Unformatted text preview: state.
6.2 MetropolisHastings algorithm The goal in MCMC is to construct a Markov Chain whose stationary dis
tribution is the posterior p(θy ). We now present the MetropolisHastings
algorithm. In addition to the distributions we have already used (likelihood
and prior), we will need a proposal distribution (or jumping distribution)
J (θ, θ' ) which will propose a new state θ' given the current state θ.
There are many options when choosing a proposal distribution which we will
discuss later. The proposal distribution will yield a random walk over the
parameter space, proposing steps θ → θ' . We accept or reject each step
depending on the relative posterior probabilities for θ and θ' . When we run
the random walk for long enough, the accepted values will simulate draws
from the posterior.
6.2.1 Some intuition into the MetropolisHastings algorithm Suppose we are considering the transition θ → θ' . If p(θ' y ) is larger than
p(θy ), then for every accepted draw of θ, we should have at least as many
accepted draws of θ' and so we should...
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This note was uploaded on 03/24/2014 for the course MIT 15.097 taught by Professor Cynthiarudin during the Spring '12 term at MIT.
 Spring '12
 CynthiaRudin

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