Fellow Bayesians:
My apologies to bother you, I am rather new to the Bayesian field myself.
I appreciate any replies to this email. Reply all especially much appreciated. Also, any directions
to other forums that may be helpful much appreciated.
I have had much luck using the Lewis-Raftery 1997 method of estimating Bayes factors using the posterior
mode.
https://bigfile.bcm.tmc.edu/outbound/mk144210/Lewis1997_EstimatingBayesFactorsviaPosteriorSimulation.pdf
However, I would like to utilize a complementary approach to verify/double check my results.
I have tried a Monte Carlo simulation as proposed in the paper:
1) Draw theta parameter vector from the priors
2) Compute the likelihood
3) Take the average over many many such draws theta
However, almost all the draws seem to compute to likelihoods of 0's within machine precision, which is
to be expected as our priors are quite diffuse as opposed to the posteriors and likelihoods.
Modeling averaging seems to be another approach, but seems to be slightly more comprehensive than simply
estimating marginal likelihoods.
In any case, if anyone has any suggestions for a method to estimate marginal likelihoods based on many
draws from the posterior (as opposed to say, just the mode), much appreciated.
Thank you
Sincerely yours
Misha Koshelev
p.s. The method we are using is based on the seminal work of Houser-Keane-McCabe:
https://bigfile.bcm.tmc.edu/outbound/mk144210/Houser_BayesType_2004.pdf
--
Misha Koshelev
MD/PhD Student
Human Neuroimaging Laboratory
One Baylor Plaza
S104
Baylor College of Medicine
Houston, TX 77030
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