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Dear All: Problem: I am currently using the method of Lewis-Raftery to estimate marginal likelihoods based on a single posterior draw (posterior mode): http://www.stat.washington.edu/raftery/Research/PDF/lewis1997.pdf I see some variation in my estimates, and would like to find ways to estimate marginal likelihoods using _all_ draws from the posterior to decrease variation. Solution: This is a work in progress. I am not sure but I hope this might be an appropriate time to update with regards to my progress. I have been recommended some excellent articles by Chib, specifically: http://www.cs.ubc.ca/~arnaud/stat535/chib_markov.pdf http://www.isds.duke.edu/~scs/Courses/Stat376/Papers/NormConstants/ChibMHJASA2001.pdf I have been warned however the second method might require some tuning. Additionally, I have found an excellent review of some methods here: http://epub.wu-wien.ac.at/dyn/virlib/wp/eng/showentry?ID=epub-wu-01_597 I have used some of the methods in section "2.1 Direct Methods" and am having good luck with the Harmonic Mean Estimator described as, for my problem, the likelihood seems invertible. I am computing log's in the case of Direct Estimation both with parameters from priors and from the posterior (the latter for the Harmonic Mean Estimator), and have written short documents summarizing the use of a "normalizing" factor in these approaches to avoid having to take the logarithms of very small numbers: http://people.hnl.bcm.edu/misha/bayes/modelselection/averageOfLikelihoods.tex http://people.hnl.bcm.edu/misha/bayes/modelselection/averageOfLikelihoods.pdf http://people.hnl.bcm.edu/misha/bayes/modelselection/averageOfLikelihoodsHME.tex http://people.hnl.bcm.edu/misha/bayes/modelselection/averageOfLikelihoodsHME.pdf Thank you so much for all your help. I will update on further progress. Misha -- Misha Koshelev MD/PhD Student Human Neuroimaging Laboratory One Baylor Plaza S104 Baylor College of Medicine Houston, TX 77030 ------------------------------------------------------------------- This list is for discussion of modelling issues and the BUGS software. For help with crashes and error messages, first mail [log in to unmask] To mail the BUGS list, mail to [log in to unmask] Before mailing, please check the archive at www.jiscmail.ac.uk/lists/bugs.html Please do not mail attachments to the list. To leave the BUGS list, send LEAVE BUGS to [log in to unmask] If this fails, mail [log in to unmask], NOT the whole list