6.1 Suppose that the posterior distribution of (3 is N(0, I ) with density h(0ly) o( exp(-0.5Bz).

(a) Use a standard normal generator to obtain M = 5000 draws from the posterior density. Use these draws to estimate the posterior mean and posterior standard deviation of 8.

@) Set up a Metropolis-Hastings sampler to obtain M = 5000 values from the target density using the random-walk proposal generator ely, @I-’) - N(OO-”. T V ) with Y = 1. Adjust the value of 7 in trial runs to ensure that approximately 35-50 percent of the proposed values are accepted.

(c) Use the posterior sample in

(b) to find the posterior mean and posterior standard deviation of 8. How do your estimates compare with those in (a)?

Are 5000 MCMC draws enough to estimate accurately these moments‘?