An Introduction to Markov Chain Monte Carlo on Finite State Spaces

03/20/2019

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by   Tobias Siems, et al.

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We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically comprehensive way. Our focus is on simplicity. We give an elementary proof for the Perron-Frobenius theorem and a convergence theorem for Markov chains. Subsequently we briefly discuss the well-known Gibbs sampler and the Metropolis- Hastings algorithm. Only basic knowledge about matrix multiplication, convergence of real sequences and stochastic is required.