Abstract:

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.