Construct a Gibbs sampler.

1.The last bivariate normal algorithm presented (the Gibbs sampler) is the multivariate analog to the univariate Gibbs sampler for sampling the mean and variance parameters from a univariate normal distribution. In Chapter 4, I also presented a Gibbs sampler using the marginal distribution (not the conditional distribution) for σ2. In that algorithm, we generated a sequence of draws for σ2, and then we simulated values for μ conditional on these samples for σ2. A similar process can be performed in the multivariate case; the only changes include (1) that the scale matrix S is constructed once, using the sample means rather than the parameters μx and μy, and (2) the degrees of freedom for the inverse Wishart distribution are one fewer. Construct this Gibbs sampler and compare results with those obtained using the algorithm presented in the chapter.

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