An Empirical Bayes Approach to Statistics

Abstract

Let X be a random variable which for simplicity we shall assume to have discrete values x and which has a probability distribution depending in a known way on an unknown real parameter A,

$$ p\left( {x|\lambda } \right) = Pr[X = x|\Lambda = \lambda ], $$

((1))

A itself being a random variable with a priori distribution function

$$ G\left( \lambda \right) = \operatorname{P} r[\Lambda {\text{ }}\underline \leqslant {\text{ }}\lambda ]. $$

((2))