BayesMarketing

BayesMarketing - The HB How Bayesian methods have changed...

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The HB How Bayesian methods have changed the face of marketing research. 20 Summer 2004

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marketing research 21 B revolution By Greg M. Allenby, David G. Bakken, and Peter E. Rossi F or most of the history of market- ing research, analytical methods have relied on “classical” statistics. We use these methods to make inferences about the characteristics of a population from the characteristics of a sample drawn from that population. Because we can never determine the true value of the population parameters from samples with complete certainty, we have regarded the sample as one realization of many that could have been realized and then quantify our uncer- tainty with a frequency concept of proba- bility. If we’re interested in the population mean for some measure (say height, for example), then the sample mean is our best guess about the mean of the population, and we conceive of uncertainty as arising from hypothetical samples that could have been selected from the population. Classical statistical methods express uncer- tainty through the variability of statistics calculated from these hypothetical samples when interpreting confidence intervals and conducting hypothesis tests. Over the last 10 years, a paradigm shift has occurred in the statistical analysis of marketing data, especially data obtained from conjoint experiments. The new paradigm reflects a different perspective on probability. This view of probability was first proposed in the 18th century by Thomas Bayes, an English clergyman who died in 1760. Bayes wrote a paper (pub- lished posthumously in 1763) in which he proposed a rule for accounting for uncer- tainty that has become known as Bayes’ Theorem. This became the foundation for Bayesian statistical inference, and Bayes most likely would be amazed by the many applications sprouting from his paper. In Bayesian statistics, probabilities reflect a belief about the sample of data under study rather than about the frequency of events across hypothetical samples. Bayes’ Theorem exploits the fact that the joint probability of two events, A and B, can be written as the product of the probability of one event and the conditional probability of the second event, given the occurrence Reprinted with permission from Marketing Research , Summer 2004, published by the American Marketing Association.
of the first event. If we consider “A” to be our “hypothesis” (H) in the absence of any observations “B” (or “D” for data), we can express the rule as follows: Pr(H|D) = Pr(D|H) ¥ Pr(H) / Pr(D) The probability of the hypothesis given (or “conditional” on—the meaning of the “|” symbol) the data is equal to the probability of the data given the hypothesis times the proba- bility of the hypothesis divided by the probability of the data. We refer to the Pr(H) as the prior

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BayesMarketing - The HB How Bayesian methods have changed...

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