with Stata Bayesian Analysis John Thompson University of Leicester A Stata Press Publication StataCorp LP College Station, Texas

Transcription

1 Bayesian Analysis with Stata John Thompson University of Leicester A Stata Press Publication StataCorp LP College Station, Texas

2 Contents List of figures List of tables Preface Acknowledgments xiii xvii xix xxi 1 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 8 2 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 24 3 Metropolis-Hastings Introduction 27

3 viii Contents 3.2 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 Centering Block updating Case study 3: Polyp counts yet again Starting points Exercises 50 4 Gibbs sampling Introduction Case study 4: A regression model for pain scores Conjugate priors Gibbs sampling with nonstandard distributions Griddy sampling Slice sampling Adaptive rejection The gbs commands Case study 4 continued: Laplace regression Starting points Exercises 72 5 Assessing convergence Introduction Detecting early drift Detecting too short a run Thinning the chain 81

4 Contents ix 5.4 Running multiple chains Convergence of functions of the parameters Case study 5: Beta-blocker trials Further reading Exercises 90 6 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 Ill 7.2 The basics of Mata Ill 7.3 Case study 6: Revisited Case study 7: Germination of broomrape Tuning the proposal distributions Using conditional distributions More efficient computation Hierarchical centering Gibbs sampling Slice, Griddy, and ARMS sampling Timings Adding new densities to logdensity() Further reading Exercises Using WinBUGS for model fitting Introduction 131

5 X Contents 8.2 Installing the software Installing OpenBUGS Installing WinBUGS Preparing a WinBUGS analysis The model file The data file The initial values file The script file Running the script Reading the results into Stata Inspecting the log file Reading WinBUGS data files Case study 8: Growth of sea cows WinBUGS or OpenBUGS Case study 9: Jawbone size Overrelaxation Changing the seed for the random-number generator Advanced features of WinBUGS Missing data Censoring and truncation Nonstandard likelihoods Nonstandard priors The cut() function GeoBUGS Programming a series of Bayesian analyses OpenBUGS under Linux Debugging WinBUGS Starting points Exercises 161

6 Contents xi 9 Model checking Introduction Bayesian residual analysis The mcmccheck command Case study 10: Models for Salmonella assays Generating the predictions in WinBUGS Plotting the predictive distributions Residual plots Empirical probability plots A summary plot Residual checking with Stata Residual checking with Mata Further reading Exercises Model selection Introduction Case study 11: Choosing a genetic model Plausible models Bayes factors 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 205

7 xii Contents 11.3 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 250 A Standard distributions 251 References 265 Author index 273 Subject index 277