Hierarchical Naive Bayes Classifiers for uncertain data

In experimental sciences many classification problems deal with variables with replicated measurements. In this case the replicates are usually summarized by their mean or median. However, such choice does not consider the information about the uncertainty associated with the measurements, thus potentially leading to over or underestimate the probability associated to each classification. In this paper we present an extension of the Naive Bayes classifier which, thanks to a Bayesian hierarchical model, is able to properly deal with replicates and uncertain measurements. We will show how to perform classification and learning with continuous and discrete variables with replicated measurements and we will describe the advantages of the proposed model over the standard Naive Bayes algorithm with a simulation study.