Notice that in the model we do not specify the

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Unformatted text preview: )mH +α−1 (1 − θt−1 )m−mH +β −1 ∗ 30 which we can easily compute. This formula and a uniform random number generator for the proposal distribution are all that is required to implement the Metropolis-Hastings algorithm. Consider the specific case of m = 25, mH = 6, and α = β = 5. The following three figures show the time sequence of proposals θ∗ for chains with r = 0.01, r = 0.1, and r = 1 respectively, with the colors indicating whether each proposed θ∗ was accepted or not, and time along the x-axis. In this first figure we see that with r = 0.01, the step sizes are too small and after 2000 proposals we have not reached the stationary distribution. In the next figure, with r = 1 the steps are too large and we reject most of the proposals. This leads to a small number of accepted draws after 2000 proposals. 31 The chain with r = 0.1 is the happy medium, where we rapidly reach the stationary distribution, and accept most of the samples. To compare this to the analytic distribution that we obtain...
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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.

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