Bayesian Hierarchical Models

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Bayesian Hierarchical Models

Peter D. Congdon
Bayesian Hierarchical Models Book PDF

Author : Peter D. Congdon
Publisher : CRC Press
Page : 580 pages
File Size : 50,8 Mb
Release : 2019-09-16
Category : Mathematics
ISBN : 9781498785914

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Bayesian Hierarchical Models by Peter D. Congdon Pdf

An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website

Probability and Bayesian Modeling

Jim Albert,Jingchen Hu
Probability and Bayesian Modeling Book PDF

Author : Jim Albert,Jingchen Hu
Publisher : CRC Press
Page : 553 pages
File Size : 46,5 Mb
Release : 2019-12-06
Category : Mathematics
ISBN : 9781351030137

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Probability and Bayesian Modeling by Jim Albert,Jingchen Hu Pdf

Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.

Applied Bayesian Hierarchical Methods

Peter D. Congdon
Applied Bayesian Hierarchical Methods Book PDF

Author : Peter D. Congdon
Publisher : CRC Press
Page : 606 pages
File Size : 50,7 Mb
Release : 2010-05-19
Category : Mathematics
ISBN : 9781584887218

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Applied Bayesian Hierarchical Methods by Peter D. Congdon Pdf

The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach

Bayes Rules!

Alicia A. Johnson,Miles Q. Ott,Mine Dogucu
Bayes Rules Book PDF

Author : Alicia A. Johnson,Miles Q. Ott,Mine Dogucu
Publisher : CRC Press
Page : 606 pages
File Size : 41,5 Mb
Release : 2022-03-03
Category : Mathematics
ISBN : 9781000529562

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Bayes Rules! by Alicia A. Johnson,Miles Q. Ott,Mine Dogucu Pdf

Praise for Bayes Rules!: An Introduction to Applied Bayesian Modeling “A thoughtful and entertaining book, and a great way to get started with Bayesian analysis.” Andrew Gelman, Columbia University “The examples are modern, and even many frequentist intro books ignore important topics (like the great p-value debate) that the authors address. The focus on simulation for understanding is excellent.” Amy Herring, Duke University “I sincerely believe that a generation of students will cite this book as inspiration for their use of – and love for – Bayesian statistics. The narrative holds the reader’s attention and flows naturally – almost conversationally. Put simply, this is perhaps the most engaging introductory statistics textbook I have ever read. [It] is a natural choice for an introductory undergraduate course in applied Bayesian statistics." Yue Jiang, Duke University “This is by far the best book I’ve seen on how to (and how to teach students to) do Bayesian modeling and understand the underlying mathematics and computation. The authors build intuition and scaffold ideas expertly, using interesting real case studies, insightful graphics, and clear explanations. The scope of this book is vast – from basic building blocks to hierarchical modeling, but the authors’ thoughtful organization allows the reader to navigate this journey smoothly. And impressively, by the end of the book, one can run sophisticated Bayesian models and actually understand the whys, whats, and hows.” Paul Roback, St. Olaf College “The authors provide a compelling, integrated, accessible, and non-religious introduction to statistical modeling using a Bayesian approach. They outline a principled approach that features computational implementations and model assessment with ethical implications interwoven throughout. Students and instructors will find the conceptual and computational exercises to be fresh and engaging.” Nicholas Horton, Amherst College An engaging, sophisticated, and fun introduction to the field of Bayesian statistics, Bayes Rules!: An Introduction to Applied Bayesian Modeling brings the power of modern Bayesian thinking, modeling, and computing to a broad audience. In particular, the book is an ideal resource for advanced undergraduate statistics students and practitioners with comparable experience. Bayes Rules! empowers readers to weave Bayesian approaches into their everyday practice. Discussions and applications are data driven. A natural progression from fundamental to multivariable, hierarchical models emphasizes a practical and generalizable model building process. The evaluation of these Bayesian models reflects the fact that a data analysis does not exist in a vacuum. Features • Utilizes data-driven examples and exercises. • Emphasizes the iterative model building and evaluation process. • Surveys an interconnected range of multivariable regression and classification models. • Presents fundamental Markov chain Monte Carlo simulation. • Integrates R code, including RStan modeling tools and the bayesrules package. • Encourages readers to tap into their intuition and learn by doing. • Provides a friendly and inclusive introduction to technical Bayesian concepts. • Supports Bayesian applications with foundational Bayesian theory.

