Comparing two multinomial samples using hierarchical Bayesian models

Andrés R. Masegosa, Antonio Torres, María Morales, Antonio Salmerón

Abstract: Two-sample statistical tests are commonly used when deciding whether two samples can be considered to be drawn from the same population. However, statistical tests face problems when confronted to situations involving extremely large volumes of data, in which case the power of the test is so high that they reject the null hypothesis even if the differences found in the data are minimal. Furthermore, the fact that they may require to explore the whole sample each time they are applied is a serious limitation, for instance, in streaming data contexts. In this paper, we apply a class of Bayesian models that have been successfully used in streaming data context, to the problem of comparing multinomial populations. The underlying tool is latent variable models with hierarchical power priors. We show how it is possible, by means of a relevant parameter, to decide whether two populations are different or not.