Bayes, prior to reading

August 16, 2011 in Data,Math

I may have to go pick up this book, which was reviewed in the NYT last week, if only because it opens with a favorite quote from Keynes. Titled The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy (Wow, titles are getting ridiculously long! Is the front cover the new inside flap?), it is a history and overview of Bayesian statistics through history and applications.

I have a very interesting relationship with Bayes: I have enormous respect for his work and the theories, but on the other hand I have extraordinary distrust of its practitioners. The mathematics of Bayes' theorem are unassailable, but its Achilles heel is the assumption of a prior distribution. Yes, you get the "right" answer with the right prior, but how do you choose that prior? I am confident that if I were a Bayesian statistician I would have a snappy and confident response, but I'm not. Instead, I'm merely a strongly applied statistician who has endured many interviews containing the following exchange:

J: So you use Bayesian statistics. Tell me how you choose your priors.

Interviewee: Well, first I look at the data...

And the interview generally ends shortly thereafter. I certainly don't claim to have a good method for deciding on a prior, well, prior to seeing the data -- but if you don't have that, what good is Bayesian statistics? It pretty much boils down to a frequentist method. It actually appears to me that the search for an objective prior has drawn considerably more intellectual horsepower to bear than Bayesian statistics themselves! When properly applied, these methods have incredible power -- look at Van Neumann utility, for example. But when improperly put to work, they can lead to disaster -- and that is not an acceptable outcome. All of statistics is fraught with pitfalls, but at the end of the day I'm much more comfortable debating which [frequentist] tool to apply than I am trying to pretend I haven't seen the data and arguing over whose prior makes more sense.

I'm not trying to start a flame war (and yes, I realize this isn't a post on politics, or something as critically important as iOS vs Andriod). I admire the elegance and abilities of Bayesian statistics. I'm just disappointed in the degree of care often put into its implementation, and find it difficult to justify one choice over another. Not that I particularly admire most frequentist statisticians for their attention to detail, either...

Anyway, I guess it would be appropriate to wonder about the probability that I'll like this book -- what's the prior of that?

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