Maximum Entropy Sequential Sampling
Prof. Dr. Peter Riegler
Fachhochschule Braunschweig/Wolfenbuettel, Germany

Abstract:

The most common procedure for measuring physical parameters is to sample the underlying physical signal equidistantly with respect to the control parameter. However, it is often not clear how the accuracy of the parameters to be measured depends on the range over which the control parameter is varied. This is typical for signals of the form exp(-t/T), which decay exponentially in the control parameter t.

For instance, if one happens to choose the maximum value of the control parameter to be much larger than the unknown decay constant T many samples would obviously be "pure noise", thus reducing the accuracy of the estimate of T.

Such difficulties in parameter estimation can be avoided by posing the question: Given the information of N data points, at which value of the control parameters should the next measurement be done? Answered in a Bayesian setting this question will lead to a criterion for the design of such experiments based on a minimax principle: The maximum gain in the information about the parameters is obtained by looking at the point where the predictive certainty is the least. In other words, the entropy of the posterior distribution of parameter values is minimized by taking measurements for those values of the control parameters where the entropy of the predictive distribution is maximum.

Based on this minimax result, an on-line algorithm will be proposed which samples optimally in the sense of maximum information gain per measurement. The algorithm will be applied to a problem of multiexponential analysis.

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