tag:blogger.com,1999:blog-5173950.post1813859846945022024..comments2024-03-28T13:37:26.314-04:00Comments on Grim's Hall: Two on Bayesian ProbabilityGrimhttp://www.blogger.com/profile/07543082562999855432noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5173950.post-7202924529602115852018-07-16T07:16:39.234-04:002018-07-16T07:16:39.234-04:00The big break for Bayes is Decision Analysis. Giv...The big break for Bayes is Decision Analysis. Given any decision under uncertainty, there is some probability of the result being Good, Medium, or Bad -- or some other set of outcomes.<br /><br />The probabilities of achieving these results are dependent on the decision taken; and usually one of the possible decisions is to gather more info.<br /><br />The math behind using probabilities these ways is from Statistics, where they developed such math with random processes and the Law of Large Numbers. It is Bayes Theorem which allows the math to be used in unique, one-time decision events.<br /><br />Bayesians look at probability as a measure of information about an events; Statisticians look at frequencies and derive probabilities from the data.<br /><br />Consider flipping a coin in the air and stepping on it. What is the probability that it is heads? The statistical answer: if there were enough flips, it would have a 50% chance.<br />But we know that in this case it is either 1 (heads) or 0 (tails).<br />The Bayesian says: our prior probability estimate is 50%, so for this first flip it's 50%.<br /><br />Tom Greyhttps://www.blogger.com/profile/15046612425809449502noreply@blogger.com