A probability for classification based on the mixture of Dirichlet process model

TL;DR

This paper introduces a modified Bayesian nonparametric classification model based on the Dirichlet process, providing explicit probability distributions and a reversible MCMC algorithm, with numerical comparisons to existing methods.

Contribution

It develops a new classification probability model derived from the Dirichlet process, with modifications for improved suitability and a novel simulation algorithm.

Findings

The model closely resembles classical hierarchical grouping rules.

The reversible MCMC algorithm effectively estimates classification probabilities.

Numerical illustrations demonstrate advantages over alternative methods.

Abstract

In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of the classification based on this model. The resulting approach then more closely resembles a classical hierarchical grouping rule in that it depends on sums of squares of neighboring values. The proposed probability model for classification relies on a simulation algorithm which will be based on a reversible MCMC algorithm for determining the probabilities, and we provide numerical illustrations comparing with alternative ideas for classification.