MIT15_097S12_lec15

Now lets plug k py j py j

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 � y on average p((θ ||y)) accepted draws of θ' . We thus accept the transition with pθ probability probability 6.2.2 p(θ� |y ) p(θ|y ) . Thus for any transition, we accept the transition with p(θ' |y ) min , 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 integ...
View Full Document

Ask a homework question - tutors are online