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Markov Chain Monte Carlo on finite state spaces

Published online by Cambridge University Press:  18 June 2020

Tobias Siems
Tobias Siems*
Affiliation:
Department of Mathematics and Computer Science, University of Greifswald, Germany
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Extract

We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we prove 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.

Type
Articles
Information
The Mathematical Gazette , Volume 104 , Issue 560 , July 2020 , pp. 281 - 287
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Copyright
© Mathematical Association 2020

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