MaxEnt Queries and Sequential Sampling

In this paper we pose the question: After gathering N data points, at what value of the control parameter should the next measurement be done? We propose an on-line algorithm which samples optimally by maximizing the gain in information on the parameters to be measured. We show analytically that the information gain is maximum for those potential measurements whose outcome is most unpredictable, i.e. for which the predictive distribution has maximum entropy. The resulting algorithm is applied to exponential analysis.