Download or read book Nonparametric Empirical Bayes Prediction in Mixed Models written by Trambak Banerjee and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixed models are classical tools in statistics for modeling repeated data on subjects, such as data on patients, customers or firms collected over time. These models extend conventional linear models to include latent parameters, called random effects, that capture between-subject variation and accommodate dependence within the repeated measurements of a subject. Traditionally, predictions in mixed models are conducted by assuming that the random effects have a zero mean Normal distribution, which leads to the classical Best Linear Unbiased Predictor (BLUP) of the random effects in these models. However, such a distributional assumption on the random effects is restrictive and may lead to inefficient predictions, especially when the true random effect distribution is far from Normal. In this article, we develop a novel framework, EBPred, for empirical Bayes prediction in mixed models. The predictions from EBPred rely on the Best Predictor (BP) of the random effects, which are constructed without any parametric assumption on the distribution of the random effects and offer a natural extension to the BLUP when the true random effect distribution is not Normal. We develop theory to show that the corresponding predictions from EBPred are asymptotically optimal in terms of mean squared error for prediction. Extensive simulation studies demonstrate that EBPred outperforms existing predictive rules in mixed models and the efficiency gain is substantial in many settings. The method is illustrated on an application involving the prediction of bank stock returns and exhibits superior prediction performance relative to extant approaches.

Download or read book A Mixture Model Approach to Empirical Bayes Testing and Estimation written by Omkar Muralidharan and published by Stanford University. This book was released on 2011 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many modern statistical problems require making similar decisions or estimates for many different entities. For example, we may ask whether each of 10,000 genes is associated with some disease, or try to measure the degree to which each is associated with the disease. As in this example, the entities can often be divided into a vast majority of "null" objects and a small minority of interesting ones. Empirical Bayes is a useful technique for such situations, but finding the right empirical Bayes method for each problem can be difficult. Mixture models, however, provide an easy and effective way to apply empirical Bayes. This thesis motivates mixture models by analyzing a simple high-dimensional problem, and shows their practical use by applying them to detecting single nucleotide polymorphisms.

Download or read book Empirical Bayes Methods in Mixed Linear Models written by Marta Lydia Zanelli and published by . This book was released on 1985 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalized Additive Mixed Models written by Daowen Zhang and published by . This book was released on 1997 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Convex Duality in Nonparametric Empirical Bayes Estimation and Prediction written by Sile Tao and published by . This book was released on 2014 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this thesis is to implement the Kiefer-Wolfowitz nonparametric empirical Bayes method for models with multivariate response, using the idea of the dual algorithm outlined in a paragraph from Koenker and Mizera (2014). The approach of Kiefer-Wolfowitz was numerically elaborated by Koenker and Mizera (2014) and applied to the univariate normal means problem. For the problems with multivariate response, their method may be not numerically feasible. If the dual problem is considered instead, we are able to come up with an adaptive algorithm, which iteratively uses unequally spaced grids to approximate the prior. In this way, we can solve the dual problem without using overly many grid points. Another objective of the thesis is to facilitate the multivariate data-analytic application of the developed algorithm. To this end, we study Tweedie's formula, which can be used to compute the posterior mean, after the estimate of the prior is obtained. Finally, the formulation of the Koenker-Mizera dual has been justified in the discretized setting as the Lagrange dual of the original (discretized) formulation.

Download or read book MULTIPERIOD PREDICTIONS FROM AN AUTOREGRESSIVE MODEL USING EMPIRICAL BAYES METHODS written by R.W. ANDREWS and published by . This book was released on 1976 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Robust Linear Mixed Models with Skew normal Independent Distributions from a Bayesian Perspective written by V. H. Lachos and published by . This book was released on 2008 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Mixture Model Approach to Empirical Bayes Testing and Estimation written by Omkar Muralidharan and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Many modern statistical problems require making similar decisions or estimates for many different entities. For example, we may ask whether each of 10,000 genes is associated with some disease, or try to measure the degree to which each is associated with the disease. As in this example, the entities can often be divided into a vast majority of "null" objects and a small minority of interesting ones. Empirical Bayes is a useful technique for such situations, but finding the right empirical Bayes method for each problem can be difficult. Mixture models, however, provide an easy and effective way to apply empirical Bayes. This thesis motivates mixture models by analyzing a simple high-dimensional problem, and shows their practical use by applying them to detecting single nucleotide polymorphisms.

