When I saw Terry’s reference to “estimate a prior distribution from the data” I checked the paper to see what they were doing. I got the impression that they estimate the prior from a subset of the data which doesn’t enter in the calculation of the likelihood. I’m not 100% sure, but I sleep better thinking that’s what they do. Empirical Bayes, on the other hand, will send you straight to Bayesian hell.

]]>I had to convince myself with simulations that these exponential decay mixtures can be fit from data. They turn out to be surprisingly robust, given that the mixture isn’t evident from plotting the data. Coincidentally, Andrew was using a mixture of exponential decays as his “hello world” model for Stan at the time, so I conveniently had the basics of the model precompiled when I saw the talk.

]]>> estimate a prior distribution from the data

This is the standard in hierarchical modeling. It can be done with full Bayes, as we almost always do in Stan, or it can be done with so-called “empirical Bayes”, where you take a point estimate of the hierarchical parameters based on a marginalized model.

Priors are no more arbitrary than likelihoods—it’s all just part of the joint model. What we’re usually interested in is posterior predictive inference, which we typically evaluate with posterior predictive checks and cross-validation.

]]>The link to the R package breathteststan requires a username and password…. ]]>

That’s exactly how I feel when I see a p-value and the conclusion that goes with it: They’re making things up.

We are trained to not think of p-value based reasoning as making things up, but often that’s just what it is.

I suggest reading the book Uncertain Judgements to take the edge off of your impression that people are making things up when they define priors.

]]>But, I’m pretty naive when it comes to Bayesian analysis, so dazzling me is not all that impressive an achievement.

]]>So thank you for creating this truly amazing environment and community. Having people like Bob, Mitzi, Ben, Michael, (and now also Lauren, very soon) visiting my lab over the years has also been a very important and educational experience for us. We would never had had any contact with these amazing people but for Stan.

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