Monte Carlo maximization of likelihood A convergence study
نویسنده
چکیده
We propose a rigorous study of an ierative maximization algo rithm introduced by Geyer and Thompson for maximum likelihood estimation of Markov random elds One step of the algorithm consists in a Monte Carlo approximation of the likelihood followed by a local maximization in the neigh borhood of the current parameter We study convergence properties of the induced process and bound the computational complexity of the procedure The main tool involved in the stochastic analysis are deviation inequalities and concentration of measure bounds applied to empirical processes
منابع مشابه
Ascent-based Monte Carlo expectation– maximization
The expectation–maximization (EM) algorithm is a popular tool for maximizing likelihood functions in the presence of missing data. Unfortunately, EM often requires the evaluation of analytically intractable and high dimensional integrals. The Monte Carlo EM (MCEM) algorithm is the natural extension of EM that employs Monte Carlo methods to estimate the relevant integrals.Typically, a very large...
متن کاملStochastic Proximal Gradient Algorithms for Penalized Mixed Models
Motivated by penalized likelihood maximization in complex models, we study optimization problems where neither the function to optimize nor its gradient have an explicit expression, but its gradient can be approximated by a Monte Carlo technique. We propose a new algorithm based on a stochastic approximation of the Proximal-Gradient (PG) algorithm. This new algorithm, named Stochastic Approxima...
متن کاملEM algorithm coupled with particle filter for maximum likelihood parameter estimation of stochastic differential mixed-effects models
Biological processes measured repeatedly among a series of individuals are standardly analyzed by mixed models. These biological processes can be adequately modeled by parametric Stochastic Differential Equations (SDEs). We focus on the parametric maximum likelihood estimation of this mixed-effects model defined by SDE. As the likelihood is not explicit, we propose a stochastic version of the E...
متن کاملAscent-Based Monte Carlo EM
The EM algorithm is a popular tool for maximizing likelihood functions in the presence of missing data. Unfortunately, EM often requires the evaluation of analytically intractable and high-dimensional integrals. The Monte Carlo EM (MCEM) algorithm is the natural extension of EM that employs Monte Carlo methods to estimate the relevant integrals. Typically, a very large Monte Carlo sample size i...
متن کاملModel Selection in Structural Equation Models With Continuous and Polytomous Data
Recently, analysis of structural equation models with polytomous and continuous variables has received a lot of attention. However, contributions to the selection of good models are limited. The main objective of this article is to investigate the maximum likelihood estimation of unknown parameters in a general LISREL-type model with mixed polytomous and continuous data and propose a model sele...
متن کامل