Download or read book Some Advances in Bayesian Nonparametric Modeling written by Abel Rodriguez and published by LAP Lambert Academic Publishing. This book was released on 2009-03 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian nonparametric and semiparametric mixture models have become extremely popular in the last 10 years because they provide flexibility and interpretability while preserving computational simplicity. This book is a contribution to this growing literature, discussing the design of models for collections of distributions and their application to density estimation and nonparametric regression. All methods introduced in this book are discussed in the context of complex scientific applications in public health, epidemiology and finance.

Download or read book Nonparametric Estimation of the Mixing Distribution in Mixed Models with Random Intercepts and Slopes written by Rabih Saab and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=?i log?f(yi,?) dG(?)where f(.,?) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector ? defined on ?.The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach.

Download or read book Nonparametric Method and Hierarchical Bayesian Approach for Parameter Estimation and Prediction written by Jing Cai and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Obtaining accurate estimates or prediction from available data is one of the important goals in statistical research. In this thesis, we propose two new statistical methods, with examples of application and simulation studies, to achieve this goal. The parametric penalized spline smoothing procedure is a flexible algorithm that requires no restricted parametric assumption and is proved to obtain more accurate estimates of curves and derivatives than available methods. In the second part of thesis, we propose a hierarchical Bayesian approach to estimate dynamic engineering model parameters and their mixed effects. This approach has the benefits of solving the identifiability problem of model parameters and accurately estimating these parameters from right censored data. It is further investigated with simulated data to perform predictions. Predicting quality with this method is proved to be better than that from procedures without considering censoring situation.

Download or read book Non parametric Empirical Bayes Procedures written by Milton V. Johns and published by . This book was released on 1957 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Nonparametric and Semiparametric Modeling Using Dirichlet Process Mixing written by Athanasios Kottas and published by . This book was released on 2000 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mixed Effects Models for Complex Data written by Lang Wu and published by CRC Press. This book was released on 2009-11-11 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.

Download or read book Models for Discrete Longitudinal Data written by Geert Molenberghs and published by Springer Science & Business Media. This book was released on 2006-08-30 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: The linear mixed model has become the main parametric tool for the analysis of continuous longitudinal data, as the authors discussed in their 2000 book. Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The authors received the American Statistical Association's Excellence in Continuing Education Award based on short courses on longitudinal and incomplete data at the Joint Statistical Meetings of 2002 and 2004.

Download or read book A Course on Small Area Estimation and Mixed Models written by Domingo Morales and published by Springer Nature. This book was released on 2021-03-12 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced textbook explores small area estimation techniques, covers the underlying mathematical and statistical theory and offers hands-on support with their implementation. It presents the theory in a rigorous way and compares and contrasts various statistical methodologies, helping readers understand how to develop new methodologies for small area estimation. It also includes numerous sample applications of small area estimation techniques. The underlying R code is provided in the text and applied to four datasets that mimic data from labor markets and living conditions surveys, where the socioeconomic indicators include the small area estimation of total unemployment, unemployment rates, average annual household incomes and poverty indicators. Given its scope, the book will be useful for master and PhD students, and for official and other applied statisticians.

Download or read book Methods and Applications of Longitudinal Data Analysis written by Xian Liu and published by Elsevier. This book was released on 2015-09-01 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods and Applications of Longitudinal Data Analysis describes methods for the analysis of longitudinal data in the medical, biological and behavioral sciences. It introduces basic concepts and functions including a variety of regression models, and their practical applications across many areas of research. Statistical procedures featured within the text include: descriptive methods for delineating trends over time linear mixed regression models with both fixed and random effects covariance pattern models on correlated errors generalized estimating equations nonlinear regression models for categorical repeated measurements techniques for analyzing longitudinal data with non-ignorable missing observations Emphasis is given to applications of these methods, using substantial empirical illustrations, designed to help users of statistics better analyze and understand longitudinal data. Methods and Applications of Longitudinal Data Analysis equips both graduate students and professionals to confidently apply longitudinal data analysis to their particular discipline. It also provides a valuable reference source for applied statisticians, demographers and other quantitative methodologists. From novice to professional: this book starts with the introduction of basic models and ends with the description of some of the most advanced models in longitudinal data analysis Enables students to select the correct statistical methods to apply to their longitudinal data and avoid the pitfalls associated with incorrect selection Identifies the limitations of classical repeated measures models and describes newly developed techniques, along with real-world examples.