Download or read book Estimating Posterior Distributions in the Nonlinear Mixed Model Using the Gibbs Sampler and the Metropolis Algorithm written by Jack Richard Gerson and published by . This book was released on 1991 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book GIBBS SAMPLING FOR BYESIAN NINCINJUGATE MODELSUSING AUXILLARY VARIABLE written by PAUL DAMIEN and published by . This book was released on 1997 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Exploring Posterior Distributions Using Markov Chains written by Luke Tierney and published by . This book was released on 1992 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several Markov chain-based methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the strategies that are available, and discusses some theoretical and practical issues in the use of these strategies. In addition, some preliminary efforts to use Markov chains to control dynamic graphics for exploring higher-dimensional posterior distributions are outlined.

Download or read book Mixed Effects Models in S and S PLUS written by José C. Pinheiro and published by Springer Science & Business Media. This book was released on 2009-04-15 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: R, linear models, random, fixed, data, analysis, fit.

Download or read book Graphics and Visualization written by and published by . This book was released on 1992 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Markov Chain Monte Carlo in Practice written by W.R. Gilks and published by CRC Press. This book was released on 1995-12-01 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France,

Download or read book Handbook of Statistical Genetics written by David J. Balding and published by John Wiley & Sons. This book was released on 2008-06-10 with total page 1616 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook for Statistical Genetics is widely regarded as the reference work in the field. However, the field has developed considerably over the past three years. In particular the modeling of genetic networks has advanced considerably via the evolution of microarray analysis. As a consequence the 3rd edition of the handbook contains a much expanded section on Network Modeling, including 5 new chapters covering metabolic networks, graphical modeling and inference and simulation of pedigrees and genealogies. Other chapters new to the 3rd edition include Human Population Genetics, Genome-wide Association Studies, Family-based Association Studies, Pharmacogenetics, Epigenetics, Ethic and Insurance. As with the second Edition, the Handbook includes a glossary of terms, acronyms and abbreviations, and features extensive cross-referencing between the chapters, tying the different areas together. With heavy use of up-to-date examples, real-life case studies and references to web-based resources, this continues to be must-have reference in a vital area of research. Edited by the leading international authorities in the field. David Balding - Department of Epidemiology & Public Health, Imperial College An advisor for our Probability & Statistics series, Professor Balding is also a previous Wiley author, having written Weight-of-Evidence for Forensic DNA Profiles, as well as having edited the two previous editions of HSG. With over 20 years teaching experience, he’s also had dozens of articles published in numerous international journals. Martin Bishop – Head of the Bioinformatics Division at the HGMP Resource Centre As well as the first two editions of HSG, Dr Bishop has edited a number of introductory books on the application of informatics to molecular biology and genetics. He is the Associate Editor of the journal Bioinformatics and Managing Editor of Briefings in Bioinformatics. Chris Cannings – Division of Genomic Medicine, University of Sheffield With over 40 years teaching in the area, Professor Cannings has published over 100 papers and is on the editorial board of many related journals. Co-editor of the two previous editions of HSG, he also authored a book on this topic.

Download or read book Markov Chain Monte Carlo written by Dani Gamerman and published by CRC Press. This book was released on 2006-05-10 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition presents a concise, accessible, and comprehensive introduction to the methods of this valuable simulation technique. The second edition includes access to an internet site that provides the code, written in R and WinBUGS, used in many of the previously existing and new examples and exercises. More importantly, the self-explanatory nature of the codes will enable modification of the inputs to the codes and variation on many directions will be available for further exploration. Major changes from the previous edition: · More examples with discussion of computational details in chapters on Gibbs sampling and Metropolis-Hastings algorithms · Recent developments in MCMC, including reversible jump, slice sampling, bridge sampling, path sampling, multiple-try, and delayed rejection · Discussion of computation using both R and WinBUGS · Additional exercises and selected solutions within the text, with all data sets and software available for download from the Web · Sections on spatial models and model adequacy The self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. The book will appeal to everyone working with MCMC techniques, especially research and graduate statisticians and biostatisticians, and scientists handling data and formulating models. The book has been substantially reinforced as a first reading of material on MCMC and, consequently, as a textbook for modern Bayesian computation and Bayesian inference courses.

