Metropolis-Hastings algorithm

Metropolis-Hastings algorithm
• Note: target distribution ib i does not need to be normalized.
– Based on ratio: P(θ proposed ) / P(θ current ) .
– Useful when target distribution P(θ) is a posterior distribution
p D| p .
proportional to
pD|
p
Bayes’ rule:
p
|
D
p D
p | D
pD|
p
– Need only evaluate the product p D| p , not the separate
likelihoods and priors.
– By evaluating p D
|
p
,
can generate random representative
values from the posterior distribution.
– Don’t need to evaluate evidence, pD.
• Can do Baysian inference with rich and complex models.