Dimension-free mixing times of Gibbs samplers for Bayesian hierarchical models

• URL: http://arxiv.org/abs/2304.06993v2
• Date: Mon, 30 Oct 2023 10:59:27 GMT
• Title: Dimension-free mixing times of Gibbs samplers for Bayesian hierarchical models
• Authors: Filippo Ascolani and Giacomo Zanella
• Abstract summary: We analyse the behaviour of total variation mixing times of Gibbs samplers targeting hierarchical models. We obtain convergence results under random data-generating assumptions for a broad class of two-level models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gibbs samplers are popular algorithms to approximate posterior distributions arising from Bayesian hierarchical models. Despite their popularity and good empirical performances, however, there are still relatively few quantitative results on their convergence properties, e.g. much less than for gradient-based sampling methods. In this work we analyse the behaviour of total variation mixing times of Gibbs samplers targeting hierarchical models using tools from Bayesian asymptotics. We obtain dimension-free convergence results under random data-generating assumptions, for a broad class of two-level models with generic likelihood function. Specific examples with Gaussian, binomial and categorical likelihoods are discussed.

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