A practical computational framework for the multidimensional moment-constrained maximum entropy principle

Authors:
Rafail Abramov
Affiliations:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., NY 10012, United States
Venue:
Journal of Computational Physics
Year:
2006

Citing 4
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The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling

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Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

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Abstract

The maximum entropy principle is a versatile tool for evaluating smooth approximations of probability density functions with a least bias beyond given constraints. In particular, the moment-based constraints are often a common prior information about a statistical state in various areas of science, including that of a forecast ensemble or a climate in atmospheric science. With that in mind, here we present a unified computational framework for an arbitrary number of phase space dimensions and moment constraints for both Shannon and relative entropies, together with a practical usable convex optimization algorithm based on the Newton method with an additional preconditioning and robust numerical integration routine. This optimization algorithm has already been used in three studies of predictability, and so far was found to be capable of producing reliable results in one- and two-dimensional phase spaces with moment constraints of up to order 4. The current work extensively references those earlier studies as practical examples of the applicability of the algorithm developed below.