J.S. Rosenthal. Theoretical rates of convergence for markov chain monte carlo. In Proceedings of Interface '94, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....developed expressions for the parameters in the relation jjf n Gamma jj i M ae where f n is the probability distribution of the chain at iteration n, M 1 and ae is related to the transition kernel of the chain. jj Delta jj i denotes the L norm, where i was either 1 or infinity. Rosenthal [84] provides similar results for the total variation distance from f n to . The second approach is to monitor the output of the chain, and to use some function of the realisation to determine convergence. As noted by Green [39] these must be used with some caution, as it is difficult to infer ....

J.S. Rosenthal. Theoretical rates of convergence for markov chain monte carlo. In Proceedings of Interface '94, 1994.

....and see Geyer (1992, Section 2) for a central limit theorem for (13) For N 0 and N large enough we are allowed to consider i as a good approximation of i . There is progress on rates of convergence of MCMC s, refer to Frigessi, Martinelli, and Stander (1993) Mengersen and Tweedie (1995) and Rosenthal (1994) and reference therein on criteria for choosing N 0 and N properly. Good approximations of the posterior moments (12) are needed, otherwise the simulated annealing step can lead off from x . In our implementation of the MCMC we run a Metropolis algorithm, but a Gibbs Sampler could also be ....

Rosenthal, J. S. (1994, December). Theoretical rates of convergence for Markov chain monte carlo. Technical report, University of Toronto, Canada.

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