Langevin type limiting processes for adaptive MCMC

G. K. Basak and Arunangshu Biswas ()
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G. K. Basak: Indian Statistical Institute
Arunangshu Biswas: Presidency University

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 2, 301-328

Abstract: Abstract Adaptive Markov Chain Monte Carlo (AMCMC) is a class of MCMC algorithms where the proposal distribution changes at every iteration of the chain. In this case it is important to verify that such a Markov Chain indeed has a stationary distribution. In this paper we discuss a diffusion approximation to a discrete time AMCMC. This diffusion approximation is different when compared to the diffusion approximation as in Gelman et al. [5] where the state space increases in dimension to ∞. In our approach the time parameter is sped up in such a way that the limiting process (as the mesh size goes to 0) approaches to a non-trivial diffusion process.

Keywords: MCMC; adaptive MCMC; diffusion approximation; tuning parameter; SDE (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0189-0

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