Markov Chain Monte Carlo on Finite State Spaces

Tobias Siems

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arXiv · 1903.09019

Markov Chain Monte Carlo on Finite State Spaces

Tobias Siems

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Abstract

We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we proof a pivotal convergence theorem for finite Markov chains and a minimal version of the Perron-Frobenius theorem. Subsequently, we briefly discuss two fundamental MCMC methods, the Gibbs and Metropolis-Hastings sampler. Only very basic knowledge about matrices, convergence of real sequences and probability theory is required.

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Tobias Siems. 2019-03-20. Markov Chain Monte Carlo on Finite State Spaces. https://arxiv.org/abs/1903.09019

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