Downloaded from https://www.everyspec.com AMCP 70e-1" (I) Each possible condition of the un- (6) If the degree-of-belief is not sharp known (in the eonceptual model) must be enough (high for only a few close-together specifled. Seriously consider using discrete conditions, and low for the rest) consider values to represent conditions, because we running more tests, are used to thinking that way. Continuous values. e.g., between 0 and 1, can be used, When a single point estimate is desired but 0ien step 2 is oftet very deceptive be.
(intead of the distribution), we can choose cause we are not used io thinking in terms .hc most probable value, the average value, of the probability density functions that are the median value, or some other that we' then needed. it's like trying to guess which prefer. If these reasonable choices are close shell the pea is under. together, it makes little difference which we choose. If they are far apart, we're in trouble (2) Assign a prior degree-of-belief to each anyway-we need more tests. of the conditions, Leaving out a condition is equivalent to assigning zero degree-of-belief Step 2 is deceptively simple looking. In to it.
Once zer degree-of-belief has been practice it is easy enough to assign a seem- assigned to a condition, or calculated for it ingly reasonable degree-of-belief to each after a test, the degree-of-belief for that con- condition. But we may well not like the dition remains zero forever after, So we must "after test" degree-of-belief we're supposed include (at least approximately) all physically to have. A story illustrates the point. A possible conditions. As we shall see in the man kept asserting to his friends that he example in par. 3-9,5, we must not assign was dead. The friends finally persuaded him too low a degree-of-belief to the unlikely to see a medical doctor.
The doctor hit upon regions. A good way of handling the assign- the idea of a test- said he, "Dead men don't ment is to pretend that we are willing to bet bleed do they?" The man readily agreed money on the outcomes at the odds we have with the assumption that dead men do not implicitly specified and that the other person bleed and that the test would be reasonable. can choose whichever side of the bet he Thereupon the doctor stuck the man's wishes thumb which bled profusely.
The man lookud at the test results and exclaimed, Exercise your model with hypothetical test "By golly, dead men do bleed!" results; see if your afterwards degrees-of-belief correspond to the calculated ones, If not, Step 2 is the place where most Bayesian go back and chaiuge your prior degrees-of- disasters occur. The utter simplicity of the belief. formulwiv belies the skill and hard work needed to apply prior probabilities properly. (3) Run a test which is lntendod to shed What you think you believe, and what you some light on the unknown. Preferably, the actually believe, after serious analysis, are :.kelihood of the test results should be quite often ve, ,, very different.
The literature different for each cotidition, abounds with examples of engineers who tried Bayesian analysis without the skill and (4) For each condition, calculate the like- hard work. lihood of the test results. If the test was chosen well, the likelihood will be quite 3-9.5 COMPLEX ILI.USTRATION different for each condition, Any assignment of prior degree-of-belief (5) Use Bayes formula to calculate the should be thoroughly checked by simtlating "after test" degree-of-belief. test results before submitting to any real .. .. . .. ... .... V% .................... Ii