Estimating probabilities from experimental frequencies

Details Estimating probabilities from experimental frequencies Estimating probabilities from experimental frequencies

2002-01-28

arxiv.org/abs/cond-mat/0201516v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 3 figures, to be published in Physical Review E

Scientific paper

10.1103/PhysRevE.65.046124

Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or frequency count 'f', of each of the possible outcomes. In this work, the probability that the true distribution be 'q', given that the frequency count 'f' was sampled, is studied. Such a probability may be written as a Gibbs distribution. A thermodynamic potential, which allows an easy evaluation of the mean Kullback-Leibler divergence between the true and measured distribution, is defined. For a large number of samples, the expectation value of any function of 'q' is expanded in powers of the inverse number of samples. As an example, the moments, the entropy and the mutual information are analyzed.

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