Methodology And Computing In Applied Probability

, Volume 4, Issue 4, pp 337–357

Langevin Diffusions and Metropolis-Hastings Algorithms

Authors

  • G. O. Roberts
    • Department of Mathematics and StatisticsLancaster University
  • O. Stramer
    • Department of Statistics and Actuarial ScienceUniversity of Iowa
Article

DOI: 10.1023/A:1023562417138

Cite this article as:
Roberts, G.O. & Stramer, O. Methodology and Computing in Applied Probability (2002) 4: 337. doi:10.1023/A:1023562417138

Abstract

We consider a class of Langevin diffusions with state-dependent volatility. The volatility of the diffusion is chosen so as to make the stationary distribution of the diffusion with respect to its natural clock, a heated version of the stationary density of interest. The motivation behind this construction is the desire to construct uniformly ergodic diffusions with required stationary densities. Discrete time algorithms constructed by Hastings accept reject mechanisms are constructed from discretisations of the algorithms, and the properties of these algorithms are investigated.

MCMCLangevin diffusions and algorithms
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© Kluwer Academic Publishers 2002