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Unformatted text preview: itive probability of eventually reaching any state from any other state.
A typical proposal distribution is a random walk J (θ, θ' ) = N (θ, σ 2 ) for some
σ 2 . There are several important features of proposal distributions that work
well in practice. First, we must be able to sample from it eﬃciently. Second,
we must be able to compute the ratio α(θ, θ' ) in an eﬃcient way. Third, the
jumps should not be too large or we will reject them frequently and the chain
will not move quickly. Fourth, the jumps should not be too small or it will
take a long time to explore the whole space. The balance between ‘too small’
and ‘too large’ is the subject of hundreds of papers on ‘adaptive MCMC’,
but there is really no good way to know which proposal distribution to use.
In practice, we often try several proposal distributions to see which is most
appropriate, for example, by adjusting σ 2 in the above proposal distribution.
6.4.2 On reaching the stationary distribution Unfortunately, it is impos...
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- Spring '12