger-of-god distortions at small scales.

The Increased Sensitivity of Irregular Peripheral Canal and Otolith Vestibular Afferents Optimizes their Encoding of Natural Stimuli

PubMed Central

Schneider, Adam D.; Jamali, Mohsen; Carriot, Jerome; Chacron, Maurice J.

2015-01-01

Efficient processing of incoming sensory input is essential for an organism's survival. A growing body of evidence suggests that sensory systems have developed coding strategies that are constrained by the statistics of the natural environment. Consequently, it is necessary to first characterize neural responses to natural stimuli to uncover the coding strategies used by a given sensory system. Here we report for the first time the statistics of vestibular rotational and translational stimuli experienced by rhesus monkeys during natural (e.g., walking, grooming) behaviors. We find that these stimuli can reach intensities as high as 1500 deg/s and 8 G. Recordings from afferents during naturalistic rotational and linear motion further revealed strongly nonlinear responses in the form of rectification and saturation, which could not be accurately predicted by traditional linear models of vestibular processing. Accordingly, we used linear–nonlinear cascade models and found that these could accurately predict responses to naturalistic stimuli. Finally, we tested whether the statistics of natural vestibular signals constrain the neural coding strategies used by peripheral afferents. We found that both irregular otolith and semicircular canal afferents, because of their higher sensitivities, were more optimized for processing natural vestibular stimuli as compared with their regular counterparts. Our results therefore provide the first evidence supporting the hypothesis that the neural coding strategies used by the vestibular system are matched to the statistics of natural stimuli. PMID:25855169

[Relationship between finger dermatoglyphics and body size indicators in adulthood among Chinese twin population from Qingdao and Lishui cities].

PubMed

Sun, Luanluan; Yu, Canqing; Lyu, Jun; Cao, Weihua; Pang, Zengchang; Chen, Weijian; Wang, Shaojie; Chen, Rongfu; Gao, Wenjing; Li, Liming

2014-01-01

To study the correlation between fingerprints and body size indicators in adulthood. Samples were composed of twins from two sub-registries of Chinese National Twin Registry (CNTR), including 405 twin pairs in Lishui and 427 twin pairs in Qingdao. All participants were asked to complete the field survey, consisting of questionnaire, physical examination and blood collection. From the 832 twin pairs, those with complete and clear demographic prints were selected as the target population. Information of Fingerprints pixel on the demographic characteristics of these 100 twin pairs and their related adulthood body type indicators were finally chosen to form this research. Descriptive statistics and mixed linear model were used for data analyses. In the mixed linear models adjusted for age and sex, data showed that the body fat percentage of those who had arches was higher than those who did not have the arches (P = 0.002), and those who had radial loops would have higher body fat percentage when compared with ones who did not (P = 0.041). After adjusted for age, there appeared no statistically significant correlation between radial loops and systolic pressure, but the correlations of arches (P = 0.031)and radial loops (P = 0.022) to diastolic pressure still remained statistically significant. Statistically significant correlations were found between fingerprint types and body size indicators, and the fingerprint types showed a useful tool to explore the effects of uterine environment on health status in one's adulthood.

Canopy reflectance modelling of semiarid vegetation

NASA Technical Reports Server (NTRS)

Franklin, Janet

1994-01-01

Three different types of remote sensing algorithms for estimating vegetation amount and other land surface biophysical parameters were tested for semiarid environments. These included statistical linear models, the Li-Strahler geometric-optical canopy model, and linear spectral mixture analysis. The two study areas were the National Science Foundation's Jornada Long Term Ecological Research site near Las Cruces, NM, in the northern Chihuahuan desert, and the HAPEX-Sahel site near Niamey, Niger, in West Africa, comprising semiarid rangeland and subtropical crop land. The statistical approach (simple and multiple regression) resulted in high correlations between SPOT satellite spectral reflectance and shrub and grass cover, although these correlations varied with the spatial scale of aggregation of the measurements. The Li-Strahler model produced estimated of shrub size and density for both study sites with large standard errors. In the Jornada, the estimates were accurate enough to be useful for characterizing structural differences among three shrub strata. In Niger, the range of shrub cover and size in short-fallow shrublands is so low that the necessity of spatially distributed estimation of shrub size and density is questionable. Spectral mixture analysis of multiscale, multitemporal, multispectral radiometer data and imagery for Niger showed a positive relationship between fractions of spectral endmembers and surface parameters of interest including soil cover, vegetation cover, and leaf area index.

Ensemble survival tree models to reveal pairwise interactions of variables with time-to-events outcomes in low-dimensional setting

PubMed Central

Dazard, Jean-Eudes; Ishwaran, Hemant; Mehlotra, Rajeev; Weinberg, Aaron; Zimmerman, Peter

2018-01-01

Unraveling interactions among variables such as genetic, clinical, demographic and environmental factors is essential to understand the development of common and complex diseases. To increase the power to detect such variables interactions associated with clinical time-to-events outcomes, we borrowed established concepts from random survival forest (RSF) models. We introduce a novel RSF-based pairwise interaction estimator and derive a randomization method with bootstrap confidence intervals for inferring interaction significance. Using various linear and nonlinear time-to-events survival models in simulation studies, we first show the efficiency of our approach: true pairwise interaction-effects between variables are uncovered, while they may not be accompanied with their corresponding main-effects, and may not be detected by standard semi-parametric regression modeling and test statistics used in survival analysis. Moreover, using a RSF-based cross-validation scheme for generating prediction estimators, we show that informative predictors may be inferred. We applied our approach to an HIV cohort study recording key host gene polymorphisms and their association with HIV change of tropism or AIDS progression. Altogether, this shows how linear or nonlinear pairwise statistical interactions of variables may be efficiently detected with a predictive value in observational studies with time-to-event outcomes. PMID:29453930

Synthetic data sets for the identification of key ingredients for RNA-seq differential analysis.

PubMed

Rigaill, Guillem; Balzergue, Sandrine; Brunaud, Véronique; Blondet, Eddy; Rau, Andrea; Rogier, Odile; Caius, José; Maugis-Rabusseau, Cathy; Soubigou-Taconnat, Ludivine; Aubourg, Sébastien; Lurin, Claire; Martin-Magniette, Marie-Laure; Delannoy, Etienne

2018-01-01

Numerous statistical pipelines are now available for the differential analysis of gene expression measured with RNA-sequencing technology. Most of them are based on similar statistical frameworks after normalization, differing primarily in the choice of data distribution, mean and variance estimation strategy and data filtering. We propose an evaluation of the impact of these choices when few biological replicates are available through the use of synthetic data sets. This framework is based on real data sets and allows the exploration of various scenarios differing in the proportion of non-differentially expressed genes. Hence, it provides an evaluation of the key ingredients of the differential analysis, free of the biases associated with the simulation of data using parametric models. Our results show the relevance of a proper modeling of the mean by using linear or generalized linear modeling. Once the mean is properly modeled, the impact of the other parameters on the performance of the test is much less important. Finally, we propose to use the simple visualization of the raw P-value histogram as a practical evaluation criterion of the performance of differential analysis methods on real data sets. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Ensemble survival tree models to reveal pairwise interactions of variables with time-to-events outcomes in low-dimensional setting.

