Markov Chain Monte Carlo Methods and Applications

Open Access
Author:
Wu, Kaiyi
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Ludmil Tomov Zikatanov, Thesis Supervisor
  • Sergei Tabachnikov, Honors Advisor
Keywords:
  • Markov Chain Monte Carlo
  • Adaptive method
Abstract:
In this paper, we consider, both computationally and theoretically, the properties of adaptive Markov Chain Monte Carlo (a-MCMC) methods. We begin our study with a famous MCMC realization, the Metropolis-Hastings algorithm. We further apply this algorithm to evaluate high-dimensional integrals. We also extend the algorithms to the case of adaptive MCMC methods and prove several results related to its basic properties, such as ergodicity and aperiodicity. We also plan to focus our efforts also on showing that a-MCMC methods are advantageous over the standard (non-adaptive) MCMC methods.