Bayesian Statistics and Marketing

Cover
Title Page
Copyright
Contents
Chapter 1 Introduction
	1.1 A Basic Paradigm for Marketing Problems
	1.2 A Simple Example
	1.3 Benefits and Costs of the Bayesian Approach
	1.4 An Overview of Methodological Material and Case Studies
	1.5 Approximate Bayes Methods and This Book
	1.6 Computing and This Book
	Acknowledgments
Chapter 2 Bayesian Essentials
	2.1 Essential Concepts from Distribution Theory
	2.2 The Goal of Inference and Bayes Theorem
		2.2.1 Bayes Theorem
	2.3 Conditioning and the Likelihood Principle
	2.4 Prediction and Bayes
	2.5 Summarizing the Posterior
	2.6 Decision Theory, Risk, and the Sampling Properties of Bayes Estimators
	2.7 Identification and Bayesian Inference
	2.8 Conjugacy, Sufficiency, and Exponential Families
	2.9 Regression and Multivariate Analysis Examples
		2.9.1 Multiple Regression
		2.9.2 Assessing Priors for Regression Models
		2.9.3 Bayesian Inference for Covariance Matrices
		2.9.4 Priors and the Wishart Distribution
		2.9.5 Multivariate Regression
		2.9.6 The Limitations of Conjugate Priors
	2.10 Integration and Asymptotic Methods
	2.11 Importance Sampling
		2.11.1 GHK Method for Evaluation of Certain Integrals of MVN
	2.12 Simulation Primer for Bayesian Problems
		2.12.1 Uniform, Normal, and Gamma Generation
		2.12.2 Truncated Distributions
		2.12.3 Multivariate Normal and Student t Distributions
		2.12.4 The Wishart and Inverted Wishart Distributions
		2.12.5 Multinomial Distributions
		2.12.6 Dirichlet Distribution
	2.13 Simulation from Posterior of Multivariate Regression Model
Chapter 3 MCMC Methods
	3.1 MCMC Methods
	3.2 A Simple Example: Bivariate Normal Gibbs Sampler
	3.3 Some Markov Chain Theory
	3.4 Gibbs Sampler
	3.5 Gibbs Sampler for the SUR Regression Model
	3.6 Conditional Distributions and Directed Graphs
	3.7 Hierarchical Linear Models
	3.8 Data Augmentation and a Probit Example
	3.9 Mixtures of Normals
		3.9.1 Identification in Normal Mixtures
		3.9.2 Performance of the Unconstrained Gibbs Sampler
	3.10 Metropolis Algorithms
		3.10.1 Independence Metropolis Chains
		3.10.2 Random Walk Metropolis Chains
		3.10.3 Scaling of the Random Walk Metropolis
	3.11 Metropolis Algorithms Illustrated with the Multinomial Logit Model
	3.12 Hybrid MCMC Methods
	3.13 Diagnostics
Chapter 4 Unit‐Level Models and Discrete Demand
	4.1 Latent Variable Models
	4.2 Multinomial Probit Model
		4.2.1 Understanding the Autocorrelation Properties of the MNP Gibbs Sampler
		4.2.2 The Likelihood for the MNP Model
	4.3 Multivariate Probit Model
	4.4 Demand Theory and Models Involving Discrete Choice
		4.4.1 A Nonhomothetic Choice Model
		4.4.2 Demand for Discrete Quantities
		4.4.3 Demand for Variety
Chapter 5 Hierarchical Models for Heterogeneous Units
	5.1 Heterogeneity and Priors
	5.2 Hierarchical Models
	5.3 Inference for Hierarchical Models
	5.4 A Hierarchical Multinomial Logit Example
	5.5 Using Mixtures of Normals
		5.5.1 A Hybrid Sampler
		5.5.2 Identification of the Number of Mixture Components
		5.5.3 Application to Hierarchical Models
	5.6 Further Elaborations of the Normal Model of Heterogeneity
	5.7 Diagnostic Checks of the First Stage Prior
	5.8 Findings and Influence on Marketing Practice
Chapter 6 Model Choice and Decision Theory
	6.1 Model Selection
	6.2 Bayes Factors in the Conjugate Setting
	6.3 Asymptotic Methods for Computing Bayes Factors
	6.4 Computing Bayes Factors Using Importance Sampling
	6.5 Bayes Factors Using MCMC Draws from the Posterior
	6.6 Bridge Sampling Methods
	6.7 Posterior Model Probabilities with Unidentified Parameters
	6.8 Chib's Method
	6.9 An Example of Bayes Factor Computation: Diagonal MNP models
	6.10 Marketing Decisions and Bayesian Decision Theory
		6.10.1 Plug‐In vs Full Bayes Approaches
		6.10.2 Use of Alternative Information Sets
		6.10.3 Valuation of Disaggregate Information
	6.11 An Example of Bayesian Decision Theory: Valuing Household Purchase Information
Chapter 7 Simultaneity
	7.1 A Bayesian Approach to Instrumental Variables
	7.2 Structural Models and Endogeneity/Simultaneity
		7.2.1 Demand Model
		7.2.2 Supply Model – Profit Maximizing Prices
		7.2.3 Bayesian Estimation
