Metropolis–Hastings algorithm: Difference between revisions

Revision as of 12:53, 28 March 2020

Revision as of 08:40, 9 April 2020

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: <math>\frac{P(x' \mid x)}{P(x \mid x')} = \frac{P(x')}{P(x)}.</math>

The approach is to separate the transition in two sub-steps; the proposal and the acceptance-rejection. The ''proposal distribution'' <math>g(x' \mid x)</math> is the conditional probability of proposing a state <math>x'</math> given <math>x</math>, and the ''acceptance distribution'' <math>A(x', x)</math> is the probability to accept the proposed state <math>x'</math>. The transition probability can be written as the product of them:

: <math>P(x'\mid x) = g(x' \mid x) A(x', x).</math>