Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian models

arXiv:2403.09416v1 Announce Type: cross
Abstract: We study general coordinate-wise MCMC schemes (such as Metropolis-within-Gibbs samplers), which are commonly used to fit Bayesian non-conjugate hierarchical models. We relate their convergence properties to the ones of the corresponding (potentially not implementable) Gibbs sampler through the notion of conditional conductance. This allows us to study the performances of popular Metropolis-within-Gibbs schemes for non-conjugate hierarchical models, in high-dimensional regimes where both number of datapoints and parameters increase. Given random data-generating assumptions, we establish dimension-free …

abstract arxiv bayesian convergence general gibbs hierarchical math.st mcmc metropolis notion scalability stat.co stat.ml stat.th study through type wise