Discussion Lead: Filippo Ascolani (Duke University), Giacomo Zanella (Bocconi University)
Topic: Coordinate-wise MCMC schemes for structured high-dimensional Bayesian models
Link:
Abstract: Coordinate-wise MCMC schemes (e.g. Gibbs and Metropolis-within-Gibbs) are popular algorithms to sample from posterior distributions arising from Bayesian models. We discuss recent developments in the analysis of such algorithms in high-dimensional scenarios.
In the first part of the talk we discuss hierarchical models with a large number of groups, obtaining dimension-free convergence results for coordinate-wise samplers 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.
In the second part we show that if the target distribution is strongly log-concave then the random scan Gibbs sampler contracts in relative entropy and provide a sharp characterization of the associated contraction rate. Extension to Metropolis-within-Gibbs schemes and a comparison with gradient-based methods are also discussed.
This is based on joint works with Gareth Roberts (University of Warwick) and Hugo Lavenant (Bocconi University).