ROBUST RANKING AND SELECTION WITH HEAVY-TAIL PRIORS AND ITS APPLICATIONS IN MARKET BASKET ANALYSIS
Ranking and selection is the problem of identifying the best units according to some parameters based on estimates for the parameters obtained from data. Various methods of ranking and selection have been developed, such as empirical Bayes methods ranking units based on a multi-stage Bayesian hierarchical model. Compared with the non-Bayesian methods, including local maximum likelihood and testing, the Bayesian methods have a number of advantages. However, Bayesian methods have the difficultly of choosing the prior. A common choice is to use the conjugate prior for mathematical convenience. We show that while this is often acceptable for many Bayesian analysis, it can have serious problems for ranking. We perform a simulation study to determine the effect of choice of prior on ranking methods. We find that a heavy-tailed prior is more robust to misspecification in many ranking problems, especially when we are focused on the top ranked units. We give an example of applying the posterior mean ranking method with t-prior and normal prior and some other ranking methods in a simulated market basket data, which provide more comparison between different ranking methods. The results of the simulation study can be applied to a range of empirical Bayesian analysis.