Download or read book Handbook of Structural Equation Modeling written by Rick H. Hoyle and published by Guilford Publications. This book was released on 2023-02-17 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible volume presents both the mechanics of structural equation modeling (SEM) and specific SEM strategies and applications. The editor, along with an international group of contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, including new and emerging topics in SEM. Each chapter provides conceptually oriented descriptions, fully explicated analyses, and engaging examples that reveal modeling possibilities for use with readers' data. Many of the chapters also include access to data and syntax files at the companion website, allowing readers to try their hands at reproducing the authors' results"--

Download or read book Bayesian Analysis for the Intraclass Model and for the Quantile Semiparametric Mixed effects Double Regression Models written by and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract : This dissertation consists of three distinct but related research projects. The first two projects focus on objective Bayesian hypothesis testing and estimation for the intraclass correlation coefficient in linear models. The third project deals with Bayesian quantile inference for the semiparametric mixed-effects double regression models. In the first project, we derive the Bayes factors based on the divergence-based priors for testing the intraclass correlation coefficient (ICC). The hypothesis testing of the ICC is used to test the uncorrelatedness in multilevel modeling, and it has not well been studied from an objective Bayesian perspective. Simulation results show that the two sorts of Bayes factors have good performance in the hypothesis testing. Moreover, the Bayes factors can be easily implemented due to their unidimensional integral expressions. In the second project, we consider objective Bayesian analysis for the ICC in the context of normal linear regression model. We first derive two objective priors for the unknown parameters and show that both result in proper posterior distributions. Within a Bayesian decision-theoretic framework, we then propose an objective Bayesian solution to the problems of hypothesis testing and point estimation of the ICC based on a combined use of the intrinsic discrepancy loss function and objective priors. The proposed solution has an appealing invariance property under one-to-one reparameterization of the quantity of interest. Simulation studies are conducted to investigate the performance the proposed solution. Finally, a real data application is provided for illustrative purposes. In the third project, we study Bayesian quantile regression for semiparametric mixed effects model, which includes both linear and nonlinear parts. We adopt the popular cubic spline functions for the nonlinear part and model the variance of the random effect as a function of the explanatory variables. An efficient Gibbs sampler with the Metropolis-Hastings algorithm is proposed to generate posterior samples of the unknown parameters from their posterior distributions. Simulation studies and a real data example are used to illustrate the performance of the proposed methodology.

Download or read book Bayesian Ideas and Data Analysis written by Ronald Christensen and published by CRC Press. This book was released on 2011-07-07 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing the use of WinBUGS and R to analyze real data, Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians presents statistical tools to address scientific questions. It highlights foundational issues in statistics, the importance of making accurate predictions, and the need for scientists and statisticians to collaborate in analyzing data. The WinBUGS code provided offers a convenient platform to model and analyze a wide range of data. The first five chapters of the book contain core material that spans basic Bayesian ideas, calculations, and inference, including modeling one and two sample data from traditional sampling models. The text then covers Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) simulation. After discussing linear structures in regression, it presents binomial regression, normal regression, analysis of variance, and Poisson regression, before extending these methods to handle correlated data. The authors also examine survival analysis and binary diagnostic testing. A complementary chapter on diagnostic testing for continuous outcomes is available on the book’s website. The last chapter on nonparametric inference explores density estimation and flexible regression modeling of mean functions. The appropriate statistical analysis of data involves a collaborative effort between scientists and statisticians. Exemplifying this approach, Bayesian Ideas and Data Analysis focuses on the necessary tools and concepts for modeling and analyzing scientific data. Data sets and codes are provided on a supplemental website.

Download or read book Markov Chain Monte Carlo Posterior Sampling with the Hamiltonian Method written by and published by . This book was released on 2001 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: A major advantage of Bayesian data analysis is that provides a characterization of the uncertainty in the model parameters estimated from a given set of measurements in the form of a posterior probability distribution. When the analysis involves a complicated physical phenomenon, the posterior may not be available in analytic form, but only calculable by means of a simulation code. In such cases, the uncertainty in inferred model parameters requires characterization of a calculated functional. An appealing way to explore the posterior, and hence characterize the uncertainty, is to employ the Markov Chain Monte Carlo technique. The goal of MCMC is to generate a sequence random of parameter x samples from a target pdf (probability density function), [pi](x). In Bayesian analysis, this sequence corresponds to a set of model realizations that follow the posterior distribution. There are two basic MCMC techniques. In Gibbs sampling, typically one parameter is drawn from the conditional pdf at a time, holding all others fixed. In the Metropolis algorithm, all the parameters can be varied at once. The parameter vector is perturbed from the current sequence point by adding a trial step drawn randomly from a symmetric pdf. The trial position is either accepted or rejected on the basis of the probability at the trial position relative to the current one. The Metropolis algorithm is often employed because of its simplicity. The aim of this work is to develop MCMC methods that are useful for large numbers of parameters, n, say hundreds or more. In this regime the Metropolis algorithm can be unsuitable, because its efficiency drops as 0.3/n. The efficiency is defined as the reciprocal of the number of steps in the sequence needed to effectively provide a statistically independent sample from [pi].