	7.3 Non‐Random Marketing Mix Variables
		7.3.1 A General Framework
		7.3.2 An Application to Detailing Allocation
		7.3.3 Conditional Modeling Approach
		7.3.4 Beyond the Conditional Model
Chapter 8 A Bayesian Perspective on Machine Learning
	8.1 Introduction
	8.2 Regularization
		8.2.1 The LASSO and Bayes
		8.2.2 Discussion: Informative Regularizers
		8.2.3 Bayesian Inference
	8.3 Bagging
		8.3.1 Bagging for Regression
		8.3.2 Bagging, Bayesian Model Averaging and Ensembles
	8.4 Boosting
		8.4.1 Boosting as Bayes
	8.5 Deep Learning
		8.5.1 A Primer on Deep Learning
		8.5.2 Bayes and Deep Learning
	8.6 Applications
		8.6.1 Bayes/ML for Flexible Heterogeneity
		8.6.2 The Need for ML
		8.6.3 Discussion
Chapter 9 Bayesian Analysis for Text Data
	9.1 Introduction
	9.2 Consumer Demand
		9.2.1 The Latent Dirichlet Allocation (LDA) Model
		9.2.2 Full Gibbs Sampler
		9.2.3 Processing Text Data for Analysis
		9.2.4 Collapsed Gibbs Sampler
		9.2.5 The Sentence Constrained LDA Model
		9.2.6 Conjunctions and Punctuation
	9.3 Integrated Models
		9.3.1 Text and Conjoint Data
		9.3.2 R Code for Text and Conjoint Data
		9.3.3 Text and Product Ratings
		9.3.4 Text and Scaled Response Data
	9.4 Discussion
Chapter 10 Case Study 1: Analysis of Choice‐Based Conjoint Data Using A Hierarchical Logit Model
	10.1 Choice‐Based Conjoint
	10.2 A Random Coefficient Logit
	10.3 Sign Constraints and Priors
	10.4 The Camera Data
		10.4.1 Panel Data in bayesm
	10.5 Running the Model
	10.6 Describing the Draws of Respondent Partworths
	10.7 Predictive Posteriors
		10.7.1 Respondent‐Level Parthworth Inferences
		10.7.2 Posterior Predictive Distributions
	10.8 COMPARISON OF STAN AND SAWTOOTH SOFTWARE TO BAYESM ROUTINES
		10.8.1 Comparison to STAN
		10.8.2 Comparison with Sawtooth Software
Chapter 11 Case Study 2: WTP and Equilibrium Analysis with Conjoint Demand
	11.1 The Demand for Product Features
		11.1.1 The Standard Choice Model for Differentiated Product Demand
		11.1.2 Estimating Demand
	11.2 Conjoint Surveys and Demand Estimation
		11.2.1 Conjoint Design
	11.3 WTP Properly Defined
		11.3.1 Pseudo‐WTP
		11.3.2 Pseudo WTP for Heterogenous Consumers
		11.3.3 True WTP
		11.3.4 Problems with All WTP Measures
	11.4 Nash Equilibrium Prices – Computation and Assumptions
		11.4.1 Assumptions
		11.4.2 A Standard Logit Model for Demand
		11.4.3 Computing Equilibrium Prices
	11.5 Camera Example
		11.5.1 WTP Computations
		11.5.2 Equilibrium Price Calculations
		11.5.3 Lessons for Conjoint Design from WTP and Equilibrium Price Computations
Chapter 12 Case Study 3: Scale Usage Heterogeneity
	12.1 Background
	12.2 Model
	12.3 Priors and MCMC Algorithm
	12.4 Data
		12.4.1 Scale Usage Heterogeneity
		12.4.2 Correlation Analysis
	12.5 Discussion
	12.6 R Implementation
Chapter 13 Case Study 4: Volumetric Conjoint
	13.1 Introduction
	13.2 Model Development
	13.3 Estimation
	13.4 Empirical Analysis
		13.4.1 Ice Cream
		13.4.2 Frozen Pizza
	13.5 Discussion
	13.6 Using the Code
	13.7 Concluding Remarks
Chapter 14 Case Study 5: Approximate Bayes and Personalized Pricing
	14.1 Heterogeneity and Heterogeneous Treatment Effects
	14.2 The Framework
		14.2.1 Introducing the ML Element
	14.3 Context and Data
	14.4 Does the Bayesian Bootstrap Work?
	14.5 A Bayesian Bootstrap Procedure for the HTE Logit
		14.5.1 The Estimator
		14.5.2 Results
	14.6 Personalized Pricing
A An Introduction to R and bayesm
	A.1 SETTING UP THE R ENVIRONMENT AND BAYESM
		A.1.1 Obtaining R
		A.1.2 Getting Started in RStudio
		A.1.3 Obtaining Help in RStudio
		A.1.4 Installing bayesm
	A.2 The R Language
		A.2.1 Using Built‐In Functions: Running a Regression
		A.2.2 Inspecting Objects and the R Workspace
		A.2.3 Vectors, Matrices, and Lists
		A.2.4 Accessing Elements and Subsetting Vectors, Arrays, and Lists
		A.2.5 Loops
		A.2.6 Implicit Loops
		A.2.7 Matrix Operations
		A.2.8 Other Useful Built‐In R Functions
		A.2.9 User‐defined Functions
		A.2.10 Debugging Functions
		A.2.11 Elementary Graphics
		A.2.12 System Information
		A.2.13 More Lessons Learned from Timing
	A.3 USING BAYESM
	A.4 OBTAINING HELP WITH BAYESM
	A.5 Tips on Using MCMC Methods
	A.6 Extending and Adapting Our Code
References
Index
EULA