1
Introduction

Abstract

While the conceptual appeal of Bayesian methods has long been recognized, the recent popularity stems from computational and modeling breakthroughs that have made Bayesian methods attractive for many marketing problems. This book provides a self‐contained and comprehensive treatment of Bayesian methods and the marketing problems for which these methods are especially appropriate. It presents a treatment of Bayesian methods that emphasizes the unique aspects of their application to marketing problems. The book emphasizes the unique aspects of the modeling problem in marketing and the modifications of method and models that researchers in marketing have devised. It also provides the requisite methodological knowledge and an appreciation of how these methods can be used to allow the reader to devise and analyze new models. The book takes a stand on customer differences by modeling differences via a probability distribution.

The past 30 years have seen a dramatic increase in the use of Bayesian methods in marketing. Bayesian analyses have been conducted over a wide range of marketing problems from new product introduction to pricing, and with a wide variety of different data sources. While the conceptual appeal of Bayesian methods has long been recognized, the recent popularity stems from computational and modeling breakthroughs that have made Bayesian methods attractive for many marketing problems. This book aims to provide a self‐contained and comprehensive treatment of Bayesian methods and the marketing problems for which these methods are especially appropriate. There are unique aspects of important problems in marketing that make particular models and specific Bayesian methods attractive. We, therefore, do not attempt to provide a generic treatment of Bayesian methods. We refer the interested reader to classic treatments by Robert and Casella [2004], Gelman et al. [2004], and Berger [1985] for more general‐purpose discussion of Bayesian methods. Instead, we provide a treatment of Bayesian methods that emphasizes the unique aspects of their application to marketing problems.

Until the mid‐1980s, Bayesian methods appeared impractical since the class of models for which the posterior inference could be computed was no larger than the class of models for which exact sampling results were available. Moreover, the Bayes approach does require assessment of a prior which some feel to be an extra cost. Simulation methods, in particular Markov Chain Monte Carlo (MCMC) methods, have freed us from computational constraints for a very wide class of models. MCMC methods are ideally suited for models built from a sequence of conditional distributions, often called hierarchical models. Bayesian hierarchical models offer tremendous flexibility and modularity and are particularly useful for marketing problems.

There is an important interaction between the availability of inference methods and the development of statistical models. Nowhere has this been more evident than in the application of hierarchical models to marketing problems. Hierarchical models are those built up through a sequence of conditional distributions. These models match rather closely the various levels at which marketing decisions are made – from individual consumers to the marketplace. Bayesian researchers in marketing have expanded on the standard set of hierarchical models to provide models useful for marketing problems. Throughout this book, we will emphasize the unique aspects of the modeling problem in marketing and the modifications of method and models that researchers in marketing have devised. We hope to provide the requisite methodological knowledge and an appreciation of how these methods can be used to allow the reader to devise and analyze new models. This departs, to some extent, from the standard model of a treatise in statistics in which one writes down a set of models and catalogues the set of methods appropriate for analysis of these models.

1.1 A BASIC PARADIGM FOR MARKETING PROBLEMS

Ultimately, marketing data results from customers taking actions in a particular context and facing a particular environment. The marketing manager can influence some aspects of this environment. Our goal is to provide models of these decision processes and then make optimal decisions conditional on these models. Fundamental to this prospective is that customers are different in their needs and wants for marketplace offerings, thus expanding the set of actions that can be taken. At the extreme, actions can be directed at specific individuals. Even if one‐on‐one interaction is not possible, the models and system of inference must be flexible enough to admit nonuniform actions.

Once the researcher acknowledges the existence of differences between customers, the modeling task expands to include a model of these differences. Throughout this book, we will take a stand on customer differences by modeling differences via a probability distribution. Those familiar with standard econometric methods will recognize this as related to a random coefficients approach. The primary difference is that we do not regard the customer level parameters as nuisance parameters but, instead, regard these parameters as the goal of inference. Inferences about customer differences are required for any marketing action, from strategic decisions associated with formulating offerings to tactical decisions of customizing prices. Individuals who are most likely to respond to these variables are those that find highest value in the offering's attributes and those that are most price sensitive, neither of whom are well described by parameters such as the mean of the random coefficients distribution.

Statistical modeling of marketing problems consists of three components:

1. Within‐unit behavior
2. Across‐unit behavior
3. Action

“Unit” refers to the particular level of aggregation dictated by the problem and data availability. In many instances, the unit is the consumer. However, it is possible to consider both less and more aggregate levels of analyses. For example, one might consider a particular consumption occasion or survey instances as the “unit” and consider changes in preferences across occasions or over time as part of the model (an example of this is in Yang et al. [2002]). In marketing practice, decisions are often made at a much higher level of aggregation such as the “key account” or sales territory. In all cases, we consider the “unit” as the lowest level of aggregation considered explicitly in the model.

The first component of problem is the conditional likelihood for the “unit‐level behavior.” We condition on unit‐specific parameters that are regarded as the sole source of between‐unit differences. The second component is a distribution of these unit‐specific parameters over the population of units. Finally, the decision problem is the ultimate goal of modeling exercise. We typically postulate a profit function and ask – what is the optimal action conditional on the model and the information in the data? Given this view of marketing problems, it is natural to consider the Bayesian approach to inference, which provides a unified treatment of all three components.

1.2 A SIMPLE EXAMPLE

As an example of the components outlined in Section 1.1, consider the case of consumers observed making choices between different products. Products are characterized by some vector of choice attribute variables that might include product characteristics, prices, and advertising. Consumers could be observed to make choices either in the marketplace or in a survey/experimental setting. We want to predict how consumers will react to a change in the marketing mix variables or in the product characteristics. Our ultimate goal is to design products or vary the marketing mix so as to optimize profitability.

We start with the “within‐unit” model of choice conditional on the observed attributes for each of the choice alternatives. A standard model for this situation is the Multinomial Logit model.

If we observe more than one observation per consumer, it is natural to consider a model that accommodates differences between consumers. That is, we have some information about each consumer's preferences and we can start to tease out these differences. However, we must recognize that in many situations, we have only a small amount of information about each consumer. To allow for the possibility that each consumer has different preferences for attributes, we index the vectors by for consumer . Given the small amount of information for each consumer, it is impractical to estimate separate and independent logits for each of the consumers. For this reason, it is useful to think about a distribution of coefficient vectors across the populations of consumers. One simple model would be to assume that the s are distributed normally over consumers.

One common use of logit models is to compute the implication of changes in marketing actions for aggregate market shares. If we want to evaluate the effect on market share for a change in for alternative , then we need to integrate over the distribution in (1.2.1). For a market with a large number of consumers, we might view the expected probability as market share and compute the derivative of market...