Compare Metropolis-Hastings Algorithm with Independent Proposal
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Compare Metropolis-Hastings Algorithm with Independent Proposal
(Accept-reject algorithm). We wish to sample the target density p (with respect to a dominating…
(Accept-reject algorithm). We wish to sample the target density π (with respect to a dominating measure λ), which is known up to a multiplicative constant. Let q be a proposal density (assumed to be easier to sample.)
We assume that there exists a constant M < ∞=”” such=”” that=”” π(x)/q(x)=”” ≤=”” m=”” for=”” all=”” x=””>∈ X. The Accept-Reject goes as follows: first, we generate Y ∼ g and, independently, we generate U ∼ U([0,1]). If Mq(Y)U ≤ π(Y), then we set X =Y. If the inequality is not satisfied, we then discard Y and U and start again.
Show that X is distributed according to π.
What is the distribution of the number of trials required per sample?
What is the average number of samples needed for one simulation?
Propose a method to estimate the normalizing constant of π.
Compare with the Metropolis-Hastings algorithm with Independent proposal.
Compare Metropolis-Hastings Algorithm with Independent Proposal
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Compare Metropolis-Hastings Algorithm with Independent Proposal