An adaptive approach to Langevin MCMC

摘要

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