Customer Reviews

Interpreting Probability: Controversies and Developments in the Early Twentieth Century (Cambridge Studies in Probability, Induction and Decision Theory)

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Howie has written a superb book on the three main controversies that occurred in the period 1910-1935 that essentially revolves around the meaning of different interpretations about what probability means.I highly recommend that any reader interested in any way about the history/historical development of probability and statistics buy this book.You will not be disappointed.The three controversies were the Keynes-Ramsey controversy over Keynes's position that most probabilities were"nonnumerical"(this is the term that Keynes used to describe his interval(set theoretic) estimate approach to probability that he combined with a logic of partial entailment),the Fisher-Neyman-(Pearson) controversy over what a confidence interval meant,and the Fisher-Jeffreys controversy over the use of inverse probabilities. The controversies portion of the book primarily focuses on the Fisher-Jeffreys exchange,with Fisher being opposed to basing scientific statistical analysis on the need to specify the apriori distribution.Fisher, instead,favored a frequency analysis of the existing data to obtain operational probabilities and a hypothesis test based on significance levels and p-value tests. Jeffreys favored the standard Bayesian approach that required the specification of an a priori distribution that would be based on the existing initial data.Howie spends a moderate degree of time on the controversy between Fisher and Neyman(Pearson) over the logical meaning and operational nature of a confidence interval.This debate should have been won hands down by Fisher since the Neyman(Pearson)argument doesn't make any sense.Neyman was a strict frequentist whose claim that the interpretation of what a confidence interval meant was up to each individual researcher's belief directly contradicts his approach.The meaning of,say,a 95 % confidence interval for a sample mean for a specific data subset can't be the frequentist claim that the researcher does a thought experiment in which he visualizes a 100 repetitions of the confidence level calculation in which 95 of the intervals contain that sample mean.Since only 1 calculation is in fact made,the probability of locating the sample statistic inside the confidence interval is either 0 or 1.This confusion of what a confidence interval means can still be found in quite a few statistics and econometrics books even today.Howie does a good job in discussing this controversy.I deducted one star from my rating because of the very poor coverage in section 4.6.3(pp.96-101;see also p.151) of the third controversy between John Maynard Keynes and Frank P Ramsey concerning Keynes's logical theory of probability and its operational capabilities.It is apparent that Howie has just accepted the conclusions of the two extremely poor book reviews made by Ramsey in 1922 and 1926 at face value.Howie accepts the unsupported claim , a claim that is generally accepted by the vast majority of philosophers and logicians in 2005,that Ramsey not only completely destoyed and devastated the logical structure of Keynes's theory and its operational applicability,but that Keynes himself accepted the critique of the boy genius and capitulated completely in the face of Ramsey's overwhelming argument.Based on his acceptance of the conventional wisdom,Howie claims that,a)Keynes accepted Ramsey's argument that all probabilities can be estimated by using precise single numbers,b)that Keynes claimed in the A Treatise on Probability(1921)that probabilities are often incalculable,c)that Keynes claimed that the ability to perceive the values of logical probabilities was intuitive.Nowhere in the A Treatise on Probability or in any book or paper published in his lifetime did Keynes EVER make any of these claims.In fact,all of these misstatements can be traced back to the wild and unsubstantiated claims of Ramsey that by the terms "nonnumerical"or"nonmeasurable"Keynes was arguing that the quantification and estimation of probabilities was ,in general ,not possible.Supposedly, all a decision maker could do,at best, was to partially ordinally rank some of the alternatives some of the time.All of these conclusions ,on the part of Ramsey and his adherents today, are false,since they are based on Ramsey's reviews,not of the entire A Treatise on Probability,but only of one chapter,chapter 3 of the TP,which is taken out of context.In chapters 15 and 17, Keynes develops and applies an interval valued approach to probability that Keynes makes the foundation of all of Part III of the TP.Thus, by "nonnumerical",Keynes meant that in general it took two numbers,not one,to estimate and quantify probabilities.These two numbers are composed of a lower bound(greatest lower bound)and an upper bound(least upper bound).Howie might consider writing another book on why the boy genius got it all wrong in this particular case .Especially interesting would be an examination of the logical consistency of Ramsey's acceptance that "Ramsey numbers"were usually intervals,but probabilities could not be intervals.