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Keywords:

  • deterministic annealing;
  • factor analysis;
  • global optimization;
  • maximum likelihood;
  • mixture model;
  • multidimensional scaling;
  • multivariate t distribution;
  • random effects model

Abstract.  Maximum likelihood estimation in many classical statistical problems is beset by multimodality. This article explores several variations of deterministic annealing that tend to avoid inferior modes and find the dominant mode. In Bayesian settings, annealing can be tailored to find the dominant mode of the log posterior. Our annealing algorithms involve essentially trivial changes to existing optimization algorithms built on block relaxation or the EM or MM principle. Our examples include estimation with the multivariate t distribution, Gaussian mixture models, latent class analysis, factor analysis, multidimensional scaling and a one-way random effects model. In the numerical examples explored, the proposed annealing strategies significantly improve the chances for locating the global maximum.