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Unformatted text preview: sible to know how many iterations it will take to
reach the stationary distribution, or even to be certain when we have arrived.
29 This is probably the largest ﬂaw in MCMC sampling. There are a large num
ber of heuristics which are used to assess convergence that generally involve
looking at how θt varies with time. In general, the initial simulations depend
strongly on the starting point and are thrown away. This is referred to as
burn-in, and often involves discarding the ﬁrst half of all draws.
To reduce the eﬀect of autocorrelations between draws, we typically only
store a small fraction of them, for example we store only 1 out of every 1000
accepted draws. This process is called thinning.
Finally, we can assess convergence by comparing the distribution of the ﬁrst
half of stored draws to the distribution of the second half of stored draws.
If the chain has reached its stationary distribution, these should have sim
ilar distributions, as assessed by various statistics. These (and similar) ap
proaches have been shown to be successful i...
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- Spring '12