Bayesian statistical methods:
Bayesian Statistical Methods provides data scientists with the foundational and computational tools needed to carry out a Bayesian analysis. This book focuses on Bayesian methods applied routinely in practice including multiple linear regression, mixed effects models and generalized linear models (G...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
2021
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| Series: | Texts in statistical science
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Bayesian Statistical Methods provides data scientists with the foundational and computational tools needed to carry out a Bayesian analysis. This book focuses on Bayesian methods applied routinely in practice including multiple linear regression, mixed effects models and generalized linear models (GLM). The authors include many examples with complete R code and comparisons with analogous frequentist procedures.In addition to the basic concepts of Bayesian inferential methods, the book covers many general topics: Advice on selecting prior distributionsComputational methods including Markov chain Monte Carlo (MCMC) Model-comparison and goodness-of-fit measures, including sensitivity to priorsFrequentist properties of Bayesian methodsCase studies covering advanced topics illustrate the flexibility of the Bayesian approach:Semiparametric regression Handling of missing data using predictive distributionsPriors for high-dimensional regression modelsComputational techniques for large datasetsSpatial data analysisThe advanced topics are presented with sufficient conceptual depth that the reader will be able to carry out such analysis and argue the relative merits of Bayesian and classical methods. A repository of R code, motivating data sets, and complete data analyses are available on the book's website.Brian J. Reich, Associate Professor of Statistics at North Carolina State University, is currently the editor-in-chief of the Journal of Agricultural, Biological, and Environmental Statistics and was awarded the LeRoy & Elva Martin Teaching Award.Sujit K. Ghosh, Professor of Statistics at North Carolina State University, has over 22 years of research and teaching experience in conducting Bayesian analyses, received the Cavell Brownie mentoring award, and served as the Deputy Director at the Statistical and Applied Mathematical Sciences Institute |
| Physical Description: | xii, 275 Illustrationen Breite 156 mm, Hoehe 234 mm |
| ISBN: | 9781032093185 |
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| adam_text | Contents Preface 1 Basics of Bayesian inference 1.1 1.2 1.3 1.4 1.5 1.6 Probability background ........................................................... 1.1.1 Univariate distributions................................................ 1.1.1.1 Discrete distributions................................... 1.1.1.2 Continuous distributions ............................. 1.1.2 Multivariate distributions............................................ 1.1.3 Marginal and conditional distributions........................ Bayes’ rule ................................................................................ 1.2.1 Discrete example of Bayes’rule................................... 1.2.2 Continuous example of Bayes’ rule............................. Introduction to Bayesian inference.......................................... Summarizing the posterior .................................................. 1.4.1 Point estimation........................................................... 1.4.2 Univariate posteriors...................................................... 1.4.3 Multivariate posteriors.................................................. The posterior predictive distribution...................................... Exercises ................................................................................... 2 From prior information to posterior inference 2.1 Conjugate priors....................................................................... 2.1.1 Beta-binomial model for a proportion........................ 2.1.2 Poisson-gamma model for a rate................................. 2.1.3
Normal-normal model for a mean................................ 2.1.4 Normal-inverse gamma model for avariance................ 2.1.5 Natural conjugate priors................................................ 2.1.6 Normal-normal model fora mean vector...................... 2.1.7 Normal-inverse Wishart model for a covariance matrix 2.1.8 Mixtures of conjugate priors.......................................... 2.2 Improper priors ....................................................................... 2.3 Objective priors ....................................................................... 2.3.1 Jeffreys’ prior................................................................. 2.3.2 Reference priors ........................................................... 2.3.3 Maximum entropy priors ............................................. 2.3.4 Empirical Bayes ........................................................... xi 1 1 2 2 6 9 10 14 16 18 21 24 25 25 27 31 34 41 42 42 45 47 48 50 51 52 56 58 59 59 61 62 62 vii
