Bayes Reading Group: Filippo Ascolani (Duke University), Giacomo Zanella (Bocconi University)

Friday Dec 13, 2024, 11:00 AM → 12:00 PM America/New_York

3rd floor conference room (162 5th Fifth Avenue )

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).