PubMed

Dazard, Jean-Eudes; Ishwaran, Hemant; Mehlotra, Rajeev; Weinberg, Aaron; Zimmerman, Peter

2018-02-17

Unraveling interactions among variables such as genetic, clinical, demographic and environmental factors is essential to understand the development of common and complex diseases. To increase the power to detect such variables interactions associated with clinical time-to-events outcomes, we borrowed established concepts from random survival forest (RSF) models. We introduce a novel RSF-based pairwise interaction estimator and derive a randomization method with bootstrap confidence intervals for inferring interaction significance. Using various linear and nonlinear time-to-events survival models in simulation studies, we first show the efficiency of our approach: true pairwise interaction-effects between variables are uncovered, while they may not be accompanied with their corresponding main-effects, and may not be detected by standard semi-parametric regression modeling and test statistics used in survival analysis. Moreover, using a RSF-based cross-validation scheme for generating prediction estimators, we show that informative predictors may be inferred. We applied our approach to an HIV cohort study recording key host gene polymorphisms and their association with HIV change of tropism or AIDS progression. Altogether, this shows how linear or nonlinear pairwise statistical interactions of variables may be efficiently detected with a predictive value in observational studies with time-to-event outcomes.

Statistical Mechanics Model of Solids with Defects

NASA Astrophysics Data System (ADS)

Kaufman, M.; Walters, P. A.; Ferrante, J.

1997-03-01

Previously(M.Kaufman, J.Ferrante,NASA Tech. Memor.,1996), we examined the phase diagram for the failure of a solid under isotropic expansion and compression as a function of stress and temperature with the "springs" modelled by the universal binding energy relation (UBER)(J.H.Rose, J.R.Smith, F.Guinea, J.Ferrante, Phys.Rev.B29, 2963 (1984)). In the previous calculation we assumed that the "springs" failed independently and that the strain is uniform. In the present work, we have extended this statistical model of mechanical failure by allowing for correlations between "springs" and for thermal fluctuations in strains. The springs are now modelled in the harmonic approximation with a failure threshold energy E0, as an intermediate step in future studies to reinclude the full non-linear dependence of the UBER for modelling the interactions. We use the Migdal-Kadanoff renormalization-group method to determine the phase diagram of the model and to compute the free energy.

Nonlinear GARCH model and 1 / f noise

NASA Astrophysics Data System (ADS)

Kononovicius, A.; Ruseckas, J.

2015-06-01

Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.

RAD-ADAPT: Software for modelling clonogenic assay data in radiation biology.

PubMed

Zhang, Yaping; Hu, Kaiqiang; Beumer, Jan H; Bakkenist, Christopher J; D'Argenio, David Z

2017-04-01

We present a comprehensive software program, RAD-ADAPT, for the quantitative analysis of clonogenic assays in radiation biology. Two commonly used models for clonogenic assay analysis, the linear-quadratic model and single-hit multi-target model, are included in the software. RAD-ADAPT uses maximum likelihood estimation method to obtain parameter estimates with the assumption that cell colony count data follow a Poisson distribution. The program has an intuitive interface, generates model prediction plots, tabulates model parameter estimates, and allows automatic statistical comparison of parameters between different groups. The RAD-ADAPT interface is written using the statistical software R and the underlying computations are accomplished by the ADAPT software system for pharmacokinetic/pharmacodynamic systems analysis. The use of RAD-ADAPT is demonstrated using an example that examines the impact of pharmacologic ATM and ATR kinase inhibition on human lung cancer cell line A549 after ionizing radiation. Copyright © 2017 Elsevier B.V. All rights reserved.

A methodology for design of a linear referencing system for surface transportation

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

Vonderohe, A.; Hepworth, T.

1997-06-01

The transportation community has recently placed significant emphasis on development of data models, procedural standards, and policies for management of linearly-referenced data. There is an Intelligent Transportation Systems initiative underway to create a spatial datum for location referencing in one, two, and three dimensions. Most recently, a call was made for development of a unified linear reference system to support public, private, and military surface transportation needs. A methodology for design of the linear referencing system was developed from geodetic engineering principles and techniques used for designing geodetic control networks. The method is founded upon the law of propagation ofmore » random error and the statistical analysis of systems of redundant measurements, used to produce best estimates for unknown parameters. A complete mathematical development is provided. Example adjustments of linear distance measurement systems are included. The classical orders of design are discussed with regard to the linear referencing system. A simple design example is provided. A linear referencing system designed and analyzed with this method will not only be assured of meeting the accuracy requirements of users, it will have the potential for supporting delivery of error estimates along with the results of spatial analytical queries. Modeling considerations, alternative measurement methods, implementation strategies, maintenance issues, and further research needs are discussed. Recommendations are made for further advancement of the unified linear referencing system concept.« less

Covariance approximation for fast and accurate computation of channelized Hotelling observer statistics

NASA Astrophysics Data System (ADS)

Bonetto, P.; Qi, Jinyi; Leahy, R. M.

2000-08-01

Describes a method for computing linear observer statistics for maximum a posteriori (MAP) reconstructions of PET images. The method is based on a theoretical approximation for the mean and covariance of MAP reconstructions. In particular, the authors derive here a closed form for the channelized Hotelling observer (CHO) statistic applied to 2D MAP images. The theoretical analysis models both the Poission statistics of PET data and the inhomogeneity of tracer uptake. The authors show reasonably good correspondence between these theoretical results and Monte Carlo studies. The accuracy and low computational cost of the approximation allow the authors to analyze the observer performance over a wide range of operating conditions and parameter settings for the MAP reconstruction algorithm.

Intelligent Systems Approaches to Product Sound Quality Analysis

NASA Astrophysics Data System (ADS)

Pietila, Glenn M.

