By Thabane L.
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Additional info for A closer look at the distribution of number needed to treat (NNT) a Bayesian approach (2003)(en)(6s)
Under proper scoring rules, indeed, the ∗ (Translator’s note:) Note that in consonance with the Italian traditional expression, the original text reads speranza matematica, literally mathematical hope. 26 2. 3. 4. 5. 6. 7. 2 Decisions and Proper Scoring Rules subject will always have an interest in stating those numbers that correspond to her own degrees of belief. It should be borne in mind that the frequency of favourable cases can be thought of as the mean truth-value of the events. As a matter of fact, Stefan Amsterdamski (1929–2005) was a Polish (rather than a Russian) philosopher and sociologist.
If we adopt this plan, our theorems will not be proved concerning an ascertained set of terms called ‘the natural numbers,’ but concerning all sets of terms having certain properties. Such a procedure is not fallacious; indeed for certain purposes it represents a valuable generalization. But from two points of view it fails to give an adequate basis for arithmetic. In the first place, it does not enable us to know whether there are any sets of terms verifying Peano’s axioms; it does not even give the faintest suggestion of any way of discovering whether there are such sets.
Probably, no die is so “perfect” as to necessarily lead everyone to be a priori certain that the various sides will come up with the same frequency. At any rate, even though this appears to be reasonably confirmed by past experiences, it could never be so in a perfect way. 7 In fact, if probability were a frequency, we should demand that each of the sides 1, 2, 3, 4, 5, 6, always had to come up the same number of times. All excessively apodictical statements can only count as a vague, general idea.
A closer look at the distribution of number needed to treat (NNT) a Bayesian approach (2003)(en)(6s) by Thabane L.