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

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

2004-09-14

arxiv.org/abs/math/0409230v1

Mathematics

Statistics Theory

18 pages, 3 figures. Submitted to the Journal of Computational Physics

Scientific paper

10.1016/j.jcp.2005.03.001

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.

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