Gibbs/Metropolis-Hastings Sampler Algorithm |

1) Initialize, and. 2) Based on Metropolis-Hastings, create using (28) with the proposal distribution, where is from variances-covariance matrix. 3) Based on Metropolis-Hastings, create using (29) with the proposal distribution, where is from variances-covariance matrix. 4) Based on Metropolis-Hastings, create using (30) with the proposal distribution, where is from variances-covariance matrix. 5) Calculate and. 6) Put . 7) Repeat steps (2 - 5) N times. 8) We get the point estimation by Bayes MCMC of (and) as (31) where M is the number of iterations (burn-in period) before the stationary distribution is accomplished and posterior variance of becomes (32) 9) The quintiles of the pattern are picked as the endpoints of the interval to calculate the reliable intervals of. Sort as . Hence, the symmetric credible interval with is (33) |