Abstract

The matching problem is known since the beginning of the eighteenth century and Bayesian solutions have been proposed. In this paper, we present a Bayesian analysis of an experiment that also leads to the matching problem. Since in this paper we consider the order in which assignments are made and not only the number of matches, our approach is different from the literature on this problem. Our approach also considers that it is possible to have different abilities for the different objects that will be guessed. Hence, we have a parameter that measures the matching ability for each specific object or assignment. As a consequence, we need to have some replicates of the experiment and a prior distribution for each of the parameters. Conjugate prior distributions for the parameters are discussed. The frequentist solution has a particular Bayesian interpretation under a non-informative prior distribution. A real data set is analyzed using the proposed methodology.