Contents viii 3 2.3.5 Penalized complexity priors........................................... 2.4 Exercises ..................................................................................... 63 ®4 Computational approaches 69 3.1 70 70 71 74 75 77 89 97 100 100 103 108 HO 112 3.2 3.3 3.4 3.5 Deterministic methods ............................................................ 3.1.1 Maximum a posteriori estimation................................. 3.1.2 Numerical integration................................................... 3.1.3 Bayesian central limit theorem (CLT) ........................ Markov chain Monte Carlo(MCMC) methods ...................... 3.2.1 Gibbs sampling............................................................... 3.2.2 Metropolis-Hastings (MH) sampling........................... MCMC software options inR.................................................... Diagnosing and improving convergence ................................. 3.4.1 Selecting initial values................................................... 3.4.2 Convergence diagnostics................................................ 3.4.3 Improving convergence .................................................... 3.4.4 Dealing with large datasets.......................................... Exercises .................................................................................... 4 Linear models 4.1 4.2 4.3 4.4 4.5 4.6 Analysis of normal means......................................................... 4.1.1 One-sample/paired analysis.......................................... 4.1.2 Comparison of two normal
means................................. Linear regression........................................................................ 4.2.1 Jeffreys prior................................................................... 4.2.2 Gaussian prior................................................................ 4.2.3 Continuous shrinkage priors.......................................... 4.2.4 Predictions...................................................................... 4.2.5 Example: Factors that affect a home’s microbiome . . Generalized linear models.......................................................... 4.3.1 Binary data...................................................................... 4.3.2 Count data...................................................................... 4.3.3 Example: Logistic regression for NBA clutch free throws 4.3.4 Example: Beta regression for microbiome data .... Random effects............................................................................ Flexible linear models................................................................ 4.5.1 Nonparametric regression............... 4.5.2 Heteroskedastic models ................................................. 4.5.3 Non-Gaussian error models........................................... 4.5.4 Linear models with correlated data.............................. Exercises ..................................................................................... 119 120 120 121 124 125 126 128 129 130 133 135 137 138 140 141 149 149 152 153 153 լ58
Contents 5 Model selection and diagnostics 5.1 5.2 5.3 5.4 5.5 5.6 5.7 ix 163 Cross validation ......................................................................... 164 Hypothesis testing and Bayes factors ..................................... 166 Stochastic search variable selection..................................... 170 Bayesian model averaging ........................................................... 175 Model selection criteria ..................................... 176 Goodness-of-fit checks . ....................................................... 186 Exercises ....................................................................................... 192 6 Case studies using hierarchicalmodeling 195 6.1 Overview of hierarchical modeling ........................................... 195 6.2 Case study1: Species distribution mapping via data fusion . 200 6.3 Case study 2: Tyrannosaurid growth curves...................... 203 6.4 Case study 3: Marathon analysis with missingdata .............. 211 6.5 Exercises . ............................ 213 7 Statistical properties of Bayesian methods 7.1 7.2 Decision theory . ............................ Frequentisi properties........................................ 7.2.1 Bias-variance tradeoff . .................................................. 7.2.2 Asymptotics .................................. 7.3 Simulation studies ......................... ....................................... ... · 7.4 Exercises . ...................... Appendices A.l A.2 A.3 A.4 A.5 Probability distributions
............................................................. List of conjugate priors................................................. Derivations . ................................................................................. Computational algorithms ...................... . ........................ Software comparison ................................................................... 217 218 220 221 223 223 227 231 231 239 241 250 255 Bibliography 265 Index 273
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| adam_txt |
Contents Preface 1 Basics of Bayesian inference 1.1 1.2 1.3 1.4 1.5 1.6 Probability background . 1.1.1 Univariate distributions. 1.1.1.1 Discrete distributions. 1.1.1.2 Continuous distributions . 1.1.2 Multivariate distributions. 1.1.3 Marginal and conditional distributions. Bayes’ rule . 1.2.1 Discrete example of Bayes’rule. 1.2.2 Continuous example of Bayes’ rule. Introduction to Bayesian inference. Summarizing the posterior . 1.4.1 Point estimation. 1.4.2 Univariate posteriors. 1.4.3 Multivariate posteriors. The posterior predictive distribution. Exercises . 2 From prior information to posterior inference 2.1 Conjugate priors. 2.1.1 Beta-binomial model for a proportion. 2.1.2 Poisson-gamma model for a rate. 2.1.3
Normal-normal model for a mean. 2.1.4 Normal-inverse gamma model for avariance. 2.1.5 Natural conjugate priors. 2.1.6 Normal-normal model fora mean vector. 2.1.7 Normal-inverse Wishart model for a covariance matrix 2.1.8 Mixtures of conjugate priors. 2.2 Improper priors . 2.3 Objective priors . 2.3.1 Jeffreys’ prior. 2.3.2 Reference priors . 2.3.3 Maximum entropy priors . 2.3.4 Empirical Bayes . xi 1 1 2 2 6 9 10 14 16 18 21 24 25 25 27 31 34 41 42 42 45 47 48 50 51 52 56 58 59 59 61 62 62 vii
