B0457
Title: Gibbs sampling for mixtures in order of appearance: The ordered allocation sampler
Authors: Pierpaolo De Blasi - University of Torino and Collegio Carlo Alberto (Italy) [presenting]
Abstract: Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable than marginal ones, they may suffer from slow mixing in infinite mixtures, where some form of truncation, either deterministic or random, is required. In mixtures with a random number of components, the exploration of parameter spaces of different dimensions can also be challenging. These issues are tackled by expressing the mixture components in the random order of appearance in an exchangeable sequence directed by the mixing distribution. A sampler is derived that is straightforward to implement for mixing distributions with tractable size-biased ordered weights, and that can be readily adapted to mixture models for which marginal samplers are not available. In infinite mixtures, no form of truncation is necessary. As for finite mixtures with random dimensions, a simple updating of the number of components is obtained by a blocking argument, thus, easing challenges found in transdimensional moves via Metropolis-Hastings steps. Additionally, sampling occurs in the space of ordered partitions with blocks labelled in the least element order, which endows the sampler with good mixing properties. The performance of the proposed algorithm is evaluated in a simulation study.
