Following on to lvm's comment: The interval estimate from MCMC certainly contains the MLE estimate of sigma2, so the fact that the point estimates differ is really not relevant, given that entirely different algorithms are employed to derive the estimates. I used your code for PROC MODEL and obtained the code for PROC MCMC from the online section Getting Started: MCMC Procedure - Simple Linear Regression. My variance estimate from MCMC was 137.3, slightly different from yours, and not wholly unexpected given differences in platforms, etc. I did duplicate your PROC MODEL output. However, I could not easily get a confidence interval for sigma2 from PROC MODEL, which would have made my point clearer. The credible intervals from MCMC for the other parameters look quite similar to the confidence intervals obtained from PROC MODEL. Steve Denham
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