Tiangang Cui

Optimization-based Sampling Approaches for Bayesian Inference

Markov chain Monte Carlo (MCMC) relies on efficient
proposals to sample from a target distribution of interest. Recent
optimization-based MCMC algorithms for Bayesian inference, e.g.,
randomize-then-optimize (RTO), repeatedly solve optimization problems
to obtain proposal samples. We interpret RTO as an invertible map
between two random functions and find that this mapping preserves the
random functions along many directions. This leads to a dimension
independent formulation of the RTO algorithm for sampling the
posterior of large-scale Bayesian inverse problems. We applied our new
methods on Hierarchical Bayesian inverse problems.