R.A. Fisher: A True Bayesian?

Abstract

Summary R.A. Fisher's claim that his fiducial argument uses the term 'probability' in the same sense as used by the Rev. Thomas Bayes is fully justifiable. But, while probability statements concerning parameters can be made, these parameters cannot be regarded as random variables in the sense of Kolmogoroff. Fisher was not a 'Bayesian' in the main current sense of the word. In the first edition (1956) of Statistical Methods and Scientific Inference, Ch. V, ? 6, R.A. Fisher discusses the logical situation arising when data of two kinds are available, one kind such as to give a fiducial distribution for the unknown parameter, the other such as to yield only a likelihood function. He imagines a charged particle recorder capable of being switched on or off at precisely chosen times. The recorder can be set to record the time at which a particle passes through, or alternatively to record whether any particles pass through in a specific time interval. Assuming the particles form a Poisson process with unknown rate 0 particles per unit time, the time t elapsing between switching on and observing the first particle has cumulative probability P(t, 0) = exp {-tO}, while the