As a product market becomes more competitive, consumers become more discriminating in the way in which they differentiate between engineered products. The consumer often makes a purchasing decision based on the sound emitted from the product during operation by using the sound to judge quality or annoyance. Therefore, in recent years, many sound quality analysis tools have been developed to evaluate the consumer preference as it relates to a product sound and to quantify this preference based on objective measurements. This understanding can be used to direct a product design process in order to help differentiate the product from competitive products or to establish an impression on consumers regarding a product's quality or robustness. The sound quality process is typically a statistical tool that is used to model subjective preference, or merit score, based on objective measurements, or metrics. In this way, new product developments can be evaluated in an objective manner without the laborious process of gathering a sample population of consumers for subjective studies each time. The most common model used today is the Multiple Linear Regression (MLR), although recently non-linear Artificial Neural Network (ANN) approaches are gaining popularity. This dissertation will review publicly available published literature and present additional intelligent systems approaches that can be used to improve on the current sound quality process. The focus of this work is to address shortcomings in the current paired comparison approach to sound quality analysis. This research will propose a framework for an adaptive jury analysis approach as an alternative to the current Bradley-Terry model. The adaptive jury framework uses statistical hypothesis testing to focus on sound pairings that are most interesting and is expected to address some of the restrictions required by the Bradley-Terry model. It will also provide a more amicable framework for an intelligent systems approach. Next, an unsupervised jury clustering algorithm is used to identify and classify subgroups within a jury who have conflicting preferences. In addition, a nested Artificial Neural Network (ANN) architecture is developed to predict subjective preference based on objective sound quality metrics, in the presence of non-linear preferences. Finally, statistical decomposition and correlation algorithms are reviewed that can help an analyst establish a clear understanding of the variability of the product sounds used as inputs into the jury study and to identify correlations between preference scores and sound quality metrics in the presence of non-linearities.

A novel framework to simulating non-stationary, non-linear, non-Normal hydrological time series using Markov Switching Autoregressive Models

NASA Astrophysics Data System (ADS)

Birkel, C.; Paroli, R.; Spezia, L.; Tetzlaff, D.; Soulsby, C.

2012-12-01

In this paper we present a novel model framework using the class of Markov Switching Autoregressive Models (MSARMs) to examine catchments as complex stochastic systems that exhibit non-stationary, non-linear and non-Normal rainfall-runoff and solute dynamics. Hereby, MSARMs are pairs of stochastic processes, one observed and one unobserved, or hidden. We model the unobserved process as a finite state Markov chain and assume that the observed process, given the hidden Markov chain, is conditionally autoregressive, which means that the current observation depends on its recent past (system memory). The model is fully embedded in a Bayesian analysis based on Markov Chain Monte Carlo (MCMC) algorithms for model selection and uncertainty assessment. Hereby, the autoregressive order and the dimension of the hidden Markov chain state-space are essentially self-selected. The hidden states of the Markov chain represent unobserved levels of variability in the observed process that may result from complex interactions of hydroclimatic variability on the one hand and catchment characteristics affecting water and solute storage on the other. To deal with non-stationarity, additional meteorological and hydrological time series along with a periodic component can be included in the MSARMs as covariates. This extension allows identification of potential underlying drivers of temporal rainfall-runoff and solute dynamics. We applied the MSAR model framework to streamflow and conservative tracer (deuterium and oxygen-18) time series from an intensively monitored 2.3 km2 experimental catchment in eastern Scotland. Statistical time series analysis, in the form of MSARMs, suggested that the streamflow and isotope tracer time series are not controlled by simple linear rules. MSARMs showed that the dependence of current observations on past inputs observed by transport models often in form of the long-tailing of travel time and residence time distributions can be efficiently explained by non-stationarity either of the system input (climatic variability) and/or the complexity of catchment storage characteristics. The statistical model is also capable of reproducing short (event) and longer-term (inter-event) and wet and dry dynamical "hydrological states". These reflect the non-linear transport mechanisms of flow pathways induced by transient climatic and hydrological variables and modified by catchment characteristics. We conclude that MSARMs are a powerful tool to analyze the temporal dynamics of hydrological data, allowing for explicit integration of non-stationary, non-linear and non-Normal characteristics.

miRNA Temporal Analyzer (mirnaTA): a bioinformatics tool for identifying differentially expressed microRNAs in temporal studies using normal quantile transformation.

PubMed

Cer, Regina Z; Herrera-Galeano, J Enrique; Anderson, Joseph J; Bishop-Lilly, Kimberly A; Mokashi, Vishwesh P

2014-01-01

Understanding the biological roles of microRNAs (miRNAs) is a an active area of research that has produced a surge of publications in PubMed, particularly in cancer research. Along with this increasing interest, many open-source bioinformatics tools to identify existing and/or discover novel miRNAs in next-generation sequencing (NGS) reads become available. While miRNA identification and discovery tools are significantly improved, the development of miRNA differential expression analysis tools, especially in temporal studies, remains substantially challenging. Further, the installation of currently available software is non-trivial and steps of testing with example datasets, trying with one's own dataset, and interpreting the results require notable expertise and time. Subsequently, there is a strong need for a tool that allows scientists to normalize raw data, perform statistical analyses, and provide intuitive results without having to invest significant efforts. We have developed miRNA Temporal Analyzer (mirnaTA), a bioinformatics package to identify differentially expressed miRNAs in temporal studies. mirnaTA is written in Perl and R (Version 2.13.0 or later) and can be run across multiple platforms, such as Linux, Mac and Windows. In the current version, mirnaTA requires users to provide a simple, tab-delimited, matrix file containing miRNA name and count data from a minimum of two to a maximum of 20 time points and three replicates. To recalibrate data and remove technical variability, raw data is normalized using Normal Quantile Transformation (NQT), and linear regression model is used to locate any miRNAs which are differentially expressed in a linear pattern. Subsequently, remaining miRNAs which do not fit a linear model are further analyzed in two different non-linear methods 1) cumulative distribution function (CDF) or 2) analysis of variances (ANOVA). After both linear and non-linear analyses are completed, statistically significant miRNAs (P < 0.05) are plotted as heat maps using hierarchical cluster analysis and Euclidean distance matrix computation methods. mirnaTA is an open-source, bioinformatics tool to aid scientists in identifying differentially expressed miRNAs which could be further mined for biological significance. It is expected to provide researchers with a means of interpreting raw data to statistical summaries in a fast and intuitive manner.

Analyzing Seasonal Variations in Suicide With Fourier Poisson Time-Series Regression: A Registry-Based Study From Norway, 1969-2007.

