Covariance of Real Estimates

[ochotona]

I would like to sum multiple psi estimates (output from Program Presence) and get a variance for the sum. to this I believe I would use the delta method and the variances and covariances. I can get the variance of the individual psi estimates but not sure how to get the covariance for 630 individual estimates (the model includes covariates so each psi value is potentially unique). Program MArk will output covariances of real estimates for user specified, mean values etc, but not all 630 at once. So how are the covariances of the real parameter estimates calculated? I'm assuming there is covariance among the psi because the detection function is shared among all the psi estimates.

Alternatively, not a being a real statistician would it be easier for me to bootstrap the encounter histories with replacement, re=evaluate the psi's and calculate the variance that way?

Alternative 2, should I use WINBUGS and get to posterior distribution of the sum of the psi's from there?

Any thoughts, comments, RTFMs, appreciated.