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Unformatted text preview: ed in (14), namely p(θ|y ) ∼ Beta (mH + α, m − mH + β ) . we run a chain with r = 0.1 until we have collected 25,000 accepted draws. We then discard the initial 200 samples (burn-in) and keep one out of every 100 samples from what remains (thinning). The next figure shows a normalized 32 histogram of the resulting draws, along with the analytical posterior. The running time to generate the MCMC draws was less than a second, and they are a reasonable approximation to the posterior. 7 MCMC with OpenBUGS There is a great deal of “art” to MCMC simulation, and a large body of research on the “right” way to do the simulations. OpenBUGS is a nice software package that has built-in years of research in MCMC and can draw posterior samples in a fairly automated way. It is great for doing Bayesian analysis without having to get your hands too dirty with MCMC details. Here we demonstrate OpenBUGS using two examples. OpenBUGS is old and is infrequently updated, but is still functional and powerful. The graphical interface version of OpenBugs is available only as a Windows executable...
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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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