The classical Statistical model describes a two-step process. Step 1, which may or may not be a chance process, determines the value of a parameter θ, but this is not observable. Step 2 is a chance process Y with probability distribution determined by the value of θ. Classical Statistics seeks, at a time when Step 1 has been carried out, rules for using Y to make inferences or decisions about this value of θ. After Y = υ has been observed, Fisher defines an event E(υ, θ) as having Fiducial Probability α if the event E(Y, θ) had probability α before Step 2 was made. Section 2 discusses Bayes' Theorem and Bayes' Essay. If Step 1 is a chance process X, and for two events A = (X ε{lunate} A) and B = (Y ε{lunate} B), and at a time before Step 1 has been made, Bayes' Theorem is a formula for computing P(A\B) from probabilities that have been specified. This theorem is only slightly related to Propositions 3 and 5 of Bayes' Essay. Temporal application of Bayes' Theorem is the assertion, at a time when one or both steps have been made and an event E observed to have occurred, that the probability of F is now the number P(F\E). But in classical Statistics this probability is now a constant θ having a set of possible values with known probabilities, and P(P\E) is only one possible estimate of θ. Other estimates are competitors, and we must decide whether values of our estimator are to be confined to the possible values of θ: The number P(F\E) may not be among these. Examples are given in section 3. © 1990.
