Hi Dan, I've tried the log likelihood, but it reaches zero again, if I work with say 1000 samples. I need an approach that would scale to quite large sample sizes. Surely I can't be the first one to encounter this problem, and I'm sure I'm missing an option that is embarrassingly obvious.
Regards Seref On Mon, Oct 17, 2011 at 6:15 PM, Nordlund, Dan (DSHS/RDA) < nord...@dshs.wa.gov> wrote: > > -----Original Message----- > > From: r-help-boun...@r-project.org [mailto:r-help-bounces@r- > > project.org] On Behalf Of Seref Arikan > > Sent: Monday, October 17, 2011 9:11 AM > > To: r-help@r-project.org > > Subject: [R] Best practices for handling very small numbers? > > > > Greetings > > I have been experimenting with sampling from posterior distributions > > using > > R. Assume that I have the following observations from a normal > > distribution, > > with an unscaled joint likelihood function: > > > > normsamples = rnorm(1000,8,3) > > > > joint_likelihood = function(observations, mean, sigma){ > > return((sigma ^ (-1 * length(observations))) * exp(-0.5 * sum( > > ((observations - mean ) ^ 2)) / (sigma ^ 2) )); > > } > > > > the joint likelihood omits the constant (1/(2Pi)^n), which is what I > > want, > > because I've been experimenting with some crude sampling methods. The > > problem is, with the samples above, the joint likelihood becomes 0 very > > quickly. > > I wanted to experiment with tens of thousands of observations, but > > without > > an implementation of a transformation that can handle very small > > values, my > > sampling algorithms would not work. > > > > This is an attempt to use some sampling algorithms for Bayesian > > parameter > > estimation. I do not want to resort to conjugacy, since I am developing > > this > > to handle non conjugate scenarios, I just wanted to test it on a > > conjugate > > scenario, but I've quickly realized that I'm in trouble due to > > likelihood > > reaching 0 quickly. > > > > Your feedback would be appreciated. It makes me wonder how JAGS/BUGS > > handles > > this problem > > > > Best regards > > Seref > > > > Maybe you should work with the log-likelihood? > > > Hope this is helpful, > > Dan > > Daniel J. Nordlund > Washington State Department of Social and Health Services > Planning, Performance, and Accountability > Research and Data Analysis Division > Olympia, WA 98504-5204 > > ______________________________________________ > 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. > [[alternative HTML version deleted]] ______________________________________________ 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.
