Bayesian supervised predictive classification and hypothesis testing toolkit for partition exchangeability

TL;DR

This paper introduces Bayesian classifiers and hypothesis tests under partition exchangeability, including a marginal and a simultaneous classifier, along with MLE and simulation tools for the underlying generative model.

Contribution

It provides novel Bayesian classifiers and hypothesis testing methods specifically designed for partition exchangeability, along with simulation functions for Ewens Sampling Formula.

Findings

The simultaneous classifier improves accuracy over the marginal classifier.

MLE effectively estimates the key parameter of the model.

Simulation functions accurately generate sequences from the Poisson-Dirichlet distribution.

Abstract

Bayesian supervised predictive classifiers, hypothesis testing, and parametric estimation under Partition Exchangeability are implemented. The two classifiers presented are the marginal classifier (that assumes test data is i.i.d.) next to a more computationally costly but accurate simultaneous classifier (that finds a labelling for the entire test dataset at once based on simultanous use of all the test data to predict each label). We also provide the Maximum Likelihood Estimation (MLE) of the only underlying parameter of the partition exchangeability generative model as well as hypothesis testing statistics for equality of this parameter with a single value, alternative, or multiple samples. We present functions to simulate the sequences from Ewens Sampling Formula as the realisation of the Poisson-Dirichlet distribution and their respective probabilities.