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 random number of components, the exploration of parameter spaces of different dimensions can also be challenging. We tackle these issues by expressing the mixture components in the random order of appearance in an exchangeable sequence directed by the mixing distribution. We derive a sampler 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 dimension, a simple updating of the number of components is obtained by a blocking argument, thus, easing challenges found in trans-dimensional 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.

翻译：摘要：吉布斯采样方法是进行混合模型后验推理的标准工具，通常分为边际采样和条件采样两类。条件采样器虽比边际采样器适用性更广，但在无限混合模型中可能面临慢混合问题，此时需要确定性或随机性截断。当混合成分数量随机时，不同维度参数空间的探索同样具有挑战性。针对这些问题，我们将混合成分表示为由混合分布驱动的可交换序列中随机出现的顺序。我们推导出一种采样器，可对具有易处理的尺寸偏倚有序权重的混合分布直接实现，并能轻易适配无法使用边际采样器的混合模型。在无限混合模型中无需任何形式的截断。对于随机维度的有限混合模型，通过分块论证可简单更新成分数量，从而缓解通过Metropolis-Hastings步骤进行跨维度移动的困难。此外，采样发生在块标签按最小元素顺序排列的有序划分空间，这赋予采样器良好的混合特性。通过仿真研究评估了所提算法的性能。