Statistical Modelling 1 (2001), 333–349
A survey of Monte Carlo
algorithms for maximizing the likelihood of a two-stage hierarchical
model
James G. Booth and James P. Hobert
Department of Statistics
University of Florida
email: jbooth@stat.ufl.edu
Wolfgang Jank
Decision & Information Technologies
Robert H. Smith School of Business
University of Maryland
Abstract:
Likelihood
inference with hierarchical models is often complicated by the fact that the
likelihood function involves intractable integrals. Numerical integration (e.g.
quadrature) is an option if the dimension of the integral is low but quickly
becomes unreliable as the dimension grows. An alternative approach is to
approximate the intractable integrals using Monte Carlo averages. Several
different algorithms based on this idea have been proposed. In this paper we
discuss the relative merits of simulated maximum likelihood, Monte Carlo EM,
Monte Carlo Newton-Raphson and stochastic approximation.
Keywords:
Efficiency, Monte Carlo EM, Monte Carlo Newton-Raphson, Rate of convergence,
Simulated maximum likelihood, Stochastic approximation.
back