Componentwise approximate Bayesian computation via Gibbs-like steps

• 成果类型: Article
• 署名作者: Clarte, Gregoire; Robert, Christian P.; Ryder, Robin J.; Stoehr, Julien
• 署名单位: Universite PSL; Universite Paris-Dauphine
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa090
• 发表日期: 2021
• 页码: 591607
• 关键词: inference

摘要

Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are, however, sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this dimension grows. To tackle this difficulty we explore a Gibbs version of the approximate Bayesian computation approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior distributions, and based on summary statistics of reduced dimensions. While lacking the standard justifications for the Gibbs sampler, the resulting Markov chain is shown to converge in distribution under some partial independence conditions. The associated stationary distribution can further be shown to be close to the true posterior distribution, and some hierarchical versions of the proposed mechanism enjoy a closed-form limiting distribution. Experiments also demonstrate the gain in efficiency brought by the Gibbs version over the standard solution.