Efficient stochastic simulation on discrete spaces

Using balancing functions to incorporate local target density information into Markov Chain Monte Carlo sampling schemes

Bachelor thesis (2022)

Authors

B.S.P. Herben Electrical Engineering, Mathematics and Computer Science

Contributors

F.H. van der Meulen Statistics - EEMCS (supervisor 1)
M. Möller Numerical Analysis - EEMCS (supervisor 2)
J.G. Spandaw Analysis - EEMCS (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2022 Bjarne Herben
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Published Date

12-07-2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

The breadth of theoretical results on efficient Markov Chain Monte Carlo (MCMC) sampling schemes on discrete spaces is slim when compared to the available theory for MCMC sampling schemes on continuous spaces. Nonetheless, in [Zan17] a simple framework to design Metropolis-Hastings (MH) proposal kernels that incorporate local information about the target is presented. The class of functions for which the resulting MH kernels are Peskun optimal in high-dimensional regimes is characterized. We will refer to these functions as extit{balancing functions} and to the class of resulting MH proposal kernels as extit{pointwise informed proposals}. In [PG19], the class of balancing functions is used to construct Markov Jump Processes (MJP) on discrete state spaces. As a result, the Zanella process is constructed. In the absence of a theoretical result on the optimal balancing function to choose from the class of balancing functions, a heuristic approach is proposed using the Zanella process. To further encourage the mixing behaviour of the simulated chain, the algebraic structure of the state space is exploited to achieve non-reversible Markov chains on short to medium timescales. Simulations are performed for all the considered MCMC sampling schemes by studying the Bayesian record linkage problem.