A Note on Convergence of the Equi-Energy Sampler |
| |
Authors: | Christophe Andrieu Arnaud Doucet Pierre Del Moral |
| |
Affiliation: | 1. Department of Mathematics , University of Bristol , Bristol, England;2. Department of Statistics , University of British Columbia , Vancouver, Canada;3. Institut de Mathematiques de Bordeaux, Universite de Bordeaux I , Talence, France |
| |
Abstract: | This paper studies maximum likelihood estimation for a parameterised elliptic diffusion in a manifold. The focus is on asymptotic properties of maximum likelihood estimates obtained from continuous time observation. These are well known when the underlying manifold is a Euclidean space. However, no systematic study exists in the case of a general manifold. The starting point is to write down the likelihood function and equation. This is achieved using the tools of stochastic differential geometry. Consistency, asymptotic normality and asymptotic optimality of maximum likelihood estimates are then proved, under regularity assumptions. Numerical computation of maximum likelihood estimates is briefly discussed. |
| |
Keywords: | Equi-energy sampler Non linear Markov chain Monte Carlo Poisson equation Uniform ergodicity |
|
|