Metropolis–Hastings algorithm: Difference between revisions

Revision as of 01:20, 23 March 2021

Revision as of 15:57, 15 April 2021

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if <math>\sigma^2</math> is too large, the acceptance rate will be very low because the proposals are likely to land in regions of much lower probability density, so <math>a_1</math> will be very small, and again the chain will converge very slowly. One typically tunes the proposal distribution so that the algorithms accepts on the order of 30% of all samples – in line with the theoretical estimates mentioned in the previous paragraph.

[[Image:3dRosenbrock.png|thumb|350px|The result of three [[Markov chain]]s running on the 3D [[Rosenbrock function]] using the Metropolis–Hastings algorithm. The algorithm samples from regions where the [[posterior probability]] is high, and the chains begin to mix in these regions. The approximate position of the maximum has been illuminated. Note that theThe red points are the ones that remain after the burn-in process. The earlier ones have been discarded.]]

==See also==