PubMed

Bramness, Jørgen G; Walby, Fredrik A; Morken, Gunnar; Røislien, Jo

2015-08-01

Seasonal variation in the number of suicides has long been acknowledged. It has been suggested that this seasonality has declined in recent years, but studies have generally used statistical methods incapable of confirming this. We examined all suicides occurring in Norway during 1969-2007 (more than 20,000 suicides in total) to establish whether seasonality decreased over time. Fitting of additive Fourier Poisson time-series regression models allowed for formal testing of a possible linear decrease in seasonality, or a reduction at a specific point in time, while adjusting for a possible smooth nonlinear long-term change without having to categorize time into discrete yearly units. The models were compared using Akaike's Information Criterion and analysis of variance. A model with a seasonal pattern was significantly superior to a model without one. There was a reduction in seasonality during the period. Both the model assuming a linear decrease in seasonality and the model assuming a change at a specific point in time were both superior to a model assuming constant seasonality, thus confirming by formal statistical testing that the magnitude of the seasonality in suicides has diminished. The additive Fourier Poisson time-series regression model would also be useful for studying other temporal phenomena with seasonal components. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Optimizing cost-efficiency in mean exposure assessment - cost functions reconsidered

PubMed Central

2011-01-01

Background Reliable exposure data is a vital concern in medical epidemiology and intervention studies. The present study addresses the needs of the medical researcher to spend monetary resources devoted to exposure assessment with an optimal cost-efficiency, i.e. obtain the best possible statistical performance at a specified budget. A few previous studies have suggested mathematical optimization procedures based on very simple cost models; this study extends the methodology to cover even non-linear cost scenarios. Methods Statistical performance, i.e. efficiency, was assessed in terms of the precision of an exposure mean value, as determined in a hierarchical, nested measurement model with three stages. Total costs were assessed using a corresponding three-stage cost model, allowing costs at each stage to vary non-linearly with the number of measurements according to a power function. Using these models, procedures for identifying the optimally cost-efficient allocation of measurements under a constrained budget were developed, and applied on 225 scenarios combining different sizes of unit costs, cost function exponents, and exposure variance components. Results Explicit mathematical rules for identifying optimal allocation could be developed when cost functions were linear, while non-linear cost functions implied that parts of or the entire optimization procedure had to be carried out using numerical methods. For many of the 225 scenarios, the optimal strategy consisted in measuring on only one occasion from each of as many subjects as allowed by the budget. Significant deviations from this principle occurred if costs for recruiting subjects were large compared to costs for setting up measurement occasions, and, at the same time, the between-subjects to within-subject variance ratio was small. In these cases, non-linearities had a profound influence on the optimal allocation and on the eventual size of the exposure data set. Conclusions The analysis procedures developed in the present study can be used for informed design of exposure assessment strategies, provided that data are available on exposure variability and the costs of collecting and processing data. The present shortage of empirical evidence on costs and appropriate cost functions however impedes general conclusions on optimal exposure measurement strategies in different epidemiologic scenarios. PMID:21600023

Optimizing cost-efficiency in mean exposure assessment--cost functions reconsidered.

PubMed

Mathiassen, Svend Erik; Bolin, Kristian

2011-05-21

Reliable exposure data is a vital concern in medical epidemiology and intervention studies. The present study addresses the needs of the medical researcher to spend monetary resources devoted to exposure assessment with an optimal cost-efficiency, i.e. obtain the best possible statistical performance at a specified budget. A few previous studies have suggested mathematical optimization procedures based on very simple cost models; this study extends the methodology to cover even non-linear cost scenarios. Statistical performance, i.e. efficiency, was assessed in terms of the precision of an exposure mean value, as determined in a hierarchical, nested measurement model with three stages. Total costs were assessed using a corresponding three-stage cost model, allowing costs at each stage to vary non-linearly with the number of measurements according to a power function. Using these models, procedures for identifying the optimally cost-efficient allocation of measurements under a constrained budget were developed, and applied on 225 scenarios combining different sizes of unit costs, cost function exponents, and exposure variance components. Explicit mathematical rules for identifying optimal allocation could be developed when cost functions were linear, while non-linear cost functions implied that parts of or the entire optimization procedure had to be carried out using numerical methods.For many of the 225 scenarios, the optimal strategy consisted in measuring on only one occasion from each of as many subjects as allowed by the budget. Significant deviations from this principle occurred if costs for recruiting subjects were large compared to costs for setting up measurement occasions, and, at the same time, the between-subjects to within-subject variance ratio was small. In these cases, non-linearities had a profound influence on the optimal allocation and on the eventual size of the exposure data set. The analysis procedures developed in the present study can be used for informed design of exposure assessment strategies, provided that data are available on exposure variability and the costs of collecting and processing data. The present shortage of empirical evidence on costs and appropriate cost functions however impedes general conclusions on optimal exposure measurement strategies in different epidemiologic scenarios.

Improved Statistical Fault Detection Technique and Application to Biological Phenomena Modeled by S-Systems.

PubMed

Mansouri, Majdi; Nounou, Mohamed N; Nounou, Hazem N

2017-09-01

In our previous work, we have demonstrated the effectiveness of the linear multiscale principal component analysis (PCA)-based moving window (MW)-generalized likelihood ratio test (GLRT) technique over the classical PCA and multiscale principal component analysis (MSPCA)-based GLRT methods. The developed fault detection algorithm provided optimal properties by maximizing the detection probability for a particular false alarm rate (FAR) with different values of windows, and however, most real systems are nonlinear, which make the linear PCA method not able to tackle the issue of non-linearity to a great extent. Thus, in this paper, first, we apply a nonlinear PCA to obtain an accurate principal component of a set of data and handle a wide range of nonlinearities using the kernel principal component analysis (KPCA) model. The KPCA is among the most popular nonlinear statistical methods. Second, we extend the MW-GLRT technique to one that utilizes exponential weights to residuals in the moving window (instead of equal weightage) as it might be able to further improve fault detection performance by reducing the FAR using exponentially weighed moving average (EWMA). The developed detection method, which is called EWMA-GLRT, provides improved properties, such as smaller missed detection and FARs and smaller average run length. The idea behind the developed EWMA-GLRT is to compute a new GLRT statistic that integrates current and previous data information in a decreasing exponential fashion giving more weight to the more recent data. This provides a more accurate estimation of the GLRT statistic and provides a stronger memory that will enable better decision making with respect to fault detection. Therefore, in this paper, a KPCA-based EWMA-GLRT method is developed and utilized in practice to improve fault detection in biological phenomena modeled by S-systems and to enhance monitoring process mean. The idea behind a KPCA-based EWMA-GLRT fault detection algorithm is to combine the advantages brought forward by the proposed EWMA-GLRT fault detection chart with the KPCA model. Thus, it is used to enhance fault detection of the Cad System in E. coli model through monitoring some of the key variables involved in this model such as enzymes, transport proteins, regulatory proteins, lysine, and cadaverine. The results demonstrate the effectiveness of the proposed KPCA-based EWMA-GLRT method over Q , GLRT, EWMA, Shewhart, and moving window-GLRT methods. The detection performance is assessed and evaluated in terms of FAR, missed detection rates, and average run length (ARL 1 ) values.

