Contaminated Gibbs-type priors

TL;DR

This paper introduces a new family of contaminated Gibbs-type priors that enhance Bayesian models by accounting for outliers and anomalies, with applications in species sampling and astronomical clustering.

Contribution

It extends Gibbs-type priors by adding a contaminant component, providing closed-form results and improved outlier detection capabilities.

Findings

Closed-form expressions for the new priors and their properties

Enhanced outlier detection in astronomical clustering

Improved predictive inference for species with many singletons

Abstract

Gibbs-type priors are widely used as key components in several Bayesian nonparametric models. By virtue of their flexibility and mathematical tractability, they turn out to be predominant priors in species sampling problems, clustering and mixture modelling. We introduce a new family of processes which extend the Gibbs-type one, by including a contaminant component in the model to account for the presence of anomalies (outliers) or an excess of observations with frequency one. We first investigate the induced random partition, the associated predictive distribution and we characterize the asymptotic behaviour of the number of clusters. All the results we obtain are in closed form and easily interpretable, as a noteworthy example we focus on the contaminated version of the Pitman-Yor process. Finally we pinpoint the advantage of our construction in different applied problems: we show how the contaminant component helps to perform outlier detection for an astronomical clustering problem and to improve predictive inference in a species-related dataset, exhibiting a high number of species with frequency one.