Contents viii 3 2.3.5 Penalized complexity priors. 2.4 Exercises . 63 ®4 Computational approaches 69 3.1 70 70 71 74 75 77 89 97 100 100 103 108 HO 112 3.2 3.3 3.4 3.5 Deterministic methods . 3.1.1 Maximum a posteriori estimation. 3.1.2 Numerical integration. 3.1.3 Bayesian central limit theorem (CLT) . Markov chain Monte Carlo(MCMC) methods . 3.2.1 Gibbs sampling. 3.2.2 Metropolis-Hastings (MH) sampling. MCMC software options inR. Diagnosing and improving convergence . 3.4.1 Selecting initial values. 3.4.2 Convergence diagnostics. 3.4.3 Improving convergence . 3.4.4 Dealing with large datasets. Exercises . 4 Linear models 4.1 4.2 4.3 4.4 4.5 4.6 Analysis of normal means. 4.1.1 One-sample/paired analysis. 4.1.2 Comparison of two normal
means. Linear regression. 4.2.1 Jeffreys prior. 4.2.2 Gaussian prior. 4.2.3 Continuous shrinkage priors. 4.2.4 Predictions. 4.2.5 Example: Factors that affect a home’s microbiome . . Generalized linear models. 4.3.1 Binary data. 4.3.2 Count data. 4.3.3 Example: Logistic regression for NBA clutch free throws 4.3.4 Example: Beta regression for microbiome data . Random effects. Flexible linear models. 4.5.1 Nonparametric regression. 4.5.2 Heteroskedastic models . 4.5.3 Non-Gaussian error models. 4.5.4 Linear models with correlated data. Exercises . 119 120 120 121 124 125 126 128 129 130 133 135 137 138 140 141 149 149 152 153 153 լ58
Contents 5 Model selection and diagnostics 5.1 5.2 5.3 5.4 5.5 5.6 5.7 ix 163 Cross validation . 164 Hypothesis testing and Bayes factors . 166 Stochastic search variable selection. 170 Bayesian model averaging . 175 Model selection criteria . 176 Goodness-of-fit checks . . 186 Exercises . 192 6 Case studies using hierarchicalmodeling 195 6.1 Overview of hierarchical modeling . 195 6.2 Case study1: Species distribution mapping via data fusion . 200 6.3 Case study 2: Tyrannosaurid growth curves. 203 6.4 Case study 3: Marathon analysis with missingdata . 211 6.5 Exercises . . 213 7 Statistical properties of Bayesian methods 7.1 7.2 Decision theory . . Frequentisi properties. 7.2.1 Bias-variance tradeoff . . 7.2.2 Asymptotics . 7.3 Simulation studies . . . · 7.4 Exercises . . Appendices A.l A.2 A.3 A.4 A.5 Probability distributions
. List of conjugate priors. Derivations . . Computational algorithms . . . Software comparison . 217 218 220 221 223 223 227 231 231 239 241 250 255 Bibliography 265 Index 273 |
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| id | DE-604.BV047681599 |
| illustrated | Illustrated |
| index_date | 2024-07-03T18:55:45Z |
| indexdate | 2024-07-10T09:19:05Z |
| institution | BVB |
| isbn | 9781032093185 |
| language | English |
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| spelling | Reich, Brian James Verfasser (DE-588)1187196657 aut Bayesian statistical methods Brian J. Reich, Sujit K. Ghosh Boca Raton ; London ; New York CRC Press 2021 xii, 275 Illustrationen Breite 156 mm, Hoehe 234 mm txt rdacontent n rdamedia nc rdacarrier Texts in statistical science Bayesian Statistical Methods provides data scientists with the foundational and computational tools needed to carry out a Bayesian analysis. This book focuses on Bayesian methods applied routinely in practice including multiple linear regression, mixed effects models and generalized linear models (GLM). The authors include many examples with complete R code and comparisons with analogous frequentist procedures.In addition to the basic concepts of Bayesian inferential methods, the book covers many general topics: Advice on selecting prior distributionsComputational methods including Markov chain Monte Carlo (MCMC) Model-comparison and goodness-of-fit measures, including sensitivity to priorsFrequentist properties of Bayesian methodsCase studies covering advanced topics illustrate the flexibility of the Bayesian approach:Semiparametric regression Handling of missing data using predictive distributionsPriors for high-dimensional regression modelsComputational techniques for large datasetsSpatial data analysisThe advanced topics are presented with sufficient conceptual depth that the reader will be able to carry out such analysis and argue the relative merits of Bayesian and classical methods. A repository of R code, motivating data sets, and complete data analyses are available on the book's website.Brian J. Reich, Associate Professor of Statistics at North Carolina State University, is currently the editor-in-chief of the Journal of Agricultural, Biological, and Environmental Statistics and was awarded the LeRoy & Elva Martin Teaching Award.Sujit K. Ghosh, Professor of Statistics at North Carolina State University, has over 22 years of research and teaching experience in conducting Bayesian analyses, received the Cavell Brownie mentoring award, and served as the Deputy Director at the Statistical and Applied Mathematical Sciences Institute Datenanalyse (DE-588)4123037-1 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s Bayes-Verfahren (DE-588)4204326-8 s Datenanalyse (DE-588)4123037-1 s DE-604 Ghosh, Sujit K. 1970- Sonstige (DE-588)124746284 oth Äquivalent Druck-Ausgabe, Hardcover 978-0-815-37864-8 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033065672&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reich, Brian James Bayesian statistical methods Datenanalyse (DE-588)4123037-1 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
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| title | Bayesian statistical methods |
| title_auth | Bayesian statistical methods |
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| title_full | Bayesian statistical methods Brian J. Reich, Sujit K. Ghosh |
| title_fullStr | Bayesian statistical methods Brian J. Reich, Sujit K. Ghosh |
| title_full_unstemmed | Bayesian statistical methods Brian J. Reich, Sujit K. Ghosh |
| title_short | Bayesian statistical methods |
| title_sort | bayesian statistical methods |
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