The Gibbs sampling algorithm is an iterative algorithm for sampling from a multivariate joint distribution via conditioning on each marginal distribution in sequence. This is useful if it is difficult to get at each marginal distribution directly via integration (or summation). To simulate a distribution we can construct a sequence of random variables (Markov chain) such that the stationary distribution . Consider the bivariate normal distribution X = (X1 , X2)with mean = 7.9 and variance/covariance matrix (. (5,4 ) (4,10 ) . To use Gibbs sampler, we need the conditional distributions. From univariate theory we know the conditional distributions of a bivariate are themselves normal. Implement the Gibbs sampler from page 354 to simulate this bivariate normal distribution, and visualize each estimated marginal distribution

TExt Book: A Course in Statistics with R