Perfect samplers for mixtures of distributions

• 成果类型: Article
• 署名作者: Casella, G; Mengersen, KL; Robert, CP; Titterington, DM
• 署名单位: Universite PSL; Universite Paris-Dauphine; State University System of Florida; University of Florida; Queensland University of Technology (QUT); Institut Polytechnique de Paris; ENSAE Paris; University of Glasgow
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/1467-9868.00360
• 发表日期: 2002
• 页码: 777-790
• 关键词: simulation

摘要

We consider the construction of perfect samplers for posterior distributions associated with mixtures of exponential families and conjugate priors, starting with a perfect slice sampler in the spirit of Mira and co-workers. The methods rely on a marginalization akin to Rao-Blackwellization and illustrate the duality principle of Diebolt and Robert. A first approximation embeds the finite support distribution on the latent variables within a continuous support distribution that is easier to simulate by slice sampling, but we later demonstrate that the approximation can be very poor. We conclude by showing that an alternative perfect sampler based on a single backward chain can be constructed. This alternative can handle much larger sample sizes than the slice sampler first proposed.