Contaminated Gibbs-type priors

08/26/2021
by   Federico Camerlenghi, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 38

page 41

03/15/2018

Hierarchical Species Sampling Models

This paper introduces a general class of hierarchical nonparametric prio...
12/22/2020

Spying on the prior of the number of data clusters and the partition distribution in Bayesian cluster analysis

Mixture models represent the key modelling approach for Bayesian cluster...
03/27/2020

Enriched Pitman-Yor processes

In Bayesian nonparametrics there exists a rich variety of discrete prior...
05/28/2020

Model selection for ecological community data using tree shrinkage priors

Researchers and managers model ecological communities to infer the bioti...
05/08/2022

The saturated pairwise interaction Gibbs point process as a joint species distribution model

In an effort to effectively model observed patterns in the spatial confi...
12/08/2015

Gibbs-type Indian buffet processes

We investigate a class of feature allocation models that generalize the ...
11/03/2021

On Johnson's "sufficientness" postulates for features-sampling models

In the 1920's, the English philosopher W.E. Johnson introduced a charact...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.