Metropolis-Hastings Algorithms

CPSC 535 Metropolis-Hastings
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Gibbs Sampler

Initialization: Select deterministically or randomly (0 ) (0 ) θ = θ 1 , ..., θ p .

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Gibbs Sampler

Initialization: Select deterministically or randomly (0 ) (0 ) θ = θ 1 , ..., θ p . Iteration i; i 1:

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Gibbs Sampler

Initialization: Select deterministically or randomly (0 ) (0 ) θ = θ 1 , ..., θ p . Iteration i; i 1:
For k = 1 : p

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Gibbs Sampler

Initialization: Select deterministically or randomly (0 ) (0 ) θ = θ 1 , ..., θ p . Iteration i; i 1:
(i ) k where (i ) (i ) (i 1 ) (i 1 ) θ 1 , ..., θ k 1 , θ k +1 , ..., θ p (i )

For k = 1 : p
Sample θ k θ
(i ) k

π θk j θ

=

.

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The Gibbs sampler requires sampling from the full conditional distributions π ( θk j θ k ) .

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The Gibbs sampler requires sampling from the full conditional distributions π ( θk j θ k ) . For many complex models, it is impossible to sample from several of these “full” conditional distributions.

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The Gibbs sampler requires sampling from the full conditional distributions π ( θk j θ k ) . For many complex models, it is impossible to sample from several of these “full” conditional distributions. Even if it is possible to implement the Gibbs sampler, the algorithm might be very ine¢ cient because the variables are very correlated or sampling from the full conditionals is extremely expensive/ine¢ cient.

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Metropolis-Hastings Algorithm

The Metropolis-Hastings algorithm is an alternative algorithm to sample from probability distribution π (θ ) known up to a normalizing constant.

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Metropolis-Hastings Algorithm

The Metropolis-Hastings algorithm is an alternative algorithm to sample from probability