MCMC Error message?

[gwhite]

Greg:
There is an implicit relationship among the 3 correlations. That is, if X1 and X2 are strongly positively correlated, and X1 and X3 are strongly positively correlated, then X2 and X3 can't be strongly negatively correlated. The MCMC algorithm doesn't know this relationship, so new proposals will sometimes be inadmissable. The proposal will then be rejected. The result is that the MCMC algorithm isn't as efficient as it could be if the relationship was enforced, but you should still get a valid sample from the posterior.
Gary

[GDistiller]

Hi Gary
OK thanks a lot for that - it makes sense. BTW I have now run the structured matrix through Mathematica as a correlation matrix. The interesting thing to emerge is that the matrix is positive definite as long as the values for the correlations are medium to low. Using 1000 combinations of values between -0.5 and 0.5 resulted in no instances where the matrix was not positive definite. Obviously as long as none of the relationships are too strong then there is no problem.

So I guess I should just let the estimation run for as long as it takes and ignore all the error messages. One of the primary objectives of the analysis is to estimate these correlations so I am a bit loath to limit the prior dbns on my rhos to improve efficiency...

Thanks again for all the input!!

Greg