CHECKERBOARD COPULAS OF MAXIMUM ENTROPY WITH PRESCRIBED MIXED MOMENTS

Copulas with maximum entropy

We shall find a multi-dimensional checkerboard copula of maximum entropy that matches an observed set of grade correlation coefficients. This problem is formulated as the maximization of a concave function on a convex polytope. Under mild constraint qualifications we show that a unique solution exists in the core of the feasible region. The theory of Fenchel duality is used to reformulate the p...

Maximum entropy in the problem of moments

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The Maximum Entropy Method Of Moments And Bayesian Probability Theory

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) ...

Maximum entropy and the problem of moments: a stable algorithm.

We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an optimal solution can be constructed iteratively. We demonstrate the performance and stability of our algorithm with several tests on numerically difficult functi...

An Alternative Model for Time-varying Moments using Maximum Entropy