Renny Doig
Title: Combining compound proposal mechanisms and annealing schemes to construct more effective modern Monte Carlo methods
Date: Tuesday, April 22nd, 2025
Time: 10:00am
Location: LIB 2020 & Zoom
Supervised by: Liangliang Wang
Abstract: Modern statistical problems produce probability distributions that require advanced, modern Monte Carlo techniques to sample from. Two of the tools in a modern algorithm toolkit are compound proposal mechanisms and annealing/tempering. The compound proposal allows for multiple candidates to be considered in a single iteration of the respective algorithm, thereby increasing sampling efficiency, reducing the length of the pre-stationary period, and improving performance for sampling problems which have features adverse for classical Monte Carlo methods based on local exploration. On the other hand, annealingbased algorithms construct a sequence of annealed distributions linking a tractable reference distribution to the complex target distribution. By using a combination of local exploration and an exchange of information between distributions in this sequence, complex target distributions can be sampled from which may be otherwise infeasible. In this thesis we present two novel algorithms. The first incorporates auxiliary variables into a compound proposal mechanism. A flexible framework for the specification of the auxiliary variables permits the incorporation of annealing-based algorithms into a compound proposal framework. We find that this can greatly improve the performance relative to compound proposals that only use local moves. The second algorithm presented in this thesis integrates an annealing algorithm based on importance sampling into a reversible MCMC framework. By combining the two, the weaknesses of the importance sampling algorithm may be ameliorated, resulting in a robust algorithm capable of both sampling from a target distribution as well as meta-analysis of the annealing algorithm. Additionally, the proposed algorithm offers a much more parallel structure than the related importance sampling algorithm, offering the potential for highly efficient parallel computing regimes.
Keywords: multiple-try Metropolis; annealed sequential Monte Carlo; normalizing constant; parallel computing