Yes, Albyn. I do not think that this is a dangerous behavior of the tool (`integrate'). It is certainly a "dangerous use" of the tool. One will be hard-pressed to find a numerical algorithm/software that is fool-proof in the sense that it always gives you either the correct results or warns you that the results could be wrong for your problem. We can always devise a problem to defeat even the most robust algorithm. So, I would argue that the ultimate responsibility lies with the user, via careful thinking/prior analysis/ and multiple types of checks, to ensure that the results are reasonably accurate.
This, of course, does not mean that `integrate' gets away scot free. I am sure it could be improved, but I am also quite certain that there are better quadrature algorithms. So, one needs to choose appropriate algorithms to suit their problem needs. Perhaps, the simplest thing to do for `integrate' might be to print a generic warning like: "The error estimate is not always reliable". Of course, this does not help the user since they would not know when it is NOT reliable. The next thing to try might be to examine how it picks the initial interval [0, x], and see if this procedure can be improved. Best, Ravi. ------------------------------------------------------- Ravi Varadhan, Ph.D. Assistant Professor, Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins University Ph. (410) 502-2619 email: rvarad...@jhmi.edu -----Original Message----- From: Albyn Jones [mailto:jo...@reed.edu] Sent: Thursday, December 02, 2010 6:41 PM To: Ravi Varadhan Cc: 'Hans W Borchers'; r-help@r-project.org Subject: Re: [R] Integral of PDF On Thu, Dec 02, 2010 at 06:23:45PM -0500, Ravi Varadhan wrote: > A simple solution is to locate the mode of the integrand, which should be > quite easy to do, and then do a coordinate shift to that point and then > integrate the mean-shifted integrand using `integrate'. > > Ravi. Translation: think before you compute! albyn ______________________________________________ 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.
