By Thabane L.
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Extra resources for A closer look at the distribution of number needed to treat (NNT) a Bayesian approach (2003)(en)(6s)
E. 0 P (A) 1 we must take account of the fact, noted in section II , that this view makes probabilities relations between instances of two properties, like the properties of landing heads and of being a toss of a coin. g. coin tosses) of those that are also G (land heads). Then the reason why, for frequentists, all probabilities lie between 1 and 0 is simply that, for any F and G, the number of F-things that are G can be neither greater than the total number of F-things nor less than 0. e. P (A) + P (¬A) = 1, is that because, for any F and G, the number of F-things that are G plus the number that are not G equals the total number of F-things, f (Gx/Fx) + f (¬Gx/Fx) = 1.
This, frequentists may then say, is what makes the relative frequency of radium atoms decaying within any given time interval a chance, which the relative frequency of planets further from the sun than we are is not. Note, however, that this view of laws and chances requires a sharp distinction between so-called deterministic laws, like the law that all humans are mortal, and statistical laws, like those of radioactivity. 1) x(Fx Gx), where ‘x’ means ‘for all x’, ‘_ …’ means ‘if _ then …’ and ‘Fx’ and ‘Gx’ in our example mean respectively that x is human and that x is mortal.
Russell (1948), part V, chapter V, discusses Keynes and indifference. Gillies (2000), chapter 2, discusses Bayes and Keynes on the indifference principle, and the latter’s solutions to its paradoxes, as well as the principle’s use in physics as a heuristic rather than a valid logical principle. Kneale’s views are discussed by Blackburn (1973), who defends a version of the indifference principle to warrant certain short-term predictions. 3 Frequencies I Credences R ecognition of the defects of classicism outlined in chapter 2 led in the nineteenth century to a quite different interpretation of probabilities, as frequencies.