MIT15_097S12_lec15

The next gure shows a normalized 32 histogram of the

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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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