This electronic edition is for non-commercial purposes only.
CONTENTS ix
9 Decision analysis 237
9.1 Bayesian decision theory in different contexts 237
9.2 Using regre ssion predictions: sur vey incentives 239
9.3 Multistage decision mak ing: medical screening 245
9.4 Hierarchical decision analysis for home ra don 246
9.5 Personal vs. institutional decision analysis 256
9.6 Bibliogra phic note 257
9.7 Exercises 257
Part III: Advanced Computation 259
10 Introduction to Bayesian computation 261
10.1 Numerical integration 261
10.2 Distributional approximations 262
10.3 Direct simulation and rejection sampling 263
10.4 Importance sampling 265
10.5 How many simulation dr aws are needed? 267
10.6 Computing environments 268
10.7 Debugging Bayesian computing 270
10.8 Bibliogra phic note 271
10.9 Exercises 272
11 Basics of Markov chain simulation 275
11.1 Gibbs sampler 276
11.2 Metropolis and Metropolis-Hastings algorithms 278
11.3 Using Gibbs and Metropolis as building blocks 280
11.4 Inference and assessing convergence 281
11.5 Effective number of simulation draws 286
11.6 Example: hierarchical normal model 288
11.7 Bibliogra phic note 291
11.8 Exercises 291
12 Computationally efficient Markov chain s imulation 293
12.1 Efficient Gibbs sa mplers 293
12.2 Efficient Metropolis jumping rules 295
12.3 Further extensions to Gibbs and Metropolis 297
12.4 Hamiltonian Monte Carlo 300
12.5 Hamiltonian Monte Carlo for a hierarchical model 305
12.6 Stan: developing a computing environment 307
12.7 Bibliogra phic note 308
12.8 Exercises 309
13 Modal and distributional approximations 311
13.1 Finding posterior modes 311
13.2 Boundary- avoiding priors for modal summaries 313
13.3 Normal and related mixture approximations 318
13.4 Finding marginal posterior modes using EM 320
13.5 Conditional and marginal pos terior approximations 325
13.6 Example: hierarchical normal model (continued) 326
13.7 Variational inference 331
13.8 Expectation propagation 338
13.9 Other approximations 343
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