RE: 95% CI of parameter estimate

From: michael_smith@sandwich.pfizer.com Subject: RE: 95% CI of parameter estimate Date: Wed, 15 Nov 2000 09:46:17 -0000 Dear Mats, Can I check my/your/our understanding of "Confidence Intervals"? If one could hypothetically re-run the experiment a number of times, repeat sampling using the same design, analyse the data with the same model then construct intervals using the same method then 95% of the intervals would contain the *true* value of the parameter of interest. A rather tortuous explanation, but thats what frequentists would have you believe. The bottom line is that you cannot make any probabilistic statement about whether any given interval does or does not contain the true value of the parameter. It seems to me that what the recently discussed methods describe (apart from perhaps method 3, and I'm thinking about that one...) is a way of constructing "credible intervals". Sampling from the "posterior" distribution of your point estimate and its variability gives you an interval which describes your uncertainty around the point estimate, but when you simulate what distribution are you using for your estimate? Normal? Surely that then leads you back to a normal approximation to the interval which you could have calculated directly from the NONMEM output? Hence the reason why all of these methods appear to have similar conclusions?? I may be missing something fundamental... If I am, please excuse me. By the way, the bayesian approach allows you to express uncertainty (in the form of an interval if you like) for all variances and covariances. It also allows one to attach probabilistic statements to intervals. Which is nice. Best wishes, Mike Michael K. Smith (Senior Statistician) BSc MSc CStat E-mail: Michael_Smith@Sandwich.Pfizer.Com Tel.: (+44) 1304 643561