Revisiting Empirical Bayes Methods and Applications to Special Types of Data

TL;DR

This paper revisits classical empirical Bayes methods, introduces new applications such as ranking, symbolic data, and microarray analysis, and demonstrates their effectiveness on real datasets using advanced statistical techniques.

Contribution

It develops new applications of empirical Bayes methods, including ranking and microarray data analysis, and simplifies their implementation with the Pearson system and saddlepoint approximations.

Findings

Methods perform well on real data

Tweedie's formula effectively analyzes microarray data

Saddlepoint approximations generalize existing results

Abstract

Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of the empirical Bayesian methods and develops new applications. We first look at a linear empirical Bayes estimator and apply it on ranking and symbolic data. Next, we consider Tweedie's formula and show how it can be applied to analyze a microarray dataset. The application of the formula is simplified with the Pearson system of distributions. Saddlepoint approximations enable us to generalize several results in this direction. The results show that the proposed methods perform well in applications to real data sets.