I think Ronald Fisher's Ph.D. was in mathtematics and he published some things on differential geometry.

He is one of the three major founders of the science of population genetics, with Wright and Haldane. His writings on biology are fairly voluminous.

He is also the originator of many of the things taught in basic theory-of-statistics courses, including sufficiency and Fisher information. He single-handedly founded the discipline of design of experiments.

He introduced fiducial inference in order to apply it to what became known as the Behrensâ€“Fisher problem. It's often hard to tell just what Fisher intended in things he wrote. Someone named Bartlett in 1936 published a proof that Fisher's fiducial intervals don't have constant coverage rates. Constant coverage rates are part of the definition of confidence intervals. Bartlett seemed to suggest that it is therefore an error to use fiducial inference. Fisher replied that he never intended his intervals to have constant coverage rates, but I haven't been able to figure out just what he did intend. Bayesian credible intervals also don't have constant coverage rates, but in that case everyone understands why that should be so. If I knew a bit more than I do about the Behrensâ€“Fisher problem, I'd an write expository paper on why it is not and cannot be really a math problem and any attempt to pretend it is one is a misunderstanding.

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