Gaussian Shift and Poisson Experiments

Abstract

This chapter is an introduction to some experiments that occur in their own right but are also very often encountered as limits of other experiments. The gaussian ones have been used and overused because of their mathematical tractability, not just because of the Central Limit Theorem. The Poisson experiments cannot be avoided when one models natural phenomena. We start with the common gaussian experiments. By “gaussian” we shall understand throughout they are the “gaussian shift” experiments, also called homoschedastic. There is a historical reason for that appellation: In 1809 Gauss introduced them (in the one-dimensional case) as those experiments where the maximum likelihood estimate coincides with the mean of the observations. This fact, however, will not concern us.