Data Analysis Using Regression and Multilevel/Hierarchical Models

Andrew Gelman,Jennifer Hill
Data Analysis Using Regression and Multilevel Hierarchical Models Book PDF

Author : Andrew Gelman,Jennifer Hill
Publisher : Cambridge University Press
Page : 654 pages
File Size : 42,9 Mb
Release : 2007
Category : Mathematics
ISBN : 052168689X

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Data Analysis Using Regression and Multilevel/Hierarchical Models by Andrew Gelman,Jennifer Hill Pdf

This book, first published in 2007, is for the applied researcher performing data analysis using linear and nonlinear regression and multilevel models.

Bayesian Nonparametrics

Nils Lid Hjort,Chris Holmes,Peter Müller,Stephen G. Walker
Bayesian Nonparametrics Book PDF

Author : Nils Lid Hjort,Chris Holmes,Peter Müller,Stephen G. Walker
Publisher : Cambridge University Press
Page : 309 pages
File Size : 46,7 Mb
Release : 2010-04-12
Category : Mathematics
ISBN : 9781139484602

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Bayesian Nonparametrics by Nils Lid Hjort,Chris Holmes,Peter Müller,Stephen G. Walker Pdf

Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.

Bayesian Hierarchical Models

Peter D. Congdon
Bayesian Hierarchical Models Book PDF

Author : Peter D. Congdon
Publisher : CRC Press
Page : 506 pages
File Size : 49,7 Mb
Release : 2019-09-16
Category : Mathematics
ISBN : 9780429532900

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Bayesian Hierarchical Models by Peter D. Congdon Pdf

An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website

Introduction to Hierarchical Bayesian Modeling for Ecological Data

Eric Parent,Etienne Rivot
Introduction to Hierarchical Bayesian Modeling for Ecological Data Book PDF

Author : Eric Parent,Etienne Rivot
Publisher : CRC Press
Page : 429 pages
File Size : 54,5 Mb
Release : 2012-08-21
Category : Mathematics
ISBN : 9781584889199

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Introduction to Hierarchical Bayesian Modeling for Ecological Data by Eric Parent,Etienne Rivot Pdf

Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models. The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts and techniques of the Bayesian paradigm from a practical point of view using real case studies. They emphasize how hierarchical Bayesian modeling supports multidimensional models involving complex interactions between parameters and latent variables. Data sets, exercises, and R and WinBUGS codes are available on the authors’ website. This book shows how Bayesian statistical modeling provides an intuitive way to organize data, test ideas, investigate competing hypotheses, and assess degrees of confidence of predictions. It also illustrates how conditional reasoning can dismantle a complex reality into more understandable pieces. As conditional reasoning is intimately linked with Bayesian thinking, considering hierarchical models within the Bayesian setting offers a unified and coherent framework for modeling, estimation, and prediction.

Hierarchical Modeling and Inference in Ecology

J. Andrew Royle,Robert M. Dorazio
Hierarchical Modeling and Inference in Ecology Book PDF

Author : J. Andrew Royle,Robert M. Dorazio
Publisher : Elsevier
Page : 464 pages
File Size : 48,6 Mb
Release : 2008-10-15
Category : Science
ISBN : 9780080559254

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Hierarchical Modeling and Inference in Ecology by J. Andrew Royle,Robert M. Dorazio Pdf

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics * Wide variety of examples involving many taxa (birds, amphibians, mammals, insects, plants) * Development of classical, likelihood-based procedures for inference, as well as Bayesian methods of analysis * Detailed explanations describing the implementation of hierarchical models using freely available software such as R and WinBUGS * Computing support in technical appendices in an online companion web site

