Metropolis–Hastings algorithm: Difference between revisions

Revision as of 06:33, 11 June 2002

Revision as of 13:33, 11 June 2002

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This algorithm can draw samples from any [[probability distribution]] P(x), requiring only that the density can be calculated at x. The algorithm generates a set of states x^t which is a [[Markov chain]] because each state x^t depends only on the previous state x^t-1. The algorithm depends on the creation of a ''proposal density'' Q(x^t,;x') which depends on the current state x^t and which can generate a new proposed sample x'. For example, the proposal density could be a Gaussian centred on the current state x^t

Q(x^t;x') ~ N(x'-x^t,σ²I).

This proposal density would generate samples centred around the current state with variance σ²I. So we draw a new proposal state from Q(x^t,x') and then calculate a value