Gibbs Sampling for Mixtures in Order of Appearance: The Ordered Allocation Sampler

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 samplers more widely applicable than ones, they may suffer from slow mixing in infinite mixtures, where some form of truncation, either deterministic or random, is required. In mixtures with random number components, the exploration parameter spaces different dimensions can also be challenging. We tackle these issues by expressing components order appearance an exchangeable sequence directed distribution. derive a sampler that straightforward implement distributions tractable size-biased ordered weights, readily adapted models which not available. no truncation necessary. As finite dimension, simple updating obtained blocking argument, thus, easing challenges found transdimensional moves via Metropolis-Hastings steps. Additionally, occurs space partitions blocks labeled least element order, endows good properties. The performance proposed algorithm evaluated simulation study. Supplementary materials this article available online.