Avoiding Zero and Infinity in Sample Based Algorithms

This document derives estimators of frequency and probability for the elimination of numerical instability when processing small samples. The analysis uses the quantitative methodology motivated in previous documents [6, 7]. In particular we show that the expectation of the mean of a Poisson sample is n + 1/2, and for a Binomial sample is (n + 1/2)/(N + 1). We argue that this is a better estimator of the underlying generator than conventional Likelihood in these cases. Some of the consequences of these results are illustrated on the ‘reference class problem’ .