This book is about these two types of probability and investigates how, in the eighteenth and nineteenth centuries, Bayesianism was discredited as a.
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- Interpreting Probability: Controversies and Developments in the Early Twentieth Century
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Principal among the estimation criteria was that of maximum likelihood. Later, he was to exploit a formal symmetry, which can arise in suitable contexts between parameter and random variable to develop what he believed to be a class of allegedly frequentist probability distributions, called fiducial distributions, over parameters.
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For Fisher, the combination of significance tests, maximum-likelihood estimation and fiducial probability was a sufficient foundation of inference from data. Jeffreys, by contrast, believed that only a systematically developed theory of Bayesian probability could furnish an adequate theory of valid uncertain inference from data. He claimed that significance testing is unsound since, based as it is on the probability according to the null hypothesis of data at least as extreme as that observed, it involves the consideration of data that have actually not been observed.
In his Theory of Probability he showed that the objection is not merely academic: He also believed, with a good many other people at the time and even more later, that fiducial probability was based on a formal confusion, and he argued, plausibly, that maximum likelihood could not give a determinate inference since any group of data can be exactly fitted by an infinity of alternative laws this is the phenomenon we now know as underdetermination, and Jeffreys himself, long before Goodman and grue, gave in his Theory of Probability a simple formal algorithm for generating such an infinity of alternatives.
All this, and more, is faithfully retailed by Howie, with a wealth of documentary and interview-based evidence, including the many letters exchanged between Fisher and Jeffreys themselves, and between them and third parties with an interest in the issue and who also contributed to its discussion, like the contemporary statisticians Bartlett, Lindley and Barnard.
Prima facie, the dispute seems a fundamental one. Nevertheless, Howie supports with some interesting details his case that much of the disagreement was merely at the sound-and-fury level. For example, Fisher himself did not rule out a subjective element in the choice of statistical model i. Secondly, the two apparently competing methodologies were actually in agreement in an extensive class of cases, in particular those where the data set was large: Jeffreys himself proved that for large independent samples posterior probability asymptotically agrees with maximum likelihood estimation i.
Thirdly, the types of scientific problem each faced were typically very different, and their methods, according to Howie, to a considerable extent reflected the peculiar features of each.
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Fisher, working at Rothampstead, could rely on highly controlled data, which could be safely assumed to come from a single population, whereas Jeffreys had to make do with sometimes sparse, and often unreliable, data from several different sources characterized by possibly quite different structural characteristics. Thus Fisherian methods were naturally confined to parameter estimation and testing without having to consider alternative underlying models a feature still present, typically without any accompanying explanation, in introductory textbooks of statistics , while Jeffreys faced uncertainty, sometimes radical, at every level of the theoretical ascent from the data.
Whether Howie is right or wrong in his overall conclusions the reader will have to judge. Indeed, he tells it like it is or was , simply and clearly, steering clear of portentous philosophizing on the one hand and a too-minute attention to mathematical and biographical detail on the other, an approach to intellectual history now relatively uncommon but most welcome where it occurs.
Interpreting Probability: Controversies and Developments in the Early Twentieth Century
Bulwer Lytton becomes Lytton Bulwer on p. That said, this is a timely and valuable contribution to our knowledge of the period and its great figures. There is a wealth of incidental, but always relevant and often fascinating, historical detail. Probability of course also has a role to play outside statistics, and Howie devotes some space to this, with brief but informative discussions of its use in the social sciences, biology and especially physics.
Another distinctive feature of his book is that, though it concerns a highly technical subject matter, his own discussion is anything but technical in any overtly formal sense: Yet he succeeds in conveying, in words, the technical ideas both precisely and clearly the lucid discussion, on pp. Its thoroughness, combined with an assured informality and lightness of touch, make the book an enlightening and entertaining read.
The term probability can be used in two main senses. In the frequency interpretation it is a limiting ratio in a sequence of repeatable events. In the Bayesian view, probability is a mental construct representing uncertainty. This book is about these two types of probability and investigates how, despite being adopted by scientists and statisticians in the eighteenth and nineteenth centuries, Bayesianism was discredited as a theory of scientific inference during the s and s. Through the examination of a dispute between two British scientists, the author argues that a choice between the two interpretations is not forced by pure logic or the mathematics of the situation, but depends on the experiences and aims of the individuals involved.
The book should be of interest to students and scientists interested in statistics and probability theories and to general readers with an interest in the history, sociology and philosophy of science. Probability up to the twentieth century 3.
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Fisher and statistical probability 4. Harold Jeffreys and inverse probability 5. The Fisher-Jeffreys exchange, —4 6. Probability during the s 7. Epilogue and conclusions Appendices Bibliography Index. David Howie This title is available for institutional purchase via Cambridge Core Cambridge Core offers access to academic eBooks from our world-renowned publishing programme.
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