Equilibrium statistical-thermal models in high-energy physics

NASA Astrophysics Data System (ADS)

Tawfik, Abdel Nasser

2014-05-01

We review some recent highlights from the applications of statistical-thermal models to different experimental measurements and lattice QCD thermodynamics that have been made during the last decade. We start with a short review of the historical milestones on the path of constructing statistical-thermal models for heavy-ion physics. We discovered that Heinz Koppe formulated in 1948, an almost complete recipe for the statistical-thermal models. In 1950, Enrico Fermi generalized this statistical approach, in which he started with a general cross-section formula and inserted into it, the simplifying assumptions about the matrix element of the interaction process that likely reflects many features of the high-energy reactions dominated by density in the phase space of final states. In 1964, Hagedorn systematically analyzed the high-energy phenomena using all tools of statistical physics and introduced the concept of limiting temperature based on the statistical bootstrap model. It turns to be quite often that many-particle systems can be studied with the help of statistical-thermal methods. The analysis of yield multiplicities in high-energy collisions gives an overwhelming evidence for the chemical equilibrium in the final state. The strange particles might be an exception, as they are suppressed at lower beam energies. However, their relative yields fulfill statistical equilibrium, as well. We review the equilibrium statistical-thermal models for particle production, fluctuations and collective flow in heavy-ion experiments. We also review their reproduction of the lattice QCD thermodynamics at vanishing and finite chemical potential. During the last decade, five conditions have been suggested to describe the universal behavior of the chemical freeze-out parameters. The higher order moments of multiplicity have been discussed. They offer deep insights about particle production and to critical fluctuations. Therefore, we use them to describe the freeze-out parameters and suggest the location of the QCD critical endpoint. Various extensions have been proposed in order to take into consideration the possible deviations of the ideal hadron gas. We highlight various types of interactions, dissipative properties and location-dependences (spatial rapidity). Furthermore, we review three models combining hadronic with partonic phases; quasi-particle model, linear sigma model with Polyakov potentials and compressible bag model.

On statistical inference in time series analysis of the evolution of road safety.

PubMed

Commandeur, Jacques J F; Bijleveld, Frits D; Bergel-Hayat, Ruth; Antoniou, Constantinos; Yannis, George; Papadimitriou, Eleonora

2013-11-01

Data collected for building a road safety observatory usually include observations made sequentially through time. Examples of such data, called time series data, include annual (or monthly) number of road traffic accidents, traffic fatalities or vehicle kilometers driven in a country, as well as the corresponding values of safety performance indicators (e.g., data on speeding, seat belt use, alcohol use, etc.). Some commonly used statistical techniques imply assumptions that are often violated by the special properties of time series data, namely serial dependency among disturbances associated with the observations. The first objective of this paper is to demonstrate the impact of such violations to the applicability of standard methods of statistical inference, which leads to an under or overestimation of the standard error and consequently may produce erroneous inferences. Moreover, having established the adverse consequences of ignoring serial dependency issues, the paper aims to describe rigorous statistical techniques used to overcome them. In particular, appropriate time series analysis techniques of varying complexity are employed to describe the development over time, relating the accident-occurrences to explanatory factors such as exposure measures or safety performance indicators, and forecasting the development into the near future. Traditional regression models (whether they are linear, generalized linear or nonlinear) are shown not to naturally capture the inherent dependencies in time series data. Dedicated time series analysis techniques, such as the ARMA-type and DRAG approaches are discussed next, followed by structural time series models, which are a subclass of state space methods. The paper concludes with general recommendations and practice guidelines for the use of time series models in road safety research. Copyright © 2012 Elsevier Ltd. All rights reserved.

Estimation of parameters in rational reaction rates of molecular biological systems via weighted least squares

NASA Astrophysics Data System (ADS)

Wu, Fang-Xiang; Mu, Lei; Shi, Zhong-Ke

2010-01-01

The models of gene regulatory networks are often derived from statistical thermodynamics principle or Michaelis-Menten kinetics equation. As a result, the models contain rational reaction rates which are nonlinear in both parameters and states. It is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. In this article, we develop a two-step method to estimate the parameters in rational reaction rates of gene regulatory networks via weighted linear least squares. This method takes the special structure of rational reaction rates into consideration. That is, in the rational reaction rates, the numerator and the denominator are linear in parameters. By designing a special weight matrix for the linear least squares, parameters in the numerator and the denominator can be estimated by solving two linear least squares problems. The main advantage of the developed method is that it can produce the analytical solutions to the estimation of parameters in rational reaction rates which originally is nonlinear parameter estimation problem. The developed method is applied to a couple of gene regulatory networks. The simulation results show the superior performance over Gauss-Newton method.

Statistical approach to the analysis of olive long-term pollen season trends in southern Spain.

PubMed

García-Mozo, H; Yaezel, L; Oteros, J; Galán, C

2014-03-01

Analysis of long-term airborne pollen counts makes it possible not only to chart pollen-season trends but also to track changing patterns in flowering phenology. Changes in higher plant response over a long interval are considered among the most valuable bioindicators of climate change impact. Phenological-trend models can also provide information regarding crop production and pollen-allergen emission. The interest of this information makes essential the election of the statistical analysis for time series study. We analysed trends and variations in the olive flowering season over a 30-year period (1982-2011) in southern Europe (Córdoba, Spain), focussing on: annual Pollen Index (PI); Pollen Season Start (PSS), Peak Date (PD), Pollen Season End (PSE) and Pollen Season Duration (PSD). Apart from the traditional Linear Regression analysis, a Seasonal-Trend Decomposition procedure based on Loess (STL) and an ARIMA model were performed. Linear regression results indicated a trend toward delayed PSE and earlier PSS and PD, probably influenced by the rise in temperature. These changes are provoking longer flowering periods in the study area. The use of the STL technique provided a clearer picture of phenological behaviour. Data decomposition on pollination dynamics enabled the trend toward an alternate bearing cycle to be distinguished from the influence of other stochastic fluctuations. Results pointed to show a rising trend in pollen production. With a view toward forecasting future phenological trends, ARIMA models were constructed to predict PSD, PSS and PI until 2016. Projections displayed a better goodness of fit than those derived from linear regression. Findings suggest that olive reproductive cycle is changing considerably over the last 30years due to climate change. Further conclusions are that STL improves the effectiveness of traditional linear regression in trend analysis, and ARIMA models can provide reliable trend projections for future years taking into account the internal fluctuations in time series. Copyright © 2013 Elsevier B.V. All rights reserved.