The Oxford Handbook of Computational and Mathematical Psychology

Jerome R. Busemeyer,Zheng Wang,James T. Townsend,Ami Eidels
The Oxford Handbook of Computational and Mathematical Psychology Book PDF

Author : Jerome R. Busemeyer,Zheng Wang,James T. Townsend,Ami Eidels
Publisher : Oxford University Press
Page : 528 pages
File Size : 46,8 Mb
Release : 2015-03-20
Category : Psychology
ISBN : 9780199958009

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The Oxford Handbook of Computational and Mathematical Psychology by Jerome R. Busemeyer,Zheng Wang,James T. Townsend,Ami Eidels Pdf

This Oxford Handbook offers a comprehensive and authoritative review of important developments in computational and mathematical psychology. With chapters written by leading scientists across a variety of subdisciplines, it examines the field's influence on related research areas such as cognitive psychology, developmental psychology, clinical psychology, and neuroscience. The Handbook emphasizes examples and applications of the latest research, and will appeal to readers possessing various levels of modeling experience. The Oxford Handbook of Computational and mathematical Psychology covers the key developments in elementary cognitive mechanisms (signal detection, information processing, reinforcement learning), basic cognitive skills (perceptual judgment, categorization, episodic memory), higher-level cognition (Bayesian cognition, decision making, semantic memory, shape perception), modeling tools (Bayesian estimation and other new model comparison methods), and emerging new directions in computation and mathematical psychology (neurocognitive modeling, applications to clinical psychology, quantum cognition). The Handbook would make an ideal graduate-level textbook for courses in computational and mathematical psychology. Readers ranging from advanced undergraduates to experienced faculty members and researchers in virtually any area of psychology--including cognitive science and related social and behavioral sciences such as consumer behavior and communication--will find the text useful.

Biopharmaceutical Applied Statistics Symposium

Karl E. Peace,Ding-Geng Chen,Sandeep Menon
Biopharmaceutical Applied Statistics Symposium Book PDF

Author : Karl E. Peace,Ding-Geng Chen,Sandeep Menon
Publisher : Springer
Page : 245 pages
File Size : 45,9 Mb
Release : 2018-08-21
Category : Medical
ISBN : 9789811078262

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Biopharmaceutical Applied Statistics Symposium by Karl E. Peace,Ding-Geng Chen,Sandeep Menon Pdf

This BASS book Series publishes selected high-quality papers reflecting recent advances in the design and biostatistical analysis of biopharmaceutical experiments – particularly biopharmaceutical clinical trials. The papers were selected from invited presentations at the Biopharmaceutical Applied Statistics Symposium (BASS), which was founded by the first Editor in 1994 and has since become the premier international conference in biopharmaceutical statistics. The primary aims of the BASS are: 1) to raise funding to support graduate students in biostatistics programs, and 2) to provide an opportunity for professionals engaged in pharmaceutical drug research and development to share insights into solving the problems they encounter. The BASS book series is initially divided into three volumes addressing: 1) Design of Clinical Trials; 2) Biostatistical Analysis of Clinical Trials; and 3) Pharmaceutical Applications. This book is the second of the 3-volume book series. The topics covered include: Statistical Approaches to the Meta-analysis of Randomized Clinical Trials, Collaborative Targeted Maximum Likelihood Estimation to Assess Causal Effects in Observational Studies, Generalized Tests in Clinical Trials, Discrete Time-to-event and Score-based Methods with Application to Composite Endpoint for Assessing Evidence of Disease Activity-Free , Imputing Missing Data Using a Surrogate Biomarker: Analyzing the Incidence of Endometrial Hyperplasia, Selected Statistical Issues in Patient-reported Outcomes, Network Meta-analysis, Detecting Safety Signals Among Adverse Events in Clinical Trials, Applied Meta-analysis Using R, Treatment of Missing Data in Comparative Effectiveness Research, Causal Estimands: A Common Language for Missing Data, Bayesian Subgroup Analysis with Examples, Statistical Methods in Diagnostic Devices, A Question-Based Approach to the Analysis of Safety Data, Analysis of Two-stage Adaptive Seamless Trial Design, and Multiplicity Problems in Clinical Trials – A Regulatory Perspective.

