Bill Harris writes:
I’m not a professional statistician, but I do use statistics in my work, and I’m increasingly attracted to Bayesian approaches.
Several colleagues have asked me to describe the difference between Bayesian analysis and classical statistics. I think I’ve not yet succeeded well, and so I was about to start a blog entry to clear that up. Then I decided to look around.
Your “‘Bayesian inference’ represents statistical estimation as the conditional distribution of parameters and unobserved data, given observed data” from “Objections to Bayesian statistics” is certainly concise, but it may be a bit too concise for managers and analysts who have some understanding of statistics. Your “Why we (usually) don’t have to worry about multiple comparisons” sounds promising, but it’s a tad long to hand to someone with a simple question.
Any ideas? Fodder for a blog posting?
I started down the path of dividing statistical analysis into three parts: setting up the problem, calculations, and communicating the results.
It’s easy to find Web pages about the first, but many dwell on the notion of subjective priors.
The second involves comparing the selection of the proper classical method (Tom Loredo has some articles pointing out those challenges, as I recall) vs. “simply” applying probability theory while often letting a computer grind through the integration. There’s more power, as your “Why we (usually) …” article points out.
The third offers the choice of focus from how one should really interpret confidence intervals and what an hypothesis test is to probabilities of events. That makes sense, but I’m still looking for ways to tighten it all up.
Bill was also pointed to this article by Kevin Murphy, which looks interesting but has almost no resemblance to Bayesian statistics as I know it.
One problem with finding statistical resources on the web, I think, is that a webpage on a technical issue is likely to have been written by a computer scientist. And what computer scientists do with data and models is often much different from what we do.
My current favorite online summary of Bayesian statistics is the article by Spiegelhalter and Rice.