Robustness of Metropolis-Hastings algorithms

• Applicant: Professor Dr. Daniel Rudolf
• Subject Area: Mathematics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 389483880

Markov chain Monte Carlo methods, in particular Metropolis-Hastings (MH) type algorithms, are one of the key tools in computational statistics for the approximation of distributions and expectations. Two types of robustness properties are particularly desirable, namely variance robustness of MH algorithms in a Bayesian inverse problem setting and noise robustness in the sense of stability of a Markov chain w.r.t. perturbations.Perturbed or noisy Markov chains are used to approximate ideal Markov chains which are difficult or impossible to implement. The goal is to derive bounds of the mixing cost of such approximating, possibly time-inhomogenous, noisy MH type algorithms as well as to compare the integration error of ideal and noisy Markov chain Monte Carlo methods. The resulting algorithms are aimed to be applied in real world scenarios of approximating doubly-intractable distributions which appear in structural biology. The second main objective is to provide a concept of variance independence for Bayesian inverse problems. The concept will be theoretically verified for certain MH type algorithms to describe the robustness observed in simulations.

• DFG Programme: Research Grants