Unformatted text preview: always accept the transition θ → θ' .
25 If p(θ' |y ) is less than p(θ|y ), then for every accepted draw θ, we should have
on average p((θ ||y)) accepted draws of θ' . We thus accept the transition with
probability 6.2.2 p(θ� |y ) p(θ|y ) . Thus for any transition, we accept the transition with
p(θ' |y )
, 1 . p(θ|y ) (24) Steps of the algorithm We now give the steps of the Metropolis-Hastings algorithm.
Step 1. Choose a starting point θ0 . Set t = 1.
Step 2. Draw θ∗ from the proposal distribution J (θt−1 , ·). The proposed move
for time t is to move from θt−1 to θ∗ .
Step 3. Compute the following: α(θ t−1 p(θ∗ |y )J (θ∗ , θt−1 )
, θ ) := min ,1
p(θt−1 |y )J (θt−1 , θ∗ ) p(y |θ∗ )p(θ∗ )J (θ∗ , θt−1 )
= min ,1
p(y |θt−1 )p(θt−1 )J (θt−1 , θ∗ )
∗ (25) We’ll explain this more soon. The fact that we can compute ratios of
posterior probabilities without having to worry about the normalization
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- Spring '12