MCMC convergence diagnosis via multivariate bounds on log-concave densities
成果类型：
Article
署名作者：
Brooks, SP
署名单位：
University of Bristol
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1998
页码：
398-433
关键词：
摘要：
We begin by showing how piecewise linear bounds may be devised, which bound both above and below any concave log-density in general dimensions. We then show how these bounds may be used to gain an upper bound to the volume in the tails outside the convex hull of the sample path in order to assess how well the sampler has explored the target distribution. This method can be used as a stand-alone diagnostic to determine when the sampler output provides a reliable basis for inference on the stationary density, or in conjunction with existing convergence diagnostics to ensure that they are based upon good sampler output. We provide an example and briefly discuss possible extensions to the method and alternative applications of the bounds.