Contaminated Gibbs-type priors
Federico Camerlenghi, Riccardo Corradin, Andrea Ongaro

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…
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Taxonomy
TopicsBayesian Methods and Mixture Models · Statistical Methods and Inference · Advanced Statistical Methods and Models
