3) Recall the Hardy-Weinberg problem described in your text (page 273-274). The multinomial distribution for random...
3) Recall the Hardy-Weinberg problem described in your text (page 273-274). The multinomial distribution for random variables Yı, Y2, Y3 (can extend to more than 3) is given by n! P(Yı y1, Y2 = y2, Y3 = ya) Ул!ур!у! Рі Р2 р. where y + y3 = n and the parameters pi,P2, P3 are subject to the constraint p1 +p2 +p3 = 1. This distribution is an extension of the binomial distribution. In fact, the distribution of each Y, i= 1,2,3 is binomial. So, for example, E[Y1] = npi and Var(Yi) = np1(1-pi). If gene frequencies are in equilibrium, the genotypes AA, Aa, and aa occur in a population with proportions (1 -0) 20(1- 0), and p3 = 0 p2 according to Hardy-Weinberg law a) Using the multinomial as the likelihood and a prior distribution of 0 ~ Beta(10, 10), find the Bayes estimator of 0. That is find E[0\y]. b) Is the Bayes estimator unbiased?
3) Recall the Hardy-Weinberg problem described in your text (page 273-274). The multinomial distribution for random variables Yı, Y2, Y3 (can extend to more than 3) is given by n! P(Yı y1, Y2 = y2, Y3 = ya) Ул!ур!у! Рі Р2 р. where y + y3 = n and the parameters pi,P2, P3 are subject to the constraint p1 +p2 +p3 = 1. This distribution is an extension of the binomial distribution. In fact, the distribution of each Y, i= 1,2,3 is binomial. So, for example, E[Y1] = npi and Var(Yi) = np1(1-pi). If gene frequencies are in equilibrium, the genotypes AA, Aa, and aa occur in a population with proportions (1 -0) 20(1- 0), and p3 = 0 p2 according to Hardy-Weinberg law a) Using the multinomial as the likelihood and a prior distribution of 0 ~ Beta(10, 10), find the Bayes estimator of 0. That is find E[0\y]. b) Is the Bayes estimator unbiased?