Bayesian Analysis with Stata is written for anyone interested in applying Bayesian methods to real data easily. The book shows how modern analyses based on Markov chain Monte Carlo (MCMC) methods are implemented in Stata both directly and by passing Stata datasets to OpenBUGS or WinBUGS for computation, allowing Stata’s data management and graphing capability to be used with OpenBUGS/WinBUGS speed and reliability.
The book emphasizes practical data analysis from the Bayesian perspective, and hence covers the selection of realistic priors, computational efficiency and speed, the assessment of convergence, the evaluation of models, and the presentation of the results. Every topic is illustrated in detail using real-life examples, mostly drawn from medical research.
The book takes great care in introducing concepts and coding tools incrementally so that there are no steep patches or discontinuities in the learning curve. The book's content helps the user see exactly what computations are done for simple standard models and shows the user how those computations are implemented. Understanding these concepts is important for users because Bayesian analysis lends itself to custom or very complex models, and users must be able to code these themselves.
List of figures
List of tables
Preface
Acknowledgments
The problem of priors
Case study 1: An early phase vaccine trial
Bayesian calculations
Benefits of a Bayesian analysis
Selecting a good prior
Starting points
Exercises
Evaluating the posterior
Introduction
Case study 1: The vaccine trial revisited
Marginal and conditional distributions
Case study 2: Blood pressure and age
Case study 2: BP and age continued
General log posteriors
Adding distributions to logdensity
Changing parameterization
Starting points
Exercises
Metropolis–Hastings
Introduction
The MH algorithm in Stata
The mhs commands
Case study 3: Polyp counts
Scaling the proposal distribution
The mcmcrun command
Multiparameter models
Case study 3: Polyp counts continued
Highly correlated parameters
Case study 3: Polyp counts yet again
Starting points
Exercises
Gibbs sampling
Introduction
Case study 4: A regression model for pain scores
Conjugate priors
Gibbs sampling with nonstandard distributions
The gbs commands
Case study 4 continued: Laplace regression
Starting points
Exercises
Assessing convergence
Introduction
Detecting early drift
Detecting too short a run
Running multiple chains
Convergence of functions of the parameters
Case study 5: Beta-blocker trials
Further reading
Exercises
Validating the Stata code and summarizing the results
Introduction
Case study 6: Ordinal regression
Validating the software
Numerical summaries
Graphical summaries
Further reading
Exercises
Bayesian analysis with Mata
Introduction
The basics of Mata
Case study 6: Revisited
Case study 7: Germination of broomrape
Further reading
Exercises
Using WinBUGS for model fitting
Introduction
Installing the software
Preparing a WinBUGS analysis
Case study 8: Growth of sea cows
Case study 9: Jawbone size
Advanced features of WinBUGS
GeoBUGS
Programming a series of Bayesian analyses
OpenBUGS under Linux
Debugging WinBUGS
Starting points
Exercises
Model checking
Introduction
Bayesian residual analysis
The mcmccheck command
Case study 10: Models for Salmonella assays
Residual checking with Stata
Residual checking with Mata
Further reading
Exercises
Model selection
Introduction
Case study 11: Choosing a genetic model
Calculating a BF
Calculating the BFs for the NTD case study
Robustness of the BF
Model averaging
Information criteria
DIC for the genetic models
Starting points
Exercises
Further case studies
Introduction
Case study 12: Modeling cancer incidence
Case study 13: Creatinine clearance
Case study 14: Microarray experiment
Case study 15: Recurrent asthma attacks
Exercises
Writing Stata programs for specific Bayesian analysis
Introduction
The Bayesian lasso
The Gibbs sampler
The Mata code
A Stata ado-file
Testing the code
Case study 16: Diabetes data
Extensions to the Bayesian lasso program
Exercises
A Standard distributions
References
Author index
Subject index
Biography
John Thompson is professor of genetic epidemiology at the University of Leicester and has many years experience working as a biostatistician on epidemiological projects.
"… the first comprehensive guide to employing Bayesian methods using Stata statistical software. … until this book, there has been no unified presentation of how to implement Bayesian methods using Stata. … A nice feature of the book is the use of real data … I recommend it for Stata users who wish to employ Bayesian modeling within the Stata environment."
—International Statistical Review, 2015
