I would like to write my philosophy comp on a topic in the philosophy of statistics. My leading idea at the moment is to take a close look at some aspect of Deborah Mayo's error-statistical account of statistical inference. The philosophy of statistics (as well as statistics itself) is roughly divided into two camps: frequentist and Bayesian. (I'll ignore likelihoodists for now.) Among philosophers, Mayo is the de facto leader of the frequentist camp. My impression is that the division between the two camps is deep enough that not many people have taken a serious, critical look at Mayo’s work. Those in the frequentist camp already, by and large, agree with her; those in the Bayesian camp can’t be bothered; and people in the philosophy of science who aren’t firmly in either camp, like me, haven’t done much work on the topic.
Bayesian philosophers of science use Bayes’ theorem as the basis for a normative theory of scientific inference. Frequentists objections to this program generally focus on the use of prior probabilities. Frequentists claim that subjective prior probabilities are out of place in science, which they claim ought to be as objective as possible. Some frequentists go further and deny that we can even speak meaningfully about the probability (prior or posterior) of a hypothesis. Orthodox Bayesians, by contrast, interpret all probabilities as subjective degrees of belief, and claim that one cannot draw valid probabilistic inferences without taking prior probabilities into account.
One topic of ongoing debate between the two camps is the claim that frequentist hypothesis testing is subject to the base-rate fallacy. From what I've seen of the literature on this debate, it seems that Bayesians are guilty of a hit-and-run: they've raised the base-rate fallacy objection, but have not made much of an effort to understand and respond to frequentist rejoinders. Bayesians are free, of course, to focus on whatever problems they find most pressing; but someone ought to engage the frequentist position in a more serious way.
In subsequent posts, I will work through some of the central papers in this debate. Here’s my bibliography so far:
- Collin Howson (1997), “Error Probabilities in Error"
- Deborah Mayo (1997), “Error Statistics and Learning from Error: Making a Virtue of Necessity”
- Ronald Giere (1997), “Scientific Inference: Two Points of View”
- Collin Howson (2000), Hume’s Problem
- Peter Achinstein (2001), The Book of Evidence
- -- (2010), “Mill’s Sin’s or Mayo’s Errors?”
- Collin Howson and Peter Urbach (2005), Scientific Reasoning: The Bayesian Approach
- Deborah Mayo (2010) “Sins of the Epistemic Probabilist: Exchanges with Achinstein”
- Aris Spanos (2010), “Is Frequentist Testing Vulnerable to the Base-Rate Fallacy?”