A genetic study has divided n = 197 animals into four categories: y = (125, 18, 20, 34). A genetic model for the population cell probabilities is given by and thus, the sampling model is a multinomial distribution: n! y1 )" ( + 4 ) " ( ) y4 p(y |0) = y1! . yz! . y3! . ya! where n = y1 + y2 + 93 + y4. Assume the prior distribution for 0 to be % (0, 1). To find the posterior distribution of 0, a Gibbs sampling algorithm can be implemented by splitting the first category into two (yo, y1 - yo) with probabilities (, "). Here yo can be viewed as another parameter (or a latent variable). Thus, n! yo y1 -yo y2 y3 y4 D p(0, yoly) x yo!(y1 - yo)! . y2! . y3! . ya