Markov Chain Monte Carlo Methods in Quantum Field Theories by Anosh Joseph

Author:Anosh Joseph
Language: eng
Format: epub
ISBN: 9783030460440
Publisher: Springer International Publishing

4.2 Metropolis Algorithm

Let be a function that is proportional to the desired (target) probability distribution .

1.Initialization. In this step we choose an arbitrary point as a first sample. Let us denote the conditional probability density given as . This arbitrary probability density suggests a candidate for the next sample value , given the previous sample value . For the Metropolis algorithm the probability p must be symmetric. That is, it must satisfy . A usual choice is to let be a Gaussian distribution centered at , so that points closer to are more likely to be visited next—making the sequence of samples into a random walk. The function p is referred to as the proposal density or jumping distribution.

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