Mon Sept 29: we continue ¡­

Mon Sept 29: we continue with Ch 3.

First: A die is thrown 100 times, resulting in respectively 15, 15, 17, 16, 13, 24 throws equal to 1, 2, 3, 4, 5, 6. Let the probability vector (theta1, ..., theta6) have a Dirichlet prior distribution with parameters (2,2,2,2,2,2). Carry out Bayesian inference for the parameters rho = theta6/theta1 and gamma = (theta2 theta3 theta4 theta5)^(1/4). Give in particular 95% credibility intervals for these two parameters and for their intercorrelation.

Exercises: From Ch 22, nos. 8, 12, 13, 22, 17.

To sample from a Dirichlet, use the fact that if G1, ... ,G6 are independent Gammas with parameters a1, ..., a6, then (G1/G, ..., G6/G) is a Dirichlet (a1, ..., a6), where G = G1 + ... + G6.