Objective and Subjective Bayes

Turns out I’m less of an objective Bayesian than I thought I was. I’m objective, and I’m Bayesian, but not really an Objective Bayesian. Last week I was at the OBayes 5 (O for objective) meeting in Branson, MO. It turns out that most of the Objective Bayes research is much more theoretical than I am. I like working with data, and I just can’t deal with prior distributions that are three pages long, even if they do have certain properties of objectiveness.

I’m not really a subjective Bayesian either. Sometimes I am–if I have prior information I’m usually happy to use it–but there are some situations (clincial trials, for example) where it really is inappropriate or even unethical/illegal to use prior information. As far as vague prior distributions go, I’m a little bit sympathetic to the following argument: “You can’t really believe that you know the model that generated the data but at the same time have no idea about the values of any of the model parameters.” Sounds like a valid point. The problem is that I don’t really agree with either part of that last statement. Sure, I usually have at least some vague notion of plausible parameter values. BUT I also don’t really believe that whatever model I’m using is the exact model that generated the data. Using a vague prior distribution then seems kind of like hedging your bets.

And that’s one of the cool things about Bayesian statistics. If you have prior information you can use it, but if you don’t have it you can still often perform an objective analysis using Bayesian methods. I think an important potential research topic is how to create objective (vague, diffuse, whatever) prior distributions that are more easily implementable in complex problems. Click here for a summary of my own stab at this problem.

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2 thoughts on “Objective and Subjective Bayes

  1. There is a philosophy PhD thesis to be written here; most of decision theory is based on the implicit assumption that you are trying to use the available evidence to make a decision (in which case a subjective approach would make sense, as anything else would involve throwing away information). In fact, though, most of the time when you are carrying out statistical analysis, you are attempting to provide support for someone else's decision, and the decision-maker might not have the same prior information as you. Hence objective Bayesianism; the science of pretending not to have information that you actually have, in order to make it clear to your boss that you're not fudging.

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