Probability Theory: The Logic of ScienceCambridge University Press, 10/04/2003 The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary. |
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الصفحة xxii
... fact in a hundred different areas. One can argue with a philosophy; it is not so easy to argue with a computer printout, which says to us: 'Independently of all your philosophy, here are the facts of actual performance.' We point this ...
... fact in a hundred different areas. One can argue with a philosophy; it is not so easy to argue with a computer printout, which says to us: 'Independently of all your philosophy, here are the facts of actual performance.' We point this ...
الصفحة 10
... fact that Boole himself (Boole, 1 854, p. 286) fell into error on this point, by mistakenly identifying two propositions which were in fact different - and then failing to see any contradiction in their different plausibilities. Three ...
... fact that Boole himself (Boole, 1 854, p. 286) fell into error on this point, by mistakenly identifying two propositions which were in fact different - and then failing to see any contradiction in their different plausibilities. Three ...
الصفحة 48
... fact, which may or may not be resolvable into a disjunction of more elementary propositions within the context of our problem. Of course, one can always force such a resolution by introducing irrelevancies; for example, even though the ...
... fact, which may or may not be resolvable into a disjunction of more elementary propositions within the context of our problem. Of course, one can always force such a resolution by introducing irrelevancies; for example, even though the ...
الصفحة 52
... with the logic of consistent reasoning from incomplete information: not with assertions of physical fact about what will be drawn from the urn (which are in any event impossible just 52 Part I Principles and elementary applications XXVI.
... with the logic of consistent reasoning from incomplete information: not with assertions of physical fact about what will be drawn from the urn (which are in any event impossible just 52 Part I Principles and elementary applications XXVI.
الصفحة 83
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عبارات ومصطلحات مألوفة
analysis appears applications argument Bayes binomial calculation Chapter coin common sense conclusions consider Cox's theorems criterion data set decision theory defined density derivation equal equations error estimate evidence example expected fact finite Fisher frequency Gaussian give given Harold Jeffreys hypothesis improper prior independent induction inductive reasoning inference infinite sets integral intuitive Jeffreys knowledge Laplace Laplace's likelihood likelihood function limit loss function mathematical maximum entropy mean measure noise normal notation noted nuisance parameters numerical values observed paradox physical plausible possible posterior distribution posterior pdf posterior probability predictions principle principle of indifference prior information prior probability probability