1 Introduction 1
1.1 A Basic Paradigm for Marketing Problems 2
1.2 A Simple Example 3
1.3 Benefits and Costs of the Bayesian Approach 4
1.4 An Overview of Methodological Material
and Case Studies 6
1.5 Computing and This Book 6
Acknowledgements 8
2 Bayesian Essentials 9
2.0 Essential Concepts from Distribution Theory 9
2.1 The Goal of Inference and Bayes’ Theorem 13
2.2 Conditioning and the Likelihood Principle 15
2.3 Prediction and Bayes 15
2.4 Summarizing the Posterior 16
2.5 Decision Theory, Risk, and the Sampling Properties of Bayes
Estimators 17
2.6 Identification and Bayesian Inference 19
2.7 Conjugacy, Sufficiency, and Exponential Families 20
2.8 Regression and Multivariate Analysis Examples 21
2.9 Integration and Asymptotic Methods 35
2.10 Importance Sampling 37
2.11 Simulation Primer for Bayesian Problems 41
2.12 Simulation from Posterior of Multivariate Regression Model 45
3 Markov Chain Monte Carlo Methods 49
3.1 Markov Chain Monte Carlo Methods 50
3.2 A Simple Example: Bivariate Normal Gibbs Sampler 52
3.3 Some Markov Chain Theory 57
3.4 Gibbs Sampler 63
3.5 Gibbs Sampler for the Seemingly Unrelated Regression Model 65
viii CONTENTS
3.6 Conditional Distributions and Directed Graphs 67
3.7 Hierarchical Linear Models 70
3.8 Data Augmentation and a Probit Example 75
3.9 Mixtures of Normals 79
3.10 Metropolis Algorithms 86
3.11 Metropolis Algorithms Illustrated with the Multinomial Logit
Model 94
3.12 Hybrid Markov Chain Monte Carlo Methods 97
3.13 Diagnostics 99
4 Unit-Level Models and Discrete Demand 103
4.1 Latent Variable Models 104
4.2 Multinomial Probit Model 106
4.3 Multivariate Probit Model 116
4.4 Demand Theory and Models Involving Discrete Choice 122
5 Hierarchical Models for Heterogeneous Units 129
5.1 Heterogeneity and Priors 130
5.2 Hierarchical Models 132
5.3 Inference for Hierarchical Models 133
5.4 A Hierarchical Multinomial Logit Example 136
5.5 Using Mixtures of Normals 142
5.6 Further Elaborations of the Normal Model of Heterogeneity 154
5.7 Diagnostic Checks of the First-Stage Prior 155
5.8 Findings and Influence on Marketing Practice 156
6 Model Choice and Decision Theory 159
6.1 Model Selection 160
6.2 Bayes Factors in the Conjugate Setting 162
6.3 Asymptotic Methods for Computing Bayes Factors 163
6.4 Computing Bayes Factors Using Importance Sampling 165
6.5 Bayes Factors Using MCMC Draws 166
6.6 Bridge Sampling Methods 169
6.7 Posterior Model Probabilities with Unidentified Parameters 170
6.8 Chib’s Method 171
6.9 An Example of Bayes Factor Computation: Diagonal Multinomial
Probit Models 173
6.10 Marketing Decisions and Bayesian Decision Theory 177
6.11 An Example of Bayesian Decision Theory: Valuing Household
Purchase Information 180
7 Simultaneity 185
7.1 A Bayesian Approach to Instrumental Variables 185
CONTENTS ix
7.2 Structural Models and Endogeneity/Simultaneity 195
7.3 Nonrandom Marketing Mix Variables 200
Case Study 1: A Choice Model for Packaged Goods: Dealing with
Discrete Quantities and Quantity Discounts 207
Background 207
Model 209
Data 214
Results 219
Discussion 222
R Implementation 224
Case Study 2: Modeling Interdependent Consumer Preferences 225
Background 225
Model 226
Data 229
Results 230
Discussion 235
R Implementation 235
Case Study 3: Overcoming Scale Usage Heterogeneity 237
Background 237
Model 240
Priors and MCMC Algorithm 244
Data 246
Discussion 251
R Implementation 252
Case Study 4: A Choice Model with Conjunctive Screening Rules 253
Background 253
Model 254
Data 255
Results 259
Discussion 264
R Implementation 266
Case Study 5: Modeling Consumer Demand for Variety 269
Background 269
Model 270
Data 271
Results 273
Discussion 273
R Implementation 277
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Appendix A An Introduction to Hierarchical Bayes Modeling in R 279
A.1 Setting Up the R Environment 279
A.2 The R Language 285
A.3 Hierarchical Bayes Modeling – An Example 303
Appendix B A Guide to Installation and Use of bayesm 323
B.1 Installing bayesm 323
B.2 Using bayesm 323
B.3 Obtaining Help on bayesm 324
B.4 Tips on Using MCMC Methods 327
B.5 Extending and Adapting Our Code 327
B.6 Updating bayesm 327
References 335
Index 341

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