David Fox writes:
As a ‘classically’ trained statistician who works on ‘real’ problems (mainly environmental ones) I have come to appreciate the utility and benefits of working within a Bayesian framework. I would not classify myself as a ‘convert’ but prefer to have an array of statistical tools from which I can select the most appropriate one for the job at hand. As they say – if all you’ve got is a hammer, then the whole world’s a nail! On the issue of choice of priors, I believe this is an absolute strength in the evaluation and setting of environmental regulatory limits. In situations characterized by high levels of data paucity but rich with expert knowledge (albeit diverse), why would you choose to ignore the latter?
However, I should get to the real purpose of this email. A rather fierce debate has been taking place among academics in our departments of Botany and Mathematics and Statistics about the use of a ‘new’ form of decision-making under extreme uncertainty. It is called Info-Gap (short for information gap) Theory and owes its existence to Prof. Yakov Ben-Haim at Technion in Israel (Ben-Haim 2006). Yakov is well known to the aforementioned academics – he visits here regularly and has done a remarkably good job at ‘selling’ his product – to the extent that some staff and students in our Botany department and The Australian Centre of Excellence in Risk Analysis (http://www.acera.unimelb.edu.au) have enthusiastically (and some would say, blindly) embraced this ‘new’ paradigm for decision-making under extreme uncertainty. I must plead mea culpa, having been swept up in the initial enthusiasm and published a couple of papers which use info-gap. However, I have a growing unease that IG is not ‘new’ but in fact a variant of existing methodologies.” While not wishing to draw you into our local debate, I was wondering if you have ever heard of info-gap theory and if you have, do you have an opinion? Prof. Ben-Haim has recently launched his own web site (http://www.info-gap.com) presumably in response to the ‘hi-jacking’ of the Wikepedia entry (http://en.wikipedia.org/wiki/Info-gap_decision_theory) by IG’s most strident local critic, Moshe Sniedovich. Sniedovich has also established a web site (http://info-gap.moshe-online.com/) and a quick look will demonstrate the ferocity of the debate.
Just today, the following paragraph in a paper I was reading [Hickey, G.L., Craig, P.S., and Hart, A. (2009) On the application of loss functions in determining assessment factors for ecological risk. Ecotoxicology and Environmental Safety, 72, 293-300] caught my attention:
“There do exist other forms of risk measurement. However, by a very well-known theorem of Wald (1950), any admissible decision rule is a Bayes rule with respect to some prior distribution (possibly an improper prior distribution), whereby admissibility is defined to mean that no other decision rule dominates it in terms of risk. It is therefore argued by many, for example, Bernardo and Smith (2000) that it is pointless to work in decision-theory outside the Bayesian framework”.
This accords with my own gut feeling that IG Theory is in fact a Bayes Rule with a non-informative prior.
My reply: I had never heard about Dr. Ben-Haim or his methods before receiving this email. I checked out the links but couldn’t really see the point in this approach. The mathematics looked complicated and appeared to be a distraction from the more important goals of modeling the decision problems directly.
For some of my thoughts on Bayesian decision analysis, see chapter 22 of Bayesian Data Analysis (second edition). Bayesian decision analysis is a lot more flexible than people realize, I think, especially when used in the context of hierarchical modeling. See here for a brief discussion of my idea of “institutional decision analysis” and here for an example of Bayesian decision analysis in action.
In my article on the boxer, the wrestler, and the coin flip, I discuss some fundamental difficulties with Bayesian robusness and similar approaches.
Finally, I don’t know that I’d agree with the statement that it’s “pointless” to work in non-Bayesian decision theory. For me, I’ve found the Bayesian approach to do the job, but I can imagine there are settings where other methods can be useful. I’m not, however, a fan of those 1950’s-style alternatives such as “minimax regret” and all the reat. I offer no comment on Info-Gap since I didn’t put in the effort to try to understand exactly what it is.