
 UCLA Soc. 210A, Topic 5, Conditional Probability 
  The reason for choosing beta distributions is that they are "conjugate" to the process of estimating a population proportion, which means that a beta prior yields a beta posterior as well, only shifting the parameter values (Leamer pp 4051; Winkler and Hays pp 498506). 
  Notice that the numbers in the prior probability column are all nonnegative, and sum to 1.0, as required of a probability distribution. 
  To complete the calculation of posterior probabilities, each of the likelihoods is multiplied by the corresponding prior, in the 4th column, and finally each of those products is divided by their sum, yielding the posterior probabilities in the 5th column. 
 www.sscnet.ucla.edu /soc/faculty/mcfarland/soc210a/prob2.htm (2605 words) 
