Downloaded from https://www.everyspec.com AMCP 706-198 Choose "IA ib High": - true. If one is to use Bayesian statistics, he ! (amust ev'aiuate the consequences of his as- ,+ (3-35) sumptions very thoroughly, before running Choose "Im is Low": any tests. (Portions of this paragraph are re, , - (.)+ v printed from Kef, 28, with pennission.) where w39,1 PROBABILITY AND BAYES aMu n(~.s.)PROBABILITY iI (3-36) Probability is a mathematical concept usud aw y n (1n aL in connection with random events, I,e., those 0 events whose occurrence is uncertain enough that the uncertainty in of concern to us, One Where plt Is used as a reference, Eqs.
3.35 of the most popular uses of probability is in become games of chunce, we speak of the odds or percentages, For example, In a pair of honest Choose "I' Is High": ! dice the probability of throwing "snake eyes" - Is 2-7/9%. the probability of rolling 7's is ( )(a/V) - 16-2/3%, In these uses of probability, it can Choose '11 is Low": I be shown that the probability is associated S- 1with the "long run" percentages. Another popular use of probability Is as For use in an actual1 situation, the Z's would degree-of-belief, We speakc of the probability be converted to x's for ease In use, Eqs.
of %inning a cane at law or of getting a pro- 3-35 and 3-37 are helpful in visualizing what motion, If a person Is prudent, his degree-of- happens when the discrimination ratio is belief is the same as the "long run" percent- changed. age, when that percentage is known, But "long run" percentages usually are associated 3-9 BAYESIAN STATISTICS with conceptual models such as unbiased coins and honest dice. It is degree-of-belief A good approach to Bayesian statistics is as to whether the coin is in fact reasonably given in Ref, 25; an Idea of Its breadth of unbiased, or the dice are actually honest. application Is found in Ref. 16:
and an easy- to-read discussion of its controversial nature The term Bayes probability has become is propounded in Ref. 27. The mathematics associated with degree-of-belief and it will be of Bayesian statistics is not controversial at used in that mense in this parnaraph. (Not ali.
It Is the interpretation of those equations everyone uses it that way-the language is in concerning knowledge as "prior", and what a state of flux.) The Bayes formula provides constitutes reasonable "prior" knowledge a means of converting the degree-of'belief we which is the source and mainstay of the had "before a test was run" to the degree-of- controversy, belief we have afterwards; degree-of-belief is not a static thing, we change it whenever we Engineers, as well as most other people, get more evidence.
Bayes formula provides tend to confuse what they hope and want the mathematics by which a rational person to be true, with what they really expect is has his degree-of-belief changed by evidence. C '" , ... ~~~~ ~ ~ ~ ~ ........ .... ....