## Electronic Journal of Statistics

### Posterior sampling from $\varepsilon$-approximation of normalized completely random measure mixtures

#### Abstract

This paper adopts a Bayesian nonparametric mixture model where the mixing distribution belongs to the wide class of normalized homogeneous completely random measures. We propose a truncation method for the mixing distribution by discarding the weights of the unnormalized measure smaller than a threshold. We prove convergence in law of our approximation, provide some theoretical properties, and characterize its posterior distribution so that a blocked Gibbs sampler is devised.

The versatility of the approximation is illustrated by two different applications. In the first the normalized Bessel random measure, encompassing the Dirichlet process, is introduced; goodness of fit indexes show its good performances as mixing measure for density estimation. The second describes how to incorporate covariates in the support of the normalized measure, leading to a linear dependent model for regression and clustering.

#### Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 3516-3547.

Dates
First available in Project Euclid: 16 November 2016

https://projecteuclid.org/euclid.ejs/1479287230

Digital Object Identifier
doi:10.1214/16-EJS1168

Mathematical Reviews number (MathSciNet)
MR3572858

Zentralblatt MATH identifier
1358.62034

#### Citation

Argiento, Raffaele; Bianchini, Ilaria; Guglielmi, Alessandra. Posterior sampling from $\varepsilon$-approximation of normalized completely random measure mixtures. Electron. J. Statist. 10 (2016), no. 2, 3516--3547. doi:10.1214/16-EJS1168. https://projecteuclid.org/euclid.ejs/1479287230

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