Linear maps preserving maximal deviation and the Jordan structure of quantum systems

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

Hamhalter, Jan

2012-12-15

In the algebraic approach to quantum theory, a quantum observable is given by an element of a Jordan algebra and a state of the system is modelled by a normalized positive functional on the underlying algebra. Maximal deviation of a quantum observable is the largest statistical deviation one can obtain in a particular state of the system. The main result of the paper shows that each linear bijective transformation between JBW algebras preserving maximal deviations is formed by a Jordan isomorphism or a minus Jordan isomorphism perturbed by a linear functional multiple of an identity. It shows that only onemore » numerical statistical characteristic has the power to determine the Jordan algebraic structure completely. As a consequence, we obtain that only very special maps can preserve the diameter of the spectra of elements. Nonlinear maps preserving the pseudometric given by maximal deviation are also described. The results generalize hitherto known theorems on preservers of maximal deviation in the case of self-adjoint parts of von Neumann algebras proved by Molnar.« less

Syndromic surveillance models using Web data: the case of scarlet fever in the UK.

PubMed

Samaras, Loukas; García-Barriocanal, Elena; Sicilia, Miguel-Angel

2012-03-01

Recent research has shown the potential of Web queries as a source for syndromic surveillance, and existing studies show that these queries can be used as a basis for estimation and prediction of the development of a syndromic disease, such as influenza, using log linear (logit) statistical models. Two alternative models are applied to the relationship between cases and Web queries in this paper. We examine the applicability of using statistical methods to relate search engine queries with scarlet fever cases in the UK, taking advantage of tools to acquire the appropriate data from Google, and using an alternative statistical method based on gamma distributions. The results show that using logit models, the Pearson correlation factor between Web queries and the data obtained from the official agencies must be over 0.90, otherwise the prediction of the peak and the spread of the distributions gives significant deviations. In this paper, we describe the gamma distribution model and show that we can obtain better results in all cases using gamma transformations, and especially in those with a smaller correlation factor.

Time Advice and Learning Questions in Computer Simulations

ERIC Educational Resources Information Center

Rey, Gunter Daniel

2011-01-01

Students (N = 101) used an introductory text and a computer simulation to learn fundamental concepts about statistical analyses (e.g., analysis of variance, regression analysis and General Linear Model). Each learner was randomly assigned to one cell of a 2 (with or without time advice) x 3 (with learning questions and corrective feedback, with…

Tests of Alignment among Assessment, Standards, and Instruction Using Generalized Linear Model Regression

ERIC Educational Resources Information Center

Fulmer, Gavin W.; Polikoff, Morgan S.

2014-01-01

An essential component in school accountability efforts is for assessments to be well-aligned with the standards or curriculum they are intended to measure. However, relatively little prior research has explored methods to determine statistical significance of alignment or misalignment. This study explores analyses of alignment as a special case…

Factor Scores, Structure and Communality Coefficients: A Primer

ERIC Educational Resources Information Center

Odum, Mary

2011-01-01

(Purpose) The purpose of this paper is to present an easy-to-understand primer on three important concepts of factor analysis: Factor scores, structure coefficients, and communality coefficients. Given that statistical analyses are a part of a global general linear model (GLM), and utilize weights as an integral part of analyses (Thompson, 2006;…

Effect Size Measure and Analysis of Single Subject Designs

ERIC Educational Resources Information Center

Swaminathan, Hariharan; Horner, Robert H.; Rogers, H. Jane; Sugai, George

2012-01-01

This study is aimed at addressing the criticisms that have been leveled at the currently available statistical procedures for analyzing single subject designs (SSD). One of the vexing problems in the analysis of SSD is in the assessment of the effect of intervention. Serial dependence notwithstanding, the linear model approach that has been…

Electronic Resource Expenditure and the Decline in Reference Transaction Statistics in Academic Libraries

ERIC Educational Resources Information Center

Dubnjakovic, Ana

2012-01-01

The current study investigates factors influencing increase in reference transactions in a typical week in academic libraries across the United States of America. Employing multiple regression analysis and general linear modeling, variables of interest from the "Academic Library Survey (ALS) 2006" survey (sample size 3960 academic libraries) were…

Power analysis to detect treatment effect in longitudinal studies with heterogeneous errors and incomplete data.

PubMed

Vallejo, Guillermo; Ato, Manuel; Fernández García, Paula; Livacic Rojas, Pablo E; Tuero Herrero, Ellián

2016-08-01

 S. Usami (2014) describes a method to realistically determine sample size in longitudinal research using a multilevel model. The present research extends the aforementioned work to situations where it is likely that the assumption of homogeneity of the errors across groups is not met and the error term does not follow a scaled identity covariance structure.   For this purpose, we followed a procedure based on transforming the variance components of the linear growth model and the parameter related to the treatment effect into specific and easily understandable indices. At the same time, we provide the appropriate statistical machinery for researchers to use when data loss is unavoidable, and changes in the expected value of the observed responses are not linear.   The empirical powers based on unknown variance components were virtually the same as the theoretical powers derived from the use of statistically processed indexes.   The main conclusion of the study is the accuracy of the proposed method to calculate sample size in the described situations with the stipulated power criteria.

-> Air entrainment and bubble statistics in three-dimensional breaking waves

NASA Astrophysics Data System (ADS)

Deike, L.; Popinet, S.; Melville, W. K.

2016-02-01

Wave breaking in the ocean is of fundamental importance for quantifying wave dissipation and air-sea interaction, including gas and momentum exchange, and for improving air-sea flux parametrizations for weather and climate models. Here we investigate air entrainment and bubble statistics in three-dimensional breaking waves through direct numerical simulations of the two-phase air-water flow using the Open Source solver Gerris. As in previous 2D simulations, the dissipation due to breaking is found to be in good agreement with previous experimental observations and inertial-scaling arguments. For radii larger than the Hinze scale, the bubble size distribution is found to follow a power law of the radius, r-10/3 and to scale linearly with the time dependent turbulent dissipation rate during the active breaking stage. The time-averaged bubble size distribution is found to follow the same power law of the radius and to scale linearly with the wave dissipation rate per unit length of breaking crest. We propose a phenomenological turbulent bubble break-up model that describes the numerical results and existing experimental results.

