Thursday, April 14, 2011

Revised Topics

My philosophy comp topic has evolved gradually, while my history comp topic has changed drastically.

My current philosophy comp project begins with a 1962 paper in which Allan Birnbaum argues that two principles frequentist statisticians typically accept—the conditionality and sufficiency principles—imply a principle they typically reject—the likelihood principle. The likelihood principle is a consequence of Bayes’ theorem, and Bayes’ theorem provides perhaps the simplest way to implement the likelihood principle in statistical inference, so Birnbaum’s argument tends to push frequentists toward Bayesianism.

Birnbaum’s argument is famous among those interested in the philosophy of statistics, but it has been criticized. Several statisticians have argued that Birnbaum’s formulation of either the conditionality principle or the sufficiency principle is too strong, and that replacing it with a suitably weakened principle would not allow Birnbaum’s argument to go through. However, these statisticians disagree among themselves about how Birnbaum’s principles should be weakened, and their specific proposals have been criticized. Joshi and Mayo have raised stronger objections to Birnbaum’s argument, arguing that there is a flaw in Birnbaum’s logic rather than in his premises.

I do not yet know what to say about Birnbaum’s argument, but I think that with enough work I am bound to find something interesting. Whether Birnbaum is right or not, there is work to be done in pinpointing exactly where either he or his critics go wrong, and the results of such an analysis are likely to have significant implications for the foundations of statistics.

I am abandoning my history comp project based on the Millikan oil-drop experiment. Millikan’s notebooks have already received careful scrutiny, and after some preliminary work it is not clear that an experimental approach will yield any significant new insights in time for the comp deadline. Moreover, it has come to my attention that there is a researcher in Germany who is way ahead of me in tracking down and investigating extant versions of Millikan’s apparatus.

Instead, I am planning to write my history comp on a puzzling passage in Darwin’s Origin of Species. I wrote a paper on this topic last year and received encouraging comments on it and suggestions for expanding it. In particular, I am planning to investigate how this passage changed through subsequent editions of the Origin and to look for evidence that might indicate why Darwin made the particular changes he did.

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