Consider the k-factor model given in Section 11.2.4.

(a) Simulate a sample of 200 observations of 15-dimensional vectors with k = 3 factors assuming 2 j = 01 +002 j j = 1 12, h1 = 15, h2 = 05, h3 =025, and 2 =036.

(b) Implement the MCMC algorithm presented in Section 11.2.5 to ex plore the posterior distribution.

(c) Implement the Metropolis-Laplace estimator of the marginal data density presented in Section 11.2.6.

(d) Use the MCMC algorithm to t factor models with number of factors equal to 12 5 to the simulated data. Consider the following prior hyperparameters: n = 1, ns2= 1, nH = 1, nHs2 H = 1, n = 22, and n s2=01.

(e) Use the Metropolis-Laplace estimator of the marginal data density to select the number of factors.