An M-estimator for reduced-rank system identification.

PubMed

Chen, Shaojie; Liu, Kai; Yang, Yuguang; Xu, Yuting; Lee, Seonjoo; Lindquist, Martin; Caffo, Brian S; Vogelstein, Joshua T

2017-01-15

High-dimensional time-series data from a wide variety of domains, such as neuroscience, are being generated every day. Fitting statistical models to such data, to enable parameter estimation and time-series prediction, is an important computational primitive. Existing methods, however, are unable to cope with the high-dimensional nature of these data, due to both computational and statistical reasons. We mitigate both kinds of issues by proposing an M-estimator for Reduced-rank System IDentification ( MR. SID). A combination of low-rank approximations, ℓ 1 and ℓ 2 penalties, and some numerical linear algebra tricks, yields an estimator that is computationally efficient and numerically stable. Simulations and real data examples demonstrate the usefulness of this approach in a variety of problems. In particular, we demonstrate that MR. SID can accurately estimate spatial filters, connectivity graphs, and time-courses from native resolution functional magnetic resonance imaging data. MR. SID therefore enables big time-series data to be analyzed using standard methods, readying the field for further generalizations including non-linear and non-Gaussian state-space models.

An M-estimator for reduced-rank system identification

PubMed Central

Chen, Shaojie; Liu, Kai; Yang, Yuguang; Xu, Yuting; Lee, Seonjoo; Lindquist, Martin; Caffo, Brian S.; Vogelstein, Joshua T.

2018-01-01

High-dimensional time-series data from a wide variety of domains, such as neuroscience, are being generated every day. Fitting statistical models to such data, to enable parameter estimation and time-series prediction, is an important computational primitive. Existing methods, however, are unable to cope with the high-dimensional nature of these data, due to both computational and statistical reasons. We mitigate both kinds of issues by proposing an M-estimator for Reduced-rank System IDentification ( MR. SID). A combination of low-rank approximations, ℓ1 and ℓ2 penalties, and some numerical linear algebra tricks, yields an estimator that is computationally efficient and numerically stable. Simulations and real data examples demonstrate the usefulness of this approach in a variety of problems. In particular, we demonstrate that MR. SID can accurately estimate spatial filters, connectivity graphs, and time-courses from native resolution functional magnetic resonance imaging data. MR. SID therefore enables big time-series data to be analyzed using standard methods, readying the field for further generalizations including non-linear and non-Gaussian state-space models. PMID:29391659

Cognitive predictors of balance in Parkinson's disease.

PubMed

Fernandes, Ângela; Mendes, Andreia; Rocha, Nuno; Tavares, João Manuel R S

2016-06-01

Postural instability is one of the most incapacitating symptoms of Parkinson's disease (PD) and appears to be related to cognitive deficits. This study aims to determine the cognitive factors that can predict deficits in static and dynamic balance in individuals with PD. A sociodemographic questionnaire characterized 52 individuals with PD for this work. The Trail Making Test, Rule Shift Cards Test, and Digit Span Test assessed the executive functions. The static balance was assessed using a plantar pressure platform, and dynamic balance was based on the Timed Up and Go Test. The results were statistically analysed using SPSS Statistics software through linear regression analysis. The results show that a statistically significant model based on cognitive outcomes was able to explain the variance of motor variables. Also, the explanatory value of the model tended to increase with the addition of individual and clinical variables, although the resulting model was not statistically significant The model explained 25-29% of the variability of the Timed Up and Go Test, while for the anteroposterior displacement it was 23-34%, and for the mediolateral displacement it was 24-39%. From the findings, we conclude that the cognitive performance, especially the executive functions, is a predictor of balance deficit in individuals with PD.

Flexible modeling improves assessment of prognostic value of C-reactive protein in advanced non-small cell lung cancer.

PubMed

Gagnon, B; Abrahamowicz, M; Xiao, Y; Beauchamp, M-E; MacDonald, N; Kasymjanova, G; Kreisman, H; Small, D

2010-03-30

C-reactive protein (CRP) is gaining credibility as a prognostic factor in different cancers. Cox's proportional hazard (PH) model is usually used to assess prognostic factors. However, this model imposes a priori assumptions, which are rarely tested, that (1) the hazard ratio associated with each prognostic factor remains constant across the follow-up (PH assumption) and (2) the relationship between a continuous predictor and the logarithm of the mortality hazard is linear (linearity assumption). We tested these two assumptions of the Cox's PH model for CRP, using a flexible statistical model, while adjusting for other known prognostic factors, in a cohort of 269 patients newly diagnosed with non-small cell lung cancer (NSCLC). In the Cox's PH model, high CRP increased the risk of death (HR=1.11 per each doubling of CRP value, 95% CI: 1.03-1.20, P=0.008). However, both the PH assumption (P=0.033) and the linearity assumption (P=0.015) were rejected for CRP, measured at the initiation of chemotherapy, which kept its prognostic value for approximately 18 months. Our analysis shows that flexible modeling provides new insights regarding the value of CRP as a prognostic factor in NSCLC and that Cox's PH model underestimates early risks associated with high CRP.

Binary recursive partitioning: background, methods, and application to psychology.

PubMed

Merkle, Edgar C; Shaffer, Victoria A

2011-02-01

Binary recursive partitioning (BRP) is a computationally intensive statistical method that can be used in situations where linear models are often used. Instead of imposing many assumptions to arrive at a tractable statistical model, BRP simply seeks to accurately predict a response variable based on values of predictor variables. The method outputs a decision tree depicting the predictor variables that were related to the response variable, along with the nature of the variables' relationships. No significance tests are involved, and the tree's 'goodness' is judged based on its predictive accuracy. In this paper, we describe BRP methods in a detailed manner and illustrate their use in psychological research. We also provide R code for carrying out the methods.

