Deborah Mayo's book

Am now reading through one of those two books I mentioned last week. I said I would report on them to you: here is a first report:

Deborah G. Mayo has an impressive resume to be writing on statistical inference. She is a winner (in 1998) of the Lakatos Prize, an award for contributions in the field of the philosophy of science.

The book I'm concerned with now though is her 2018 publication, via the Cambridge University Press, Statistical Inference as Severe Testing. The subtitle she gives it is "How to Get Beyond the Statistics Wars".

What are these wars? They are generally philosophical disputes about what kind of thing we are doing when we talk about statistics and probability. By the warring sides she means especially Bayesians on the one hand and frequentists on the other.

Bayesians acknowledge subjectivity in probabilistic inferences. After all, you must start with a "prior," and you may start with a very different prior from the one I start with on the same issue. Our inferences may converge over time, but the snake of a subjective starting place may leave its mark.

Frequentism deny subjectivity. It tells us that the logic of induction must simply (Mayo's words here) "focus on the relationships between given data and hypotheses -- so outcomes other than the one observed drop out." The subjective snake eventually does disappear.

"The warring sides talk past each other," she complains. It sound as if she is going to transcend their differences, maybe offer the synthesis in which they can be reconciled. "We need a new perspective on the role of probability in statistical Inference ... that will illuminate, and let us get beyond, this battle."

Those quotes are from p. 54.

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