35 research outputs found
Resampling from the past to improve on MCMC algorithms
We introduce the idea that resampling from past observations in a Markov Chain Monte Carlo sampler can fasten convergence. We prove that proper resampling from the past does not disturb the limit distribution of the algorithm. We illustrate the method with two examples. The first on a Bayesian analysis of stochastic volatility models and the other on Bayesian phylogeny reconstruction.Monte Carlo methods, Resampling, Stochastic volatility models, Bayesian phylogeny reconstruction.
An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift
This paper proposes an adaptive version for the Metropolis adjusted Langevin algorithm with a truncated drift (T-MALA). The scale parameter and the covariance matrix of the proposal kernel of the algorithm are simultaneously and recursively updated in order to reach the optimal acceptance rate of 0:574 (see Roberts and Rosenthal (2001)) and to estimate and use the correlation structure of the target distribution. We develop some convergence results for the algorithm. A simulation example is presented.Markov Chain Monte Carlo, Stochastic approximation algorithms, Metropolis Adjusted Langevin algorithm, geometric rate of convergence.
Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part II
We prove a central limit theorem for a general class of adaptive Markov Chain
Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We
discuss in detail the special case of stochastic approximation. We use the
result to analyze the asymptotic behavior of an adaptive version of the
Metropolis Adjusted Langevin algorithm with a heavy tailed target density.Comment: 34 page
Estimation of Network structures from partially observed Markov random fields
We consider the estimation of high-dimensional network structures from
partially observed Markov random field data using a penalized pseudo-likelihood
approach. We fit a misspecified model obtained by ignoring the missing data
problem. We study the consistency of the estimator and derive a bound on its
rate of convergence. The results obtained relate the rate of convergence of the
estimator to the extent of the missing data problem. We report some simulation
results that empirically validate some of the theoretical findings.Comment: 24 pages 1 figur
Bayesian computation for statistical models with intractable normalizing constants
This paper deals with some computational aspects in the Bayesian analysis of
statistical models with intractable normalizing constants. In the presence of
intractable normalizing constants in the likelihood function, traditional MCMC
methods cannot be applied. We propose an approach to sample from such posterior
distributions. The method can be thought as a Bayesian version of the MCMC-MLE
approach of Geyer and Thompson (1992). To the best of our knowledge, this is
the first general and asymptotically consistent Monte Carlo method for such
problems. We illustrate the method with examples from image segmentation and
social network modeling. We study as well the asymptotic behavior of the
algorithm and obtain a strong law of large numbers for empirical averages.Comment: 20 pages, 4 figures, submitted for publicatio