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I gave a talk last week as part of the VT Department of Philosophy’s “brown bag” series. Here’s the blurb:
What is the Philosophy of Statistics? (and how I was drawn to it)
I give an introductory discussion of two key philosophical controversies in statistics in relation to today’s “replication crisis” in science: the role of probability, and the nature of evidence, in error-prone inference. I begin with a simple principle: We don’t have evidence for a claim C if little, if anything, has been done that would have found C false (or specifically flawed), even if it is. Along the way, I sprinkle in some autobiographical reflections.
My slides are at the end of this post: Continue reading
A seminal controversy in statistical inference is whether error probabilities associated with an inference method are evidentially relevant once the data are in hand. Frequentist error statisticians say yes; Bayesians say no. A “no” answer goes hand in hand with holding the Likelihood Principle (LP), which follows from inference by Bayes theorem. A “yes” answer violates the LP (also called the strong LP). The reason error probabilities drop out according to the LP is that it follows from the LP that all the evidence from the data is contained in the likelihood ratios (at least for inference within a statistical model). For the error statistician, likelihood ratios are merely measures of comparative fit, and omit crucial information about their reliability. A dramatic illustration of this disagreement involves optional stopping, and it’s the one to which Roderick Little turns in the chapter “Do you like the likelihood principle?” in 
Error Statistics Philosophy 