An adaptive approach to Langevin MCMC

  • Authors:
  • Tristan Marshall;Gareth Roberts

  • Affiliations:
  • Department of Statistics, University of Warwick, Coventry, UK CV4 7AL and Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster, UK LA1 4YF;Department of Statistics, University of Warwick, Coventry, UK CV4 7AL

  • Venue:
  • Statistics and Computing
  • Year:
  • 2012

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Abstract

We consider a class of adaptive MCMC algorithms using a Langevin-type proposal density. We state and prove regularity conditions for the convergence of these algorithms. In addition to these theoretical results we introduce a number of methodological innovations that can be applied much more generally. We assess the performance of these algorithms with simulation studies, including an example of the statistical analysis of a point process driven by a latent log-Gaussian Cox process.