Near-road air pollutant concentrations of CO and PM 2.5: A comparison of MOBILE6.2/CALINE4 and generalized additive models

NASA Astrophysics Data System (ADS)

Zhang, Kai; Batterman, Stuart

2010-05-01

The contribution of vehicular traffic to air pollutant concentrations is often difficult to establish. This paper utilizes both time-series and simulation models to estimate vehicle contributions to pollutant levels near roadways. The time-series model used generalized additive models (GAMs) and fitted pollutant observations to traffic counts and meteorological variables. A one year period (2004) was analyzed on a seasonal basis using hourly measurements of carbon monoxide (CO) and particulate matter less than 2.5 μm in diameter (PM 2.5) monitored near a major highway in Detroit, Michigan, along with hourly traffic counts and local meteorological data. Traffic counts showed statistically significant and approximately linear relationships with CO concentrations in fall, and piecewise linear relationships in spring, summer and winter. The same period was simulated using emission and dispersion models (Motor Vehicle Emissions Factor Model/MOBILE6.2; California Line Source Dispersion Model/CALINE4). CO emissions derived from the GAM were similar, on average, to those estimated by MOBILE6.2. The same analyses for PM 2.5 showed that GAM emission estimates were much higher (by 4-5 times) than the dispersion model results, and that the traffic-PM 2.5 relationship varied seasonally. This analysis suggests that the simulation model performed reasonably well for CO, but it significantly underestimated PM 2.5 concentrations, a likely result of underestimating PM 2.5 emission factors. Comparisons between statistical and simulation models can help identify model deficiencies and improve estimates of vehicle emissions and near-road air quality.

An optimization model to agroindustrial sector in antioquia (Colombia, South America)

NASA Astrophysics Data System (ADS)

Fernandez, J.

2015-06-01

This paper develops a proposal of a general optimization model for the flower industry, which is defined by using discrete simulation and nonlinear optimization, whose mathematical models have been solved by using ProModel simulation tools and Gams optimization. It defines the operations that constitute the production and marketing of the sector, statistically validated data taken directly from each operation through field work, the discrete simulation model of the operations and the linear optimization model of the entire industry chain are raised. The model is solved with the tools described above and presents the results validated in a case study.

A performance model for GPUs with caches

DOE PAGES

Dao, Thanh Tuan; Kim, Jungwon; Seo, Sangmin; ...

2014-06-24

To exploit the abundant computational power of the world's fastest supercomputers, an even workload distribution to the typically heterogeneous compute devices is necessary. While relatively accurate performance models exist for conventional CPUs, accurate performance estimation models for modern GPUs do not exist. This paper presents two accurate models for modern GPUs: a sampling-based linear model, and a model based on machine-learning (ML) techniques which improves the accuracy of the linear model and is applicable to modern GPUs with and without caches. We first construct the sampling-based linear model to predict the runtime of an arbitrary OpenCL kernel. Based on anmore » analysis of NVIDIA GPUs' scheduling policies we determine the earliest sampling points that allow an accurate estimation. The linear model cannot capture well the significant effects that memory coalescing or caching as implemented in modern GPUs have on performance. We therefore propose a model based on ML techniques that takes several compiler-generated statistics about the kernel as well as the GPU's hardware performance counters as additional inputs to obtain a more accurate runtime performance estimation for modern GPUs. We demonstrate the effectiveness and broad applicability of the model by applying it to three different NVIDIA GPU architectures and one AMD GPU architecture. On an extensive set of OpenCL benchmarks, on average, the proposed model estimates the runtime performance with less than 7 percent error for a second-generation GTX 280 with no on-chip caches and less than 5 percent for the Fermi-based GTX 580 with hardware caches. On the Kepler-based GTX 680, the linear model has an error of less than 10 percent. On an AMD GPU architecture, Radeon HD 6970, the model estimates with 8 percent of error rates. As a result, the proposed technique outperforms existing models by a factor of 5 to 6 in terms of accuracy.« 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 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

Application of Linear Mixed-Effects Models in Human Neuroscience Research: A Comparison with Pearson Correlation in Two Auditory Electrophysiology Studies

PubMed Central

Koerner, Tess K.; Zhang, Yang

2017-01-01

Neurophysiological studies are often designed to examine relationships between measures from different testing conditions, time points, or analysis techniques within the same group of participants. Appropriate statistical techniques that can take into account repeated measures and multivariate predictor variables are integral and essential to successful data analysis and interpretation. This work implements and compares conventional Pearson correlations and linear mixed-effects (LME) regression models using data from two recently published auditory electrophysiology studies. For the specific research questions in both studies, the Pearson correlation test is inappropriate for determining strengths between the behavioral responses for speech-in-noise recognition and the multiple neurophysiological measures as the neural responses across listening conditions were simply treated as independent measures. In contrast, the LME models allow a systematic approach to incorporate both fixed-effect and random-effect terms to deal with the categorical grouping factor of listening conditions, between-subject baseline differences in the multiple measures, and the correlational structure among the predictor variables. Together, the comparative data demonstrate the advantages as well as the necessity to apply mixed-effects models to properly account for the built-in relationships among the multiple predictor variables, which has important implications for proper statistical modeling and interpretation of human behavior in terms of neural correlates and biomarkers. PMID:28264422

Grain-Size Based Additivity Models for Scaling Multi-rate Uranyl Surface Complexation in Subsurface Sediments

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

Zhang, Xiaoying; Liu, Chongxuan; Hu, Bill X.

This study statistically analyzed a grain-size based additivity model that has been proposed to scale reaction rates and parameters from laboratory to field. The additivity model assumed that reaction properties in a sediment including surface area, reactive site concentration, reaction rate, and extent can be predicted from field-scale grain size distribution by linearly adding reaction properties for individual grain size fractions. This study focused on the statistical analysis of the additivity model with respect to reaction rate constants using multi-rate uranyl (U(VI)) surface complexation reactions in a contaminated sediment as an example. Experimental data of rate-limited U(VI) desorption in amore » stirred flow-cell reactor were used to estimate the statistical properties of multi-rate parameters for individual grain size fractions. The statistical properties of the rate constants for the individual grain size fractions were then used to analyze the statistical properties of the additivity model to predict rate-limited U(VI) desorption in the composite sediment, and to evaluate the relative importance of individual grain size fractions to the overall U(VI) desorption. The result indicated that the additivity model provided a good prediction of the U(VI) desorption in the composite sediment. However, the rate constants were not directly scalable using the additivity model, and U(VI) desorption in individual grain size fractions have to be simulated in order to apply the additivity model. An approximate additivity model for directly scaling rate constants was subsequently proposed and evaluated. The result found that the approximate model provided a good prediction of the experimental results within statistical uncertainty. This study also found that a gravel size fraction (2-8mm), which is often ignored in modeling U(VI) sorption and desorption, is statistically significant to the U(VI) desorption in the sediment.« less

Structural kinetic modeling of metabolic networks.

PubMed

Steuer, Ralf; Gross, Thilo; Selbig, Joachim; Blasius, Bernd

2006-08-08

To develop and investigate detailed mathematical models of metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, kinetic modeling is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a quantitative account of the dynamical capabilities of a metabolic system, without requiring any explicit information about the functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a statistical exploration of the comprehensive parameter space. The method is exemplified on two paradigmatic metabolic systems: the glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.