Subhash Lele writes:
I was wondering if you might know some good references to Bayesian treatment of parameter estimation for U(0,b) type distributions. I am looking for cases where the parameter is on the boundary. I would appreciate any help and advice you could provide. I am, in particular, looking for an MCMC (preferably in WinBUGS) based approach. I figured out the WinBUGS part but I am still curious about the theoretical papers, asymptotics etc.
I actually can’t think of any examples! But maybe you, the readers, can.
We also should think of the best way to implement this model in Stan. We like to transform to avoid hard boundary constraints, but it seems a bit tacky to do a data-based transformation (which itself would not work if there are latent variables).
P.S. I actually saw Lele speak at a statistics conference around 20 years ago. There was a lively exchange between Lele and an older guy who was working on similar problems using a different method. The other guy couldn’t stand what Lele was doing and was upset that at the conference organizers for not disavowing Lele’s talk. I don’t remember all the details but there was some real fury. In retrospect it all seems pretty silly but I imagine it was upsetting to Lele at the time. I speak by analogy to my own very disturbing experience having my research loudly denounced by people who worked on similar problems and seemed to think I was a complete idiot. (I’m not speaking, by the way, of the people who didn’t want to tenure me at Berkeley. Oddly enough, one of them told me they all agreed I was “brilliant.” Which was odd in its own way.)