Moment-Constrained Maximum Entropy Method for Expanded Uncertainty Evaluation

Spectral moment matching in the maximum entropy spectral analysis method

The formula for the spectral moments is expanded in a series consisting of autocorrelation terms. By using the autocorrelation extrapolation inherent in the maximum entropy method (MEM) for spectral analysis, it is found that good estimates of the moments can be found from a very low order autoregressive model. The motivation for this investigation came from results obtained during spectral ana...

Maximum Entropy method with non-linear moment constraints: challenges

Traditionally, the Method of (Shannon-Kullback’s) Relative Entropy Maximization (REM) is considered with linear moment constraints. In this work, the method is studied under frequency moment constraints which are non-linear in probabilities. The constraints challenge some justifications of REM since a) axiomatic systems are developed for classical linear moment constraints, b) the feasible set ...

Continuous Relaxations for Constrained Maximum-Entropy Sampling

We consider a new nonlinear relaxation for the Constrained Maximum Entropy Sampling Problem { the problem of choosing the s s principal submatrix with maximal determinant from a given n n positive deenite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous imple...

Maximum Entropy and the Moment Problem

Introduction. The trigonometric moment problem stands at the source of several major streams in analysis. From it flow developments in function theory, in spectral representation of operators, in probability, in approximation, and in the study of inverse problems. Here we connect it also with a group of questions centering on entropy and prediction. In turn, this will suggest a simple approach,...

Maximum Entropy Method for Composition Vector Method