A maximum likelihood algorithm for the estimation and renormalization of exponential densities

  • Authors:

  • Panagiotis Stinis

  • Affiliations:

  • Department of Mathematics, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

We present an algorithm based on maximum likelihood for the estimation and renormalization (marginalization) of exponential densities. The moment-matching problem resulting from the maximization of the likelihood is solved as an optimization problem using the Levenberg-Marquardt algorithm. In the case of renormalization, the moments needed to set up the moment-matching problem are evaluated using Swendsen's renormalization method. We focus on the renormalization version of the algorithm, where we demonstrate its use by computing the critical temperature of the two-dimensional Ising model. Possible applications of the algorithm are discussed.