ired the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named (Bayes 1763, pg. 376)". This problem and the solution it entails have come to be referred to as inverse statistics.Logue put it this was,Thus Bayes, in his famous [1763] essay, having defined probability as 'the ratio between the value at which the expectation depending upon the happening of the event ought to be computed, and the value of the thing expected upon its happening', then equivocates upon 'expect', sometimes taking it as wholly relative to an individual's mental state, sometimes as though expectations were externally fixed values. (1995, pg.95)The theorem was eventually accepted by mathematicians of the time. The mathematician LaPlace later accepted it as a valid process as Jaynes (1995) points out, "In almost his first published work (1774), Laplace rediscovered Bayes' principle in greater clarity and generality, and then for the next 40 years proceeded to apply it to problems of astronomy, geodesy, meteorology, populations statistics and even jurisprudence" (pg. 2). LaPlace generalized Bayes' approach, which was later generalized further into what we now call Bayes' theorem. Essentially, the theorem is supposed to quantify the value of a hunch, factor in the knowledge that exists in people beyond their conscious minds. You see, according to Bayes' theorem, one can always start with a belief with regard to the probability of an outcome and use that in the equation. If one has no prior knowledge, the prior distribution would be diffuse (spread out).CHAPTER III BAYES THEOREM EXPLAINEDBayes theorem for conditional probabilities is described by equation 1: where the marginal probability of A occurring given B has occurred is represented by P(A|B). Said another way, the theorem allows you, knowing little more than the probability of A given B to find the probability of B g...
