Bayesian Group Analysis

Abstract

In many fields of research the following problem is encountered: a large collection of data is given for which a detailed theory is yet missing. To gain insight into the underlying problem it is important to reveal the interrelationships in the data and to determine the relevant input and response quantities. A central part of this task is to find the natural splitting of the data into groups and to analyze the respective characteristics. Bayesian probability theory is invoked for a consistent treatment of these problems. Due to Ockham’s Razor, which is an integral part of the theory, the simplest group configuration that still fits the data has the highest probability. In addition the Bayesian approach allows to eliminate outliers, which otherwise could lead to erroneous conclusions. Simple textbook and mock data sets are analyzed in order to assess the Bayesian approach.