Empirical Bayes, Naive Bayes and All That about Data Analysis

Abstract

?Empirical Bayes method has attracted considerable attention in large-scale inference recently as highlighted in Efron (2010). Naive Bayes classifier is an important benchmark method for classification problems. In this talk, I'll use a high-dimensional categorical dataset to investigate some critical issues of empirical Bayes method and Naive Bayes classifier. In particular, a new statistic, useful in describing relationship among high-dimensional categorical variables, and a new interpretation of a famous formula in nonparametric empirical Bayes, which leads to a counter-intuitive data analysis procedure with superior results, will be presented. Naive Bayes classifier as a low-dimension logistic regression model will also be discussed.