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.
Citation
Raffaele Argiento. Ilaria Bianchini. Alessandra Guglielmi. "Posterior sampling from $\varepsilon$-approximation of normalized completely random measure mixtures." Electron. J. Statist. 10 (2) 3516 - 3547, 2016. https://doi.org/10.1214/16-EJS1168
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