The Accepted Bayes Method of Estimation

Abstract

 We give a brief description of the structure of Bayes estimates with the help of formal mathematical constructions of the Bayes theory. The Bayes scheme of the decision theory includes the following four components.

• 1) The statistical model, represented by the probability space.

• 2) The probability space (Θ,ε ,H) for the parameter θ which is assumed to be random.

• 3) The set of such possible decisions D that each element d from D is a measurable function on Ω.

• 4) The set of such possible decisions D that each element d from D is a measurable function on Ω. The loss functions L(θ ,d) (or L(R(θ ),d)) determined on Θ×D.