RE: 95% CI of parameter estimate

From: "J.G. Wright" <J.G.Wright@newcastle.ac.uk> Subject: RE: 95% CI of parameter estimate Date: Wed, 15 Nov 2000 17:52:14 +0000 (GMT) Dear nmusers, A few comments:- In the message below I think "true" is intended to mean "estimated". CIs intervals calculated often employ a normal approximation for the distribution for the distribution of the estimate, this is a weaker assumption than assuming the error is normally distributed. CIs are almost always predicated upon the model being accurately specified (in its fitted form, including linearization)in every component. If one is in serious doubt between a family of models, it is possible to set up Bayesian models which make inference across models - but which are still predicated upon the models considered. CIs are also predicated on experimental design, whether one takes a Bayesian or frequentist approach. Hence, if the design doesn't allow you to estimate a variance component, neither will repeating the experiment in all likelihood (freequentists)t.Nor will the posterior density influence the prior. Of course, this assumes your experiment wasn't so fragile that your sample was totally unrepresentative. I would suggest that if you are going to simulate CIs, don't just use point estimates but allow for some variation - sounds like MCMC again...this thread is very similar to one concerning SEs which took place recently. GLS is more robust to variance function misspecification than joint normal theory maximum likelihood, incidentally. Good luck to the valiant quantifiers of uncertainty, James Wright