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Statistica Sinica 20 (2010), 343-364





ADAPTIVELY SCALING THE METROPOLIS ALGORITHM

USING EXPECTED SQUARED JUMPED DISTANCE


Cristian Pasarica and Andrew Gelman


J. P. Morgan and Columbia University


Abstract: A good choice of the proposal distribution is crucial for the rapid convergence of the Metropolis algorithm. In this paper, given a family of parametric Markovian kernels, we develop an adaptive algorithm for selecting the best kernel that maximizes the expected squared jumped distance, an objective function that characterizes the Markov chain. We demonstrate the effectiveness of our method in several examples.



Key words and phrases: Acceptance rates, Bayesian computation, iterative simulation, Markov chain Monte Carlo, multiple importance sampling.

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