Thanks for the reply! On Tue, Dec 2, 2008 at 6:34 PM, Prof Brian Ripley <[EMAIL PROTECTED]> wrote: > I wonder if you are using this term in its correct technical sense. > A linear functional relationship is > > V = a + bU > X = U + e > Y = V + f > > e and f are random errors (often but not necessarily independent) with > distributions possibly depending on U and V respectively.
This is indeed what I mean, poor phrasing of me. What I have is the effectively the PDF for e & f for each instance, and I wish to get a & b. For Gaussian errors there are certainly various ways to approach it and the maximum-likelihood estimator is fine and is what I normally use when my errors are sort-of-normal. However in this instance my uncertainty estimates are strongly non-Gaussian and even defining the mode of the distribution becomes rather iffy so I really prefer to sample the likelihoods properly. Using the maximum-likelihood estimator naively in this case is not terribly useful and I have no idea what the derived confidence limits "means". Ah well, I guess what I have to do at the moment is to use brute force and try to calculate P(a,b|X,Y) properly using a marginalisation over U (I hadn't done that before, I expect that was part of my problem). Hopefully that will give reasonable uncertainty estimates, lots of pain for a figure nobody will look at for much time :) Thanks, Jarle. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.