By E. T. Jaynes
Going past the normal arithmetic of likelihood idea, this research perspectives the topic in a much wider context. It discusses new effects, in addition to purposes of likelihood conception to quite a few difficulties. The e-book comprises many workouts and is acceptable to be used as a textbook on graduate-level classes regarding information research. aimed toward readers already acquainted with utilized arithmetic at a complicated undergraduate point or larger, it's of curiosity to scientists fascinated about inference from incomplete details.
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Extra resources for Probability Theory: The Logic of Science
Sample text
An ad writer for a chemical trade journal fouled this up into: \Power is Knowledge", an absurd { indeed, obscene { falsity. These examples remind us that the verb \is" has, like any other verb, a subject and a predicate; but it is seldom noted that this verb has two entirely di erent meanings. " But in Turkish these meanings are rendered by di erent words, which makes the distinction so clear that a visitor who uses the wrong word will not be understood. The latter statement is ontological, asserting the physical existence of something, while the former is epistemological, expressing only the speaker's personal perception.
2{22) becomes jC ) : (2{24) w(AB jC ) = w(AjC ) S [w(BjAC )] = w(AjC ) S ww(AB (AjC ) Again, we invoke commutativity: w(AB jC ) is symmetric in A, B , and so consistency requires that jC ) = w(BjC ) S w(BAjC ) : w(AjC ) S ww((AB AjC ) w(BjC ) This must hold for all propositions A; B; C ; in particular, (2{25) must hold when (2{25) 207 Chap. 2: THE QUANTITATIVE RULES B = AD 207 (2{26) where D is any new proposition. But then we have the truth{values noted before in (1{8): and in (2{25) we may write AB = B ; BA = A ; w(AB jC ) = w(BjC ) = S [w(BjC )] w(BAjC ) = w(AjC ) = S [w(AjC )] : (2{27) (2{28) Therefore, using now the abbreviations x w(AjC ) ; y w(B jC ) (2{29) Eq.
The domain of validity given in (2{30) is found as follows. The proposition D is arbitrary, and so by various choices of D we can achieve all values of w(DjAC ) in 0 w(DjAC ) 1 : (2{32) But S (y ) = w(ADjC ) = w(AjC )w(DjAC ), and so (2{32) is just (0 S (y ) x), as stated in (2{30). This domain is symmetric in x; y ; it can be written equally well with them interchanged. Geometrically, it consists of all points in the x y plane lying in the unit square (0 x; y 1) and on or above the curve y = S (x).