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.

Download or read book Linear and Generalized Linear Mixed Models and Their Applications written by Jiming Jiang and published by Springer Science & Business Media. This book was released on 2007-05-30 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2002 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The SAGE Handbook of Quantitative Methods in Psychology written by Roger E Millsap and published by SAGE Publications. This book was released on 2009-08-05 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: `I often... wonder to myself whether the field needs another book, handbook, or encyclopedia on this topic. In this case I think that the answer is truly yes. The handbook is well focused on important issues in the field, and the chapters are written by recognized authorities in their fields. The book should appeal to anyone who wants an understanding of important topics that frequently go uncovered in graduate education in psychology' - David C Howell, Professor Emeritus, University of Vermont Quantitative psychology is arguably one of the oldest disciplines within the field of psychology and nearly all psychologists are exposed to quantitative psychology in some form. While textbooks in statistics, research methods and psychological measurement exist, none offer a unified treatment of quantitative psychology. The SAGE Handbook of Quantitative Methods in Psychology does just that. Each chapter covers a methodological topic with equal attention paid to established theory and the challenges facing methodologists as they address new research questions using that particular methodology. The reader will come away from each chapter with a greater understanding of the methodology being addressed as well as an understanding of the directions for future developments within that methodological area. Drawing on a global scholarship, the Handbook is divided into seven parts: Part One: Design and Inference: addresses issues in the inference of causal relations from experimental and non-experimental research, along with the design of true experiments and quasi-experiments, and the problem of missing data due to various influences such as attrition or non-compliance. Part Two: Measurement Theory: begins with a chapter on classical test theory, followed by the common factor analysis model as a model for psychological measurement. The models for continuous latent variables in item-response theory are covered next, followed by a chapter on discrete latent variable models as represented in latent class analysis. Part Three: Scaling Methods: covers metric and non-metric scaling methods as developed in multidimensional scaling, followed by consideration of the scaling of discrete measures as found in dual scaling and correspondence analysis. Models for preference data such as those found in random utility theory are covered next. Part Four: Data Analysis: includes chapters on regression models, categorical data analysis, multilevel or hierarchical models, resampling methods, robust data analysis, meta-analysis, Bayesian data analysis, and cluster analysis. Part Five: Structural Equation Models: addresses topics in general structural equation modeling, nonlinear structural equation models, mixture models, and multilevel structural equation models. Part Six: Longitudinal Models: covers the analysis of longitudinal data via mixed modeling, time series analysis and event history analysis. Part Seven: Specialized Models: covers specific topics including the analysis of neuro-imaging data and functional data-analysis.

Download or read book Bayesian Computation with R written by Jim Albert and published by Springer Science & Business Media. This book was released on 2009-04-20 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been dramatic growth in the development and application of Bayesian inference in statistics. Berger (2000) documents the increase in Bayesian activity by the number of published research articles, the number of books,andtheextensivenumberofapplicationsofBayesianarticlesinapplied disciplines such as science and engineering. One reason for the dramatic growth in Bayesian modeling is the availab- ity of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern c- puters, it is now possible to use the Bayesian paradigm to ?t very complex models that cannot be ?t by alternative frequentist methods. To ?t Bayesian models, one needs a statistical computing environment. This environment should be such that one can: write short scripts to de?ne a Bayesian model use or write functions to summarize a posterior distribution use functions to simulate from the posterior distribution construct graphs to illustrate the posterior inference An environment that meets these requirements is the R system. R provides a wide range of functions for data manipulation, calculation, and graphical d- plays. Moreover, it includes a well-developed, simple programming language that users can extend by adding new functions. Many such extensions of the language in the form of packages are easily downloadable from the Comp- hensive R Archive Network (CRAN).