Comments on: Moment-Matching “Empirical” Bayes Beta Priors for Batting Averages

By: Bob Carpenter

Bob Carpenter — Thu, 31 Mar 2011 17:23:18 +0000

I’d really rather just put a prior on the beta parameters and then sample from the posterior. It fits in nicely with the rest of Bayesian inference that way. Jim Albert’s book on Monte Carlo methods in R gives you some idea of how to sample from the posterior given some kind of prior on the Beta parameters, or you could just use BUGS as I do in the follow-up to this post.

Won’t it be hard to sample the beta parameters densely enough to get a good estimate in the method you describe? I’m thinking that you probably don’t need to sample anyway, because you can analytically compute statistics like means and variances given that you have a beta-binomial form for the sampling distributions. So you could probably just optimize if you want a point estimate based on the kind of matching you suggest.

By: Sunny Mehta

Sunny Mehta — Thu, 31 Mar 2011 15:12:54 +0000

one way of finding a beta prior is to write a script to randomly select a bunch of beta curves and then simulate 10,000 “seasons” from each one where every batters’ hits (s) and outs (f) are simulated binomially according to his at-bats (n). then you measure the average spread (you can use sd, var, or probably most preferably median absolute deviation to temper the outliers) over the 10,000 seasons and see which beta curve resulted in the spread most similar to the empirical spread of batting averages.

jim albert taught me that.

By: lingpipe

lingpipe — Wed, 02 Dec 2009 07:39:15 +0000

I’m not sure how to estimate that other than with the methods I used in the followups. How can I calculate population variance with the set of hits and at-bats I have?

By: Rufus

Rufus — Tue, 01 Dec 2009 09:25:03 +0000

When you derived your empirical Bayes estimates, you used the sample variance. Wouldn’t it be more accurate to use the population variance (which you can estimate using the random variance in binomials)? Although finding the population variance in a population with a wide range of observations (ABs) isn’t so straightforward…