Dominique Lord writes,
My area of research is in highway safety and most of my work has been on the development of statistical models for modeling motor vehicle collisions (I have a good knowledge of statistics, but I am not a statistician). Unfortunately, the types of databases we use are often plagued by the two characteristics above. Consequently, statistical models (Poisson and Poisson-gamma in particular) estimated using the MLE or full-Bayes methods are likely to be biased.
His paper is here. (And here‘s his earlier paper.)
I don’t have much to say here except that, since model fit is a concern, I’d like to see some posterior predictive checks–that is, simulations of fake datasets from the fitted model–which can then be compared, visually and otherwise, to the actual data being fit. That is probably the most helpful suggestion I can give. Also, at the technical level, I would avoid those gamma(.01,.01) hyperprior distributions–these are nothing but trouble.
Why is a Gamma(.01,.01) prior bad in a Poisson-gamma model?
Bob
Bob,
I haven't thought about it in detail. From that other paper, I grew to dislike Gamma(epsilon,epsilon) prior distributions–they're not as "noninformative" as they look. In this case, Dom is using a Gamma(.01,.01) prior distribution for the variance parameter in a normal distribution for group-level parameters, which I think pretty much falls under the bailiwick of my paper on variance parameters.
"Unfortunately, the types of databases we use are often plagued by the two characteristics above."
What are the two characteristics referred to?
Never mind. The paper reveals that the two characteristics referred to are low sample mean values and small sample sizes.
OK, fair enough for precisions of normals.
Incidentally, have you looked at putting gamma/exponential priors on variances?
Bob
Hello,
I would like to thank Andrew for putting the paper on his blog and for providing comments. Since we are not statisticians, we would greatly appreciate any feedback that would help us improve the content of the paper. We sent the paper to Andrew for this purpose last week. I noticed a few typos after sending it to him. You can find the latest version here: http://ceprofs.tamu.edu/dlord/Papers/Lord_&_Miran…
Best regards,
Dom
[email protected]