Bayesian Data Analysis, Third Edition

Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin
Bayesian Data Analysis Third Edition Book PDF

Author : Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin
Publisher : CRC Press
Page : 677 pages
File Size : 52,7 Mb
Release : 2013-11-01
Category : Mathematics
ISBN : 9781439840955

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Bayesian Data Analysis, Third Edition by Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin Pdf

Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Doing Meta-Analysis with R

Mathias Harrer,Pim Cuijpers,Toshi A. Furukawa,David D. Ebert
Doing Meta Analysis with R Book PDF

Author : Mathias Harrer,Pim Cuijpers,Toshi A. Furukawa,David D. Ebert
Publisher : CRC Press
Page : 500 pages
File Size : 54,8 Mb
Release : 2021-09-15
Category : Mathematics
ISBN : 9781000435634

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Doing Meta-Analysis with R by Mathias Harrer,Pim Cuijpers,Toshi A. Furukawa,David D. Ebert Pdf

Doing Meta-Analysis with R: A Hands-On Guide serves as an accessible introduction on how meta-analyses can be conducted in R. Essential steps for meta-analysis are covered, including calculation and pooling of outcome measures, forest plots, heterogeneity diagnostics, subgroup analyses, meta-regression, methods to control for publication bias, risk of bias assessments and plotting tools. Advanced but highly relevant topics such as network meta-analysis, multi-three-level meta-analyses, Bayesian meta-analysis approaches and SEM meta-analysis are also covered. A companion R package, dmetar, is introduced at the beginning of the guide. It contains data sets and several helper functions for the meta and metafor package used in the guide. The programming and statistical background covered in the book are kept at a non-expert level, making the book widely accessible. Features • Contains two introductory chapters on how to set up an R environment and do basic imports/manipulations of meta-analysis data, including exercises • Describes statistical concepts clearly and concisely before applying them in R • Includes step-by-step guidance through the coding required to perform meta-analyses, and a companion R package for the book

Doing Bayesian Data Analysis

John Kruschke
Doing Bayesian Data Analysis Book PDF

Author : John Kruschke
Publisher : Academic Press
Page : 673 pages
File Size : 46,8 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9780123814869

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Doing Bayesian Data Analysis by John Kruschke Pdf

There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis tractable and accessible to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS, is for first year graduate students or advanced undergraduates and provides an accessible approach, as all mathematics is explained intuitively and with concrete examples. It assumes only algebra and ‘rusty’ calculus. Unlike other textbooks, this book begins with the basics, including essential concepts of probability and random sampling. The book gradually climbs all the way to advanced hierarchical modeling methods for realistic data. The text provides complete examples with the R programming language and BUGS software (both freeware), and begins with basic programming examples, working up gradually to complete programs for complex analyses and presentation graphics. These templates can be easily adapted for a large variety of students and their own research needs.The textbook bridges the students from their undergraduate training into modern Bayesian methods. Accessible, including the basics of essential concepts of probability and random sampling Examples with R programming language and BUGS software Comprehensive coverage of all scenarios addressed by non-bayesian textbooks- t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis). Coverage of experiment planning R and BUGS computer programming code on website Exercises have explicit purposes and guidelines for accomplishment

Bayesian Models

N. Thompson Hobbs,Mevin Hooten
Bayesian Models Book PDF

Author : N. Thompson Hobbs,Mevin Hooten
Publisher : Princeton University Press
Page : 315 pages
File Size : 49,6 Mb
Release : 2015-08-04
Category : Science
ISBN : 9781400866557

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Bayesian Models by N. Thompson Hobbs,Mevin Hooten Pdf

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals. This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management. Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticians Covers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and more Deemphasizes computer coding in favor of basic principles Explains how to write out properly factored statistical expressions representing Bayesian models