Bayesian Statistics and Marketing illustrates the potential for applying a Bayesian approach to some of the most challenging and important problems in marketing. Analyzing household and consumer data, predicting product performance, and custom-targeting campaigns are only a few of the areas in which Bayesian approaches promise revolutionary results. This book provides a comprehensive, accessible overview of this subject essential for any statistically informed marketing researcher or practitioner.
Economists and other social scientists will find a comprehensive treatment of many Bayesian methods that are central to the problems in social science more generally. This includes a practical approach to computationally challenging problems in random coefficient models, non-parametrics, and the problems of endogeneity.
Readers of the second edition of Bayesian Statistics and Marketing will also find: - Discussion of Bayesian methods in text analysis and Machine Learning - Updates throughout reflecting the latest research and applications - Discussion of modern statistical software, including an introduction to the R package bayesm, which implements all models incorporated here - Extensive case studies throughout to link theory and practice
Bayesian Statistics and Marketing is ideal for advanced students and researchers in marketing, business, and economics departments, as well as for any statistically savvy marketing practitioner.
Table of Contents
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 5
1.4 An Overview of Methodological Material and Case Studies 6
1.5 Approximate Bayes Methods and This Book 7
1.6 Computing and This Book 8
2 Bayesian Essentials 11
2.1 Essential Concepts from Distribution Theory 11
2.2 The Goal of Inference and Bayes Theorem 15
2.3 Conditioning and the Likelihood Principle 16
2.4 Prediction and Bayes 17
2.5 Summarizing the Posterior 17
2.6 Decision Theory, Risk, and the Sampling Properties of Bayes Estimators 18
2.7 Identification and Bayesian Inference 20
2.8 Conjugacy, Sufficiency, and Exponential Families 21
2.9 Regression and Multivariate Analysis Examples 23
2.10 Integration and Asymptotic Methods 37
2.11 Importance Sampling 38
2.12 Simulation Primer for Bayesian Problems 42
2.13 Simulation from Posterior of Multivariate Regression Model 47
3 MCMC Methods 49
3.1 MCMC 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 SUR Regression Model 64
3.6 Conditional Distributions and Directed Graphs 66
3.7 Hierarchical Linear Models 69
3.8 Data Augmentation and a Probit Example 74
3.9 Mixtures of Normals 78
3.10 Metropolis Algorithms 85
3.11 Metropolis Algorithms Illustrated with the Multinomial Logit Model 92
3.12 Hybrid MCMC Methods 95
3.13 Diagnostics 98
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 121
5 Hierarchical Models for Heterogeneous Units 129
5.1 Heterogeneity and Priors 130
5.2 Hierarchical Models 132
5.3 Inference for Hierarchical Models 134
5.4 A Hierarchical Multinomial Logit Example 137
5.5 Using Mixtures of Normals 143
5.6 Further Elaborations of the Normal Model of Heterogeneity 152
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 from the Posterior 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 MNP models 172
6.10 Marketing Decisions and Bayesian Decision Theory 178
6.11 An Example of Bayesian Decision Theory: Valuing Household Purchase Information 180
7 Simultaneity 185
7.1 A Bayesian Approach to Instrumental Variables 186
7.2 Structural Models and Endogeneity/Simultaneity 195
7.3 Non-Random Marketing Mix Variables 200
8 A Bayesian Perspective on Machine Learning 207
8.1 Introduction 207
8.2 Regularization 209
8.3 Bagging 212
8.4 Boosting 216
8.5 Deep Learning 217
8.6 Applications 223
9 Bayesian Analysis for Text Data 227
9.1 Introduction 227
9.2 Consumer Demand 228
9.3 Integrated Models 236
9.4 Discussion 252
10 Case Study 1: Analysis of Choice-Based Conjoint Data Using A Hierarchical Logit Model 255
10.1 Choice-Based Conjoint 255
10.2 A Random Coefficient Logit 258
10.3 Sign Constraints and Priors 258
10.4 The Camera Data 262
10.5 Running the Model 266
10.6 Describing the Draws of Respondent Partworths 268
10.7 Predictive Posteriors 270
10.8 Comparison of Stan and Sawtooth Software to bayesm Routines 273
11 Case Study 2: WTP and Equilibrium Analysis with Conjoint Demand 277
11.1 The Demand for Product Features 278
11.2 Conjoint Surveys and Demand Estimation 282
11.3 WTP Properly Defined 287
11.4 Nash Equilibrium Prices -- Computation and Assumptions 294
11.5 Camera Example 298
12 Case Study 3: Scale Usage Heterogeneity 307
12.1 Background 307
12.2 Model 310
12.3 Priors and MCMC Algorithm 314
12.4 Data 316
12.5 Discussion 320
12.6 R Implementation 322
13 Case Study 4: Volumetric Conjoint 323
13.1 Introduction 323
13.2 Model Development 324
13.3 Estimation 329
13.4 Empirical Analysis 331
13.5 Discussion 339
13.6 Using the Code 342
13.7 Concluding Remarks 342
14 Case Study 5: Approximate Bayes and Personalized Pricing 343
14.1 Heterogeneity and Heterogeneous Treatment Effects 343
14.2 The Framework 344
14.3 Context and Data 345
14.4 Does the Bayesian Bootstrap Work? 346
14.5 A Bayesian Bootstrap Procedure for the HTE Logit 349
14.6 Personalized Pricing 351
Appendix A An Introduction to R and bayesm 357
A.1 Setting up the R Environment and bayesm 357
A.2 The R Language 360
A.3 Using bayesm 379
A.4 Obtaining Help on bayesm 379
A.5 Tips on Using MCMC Methods 381
A.6 Extending and Adapting Our Code 381
References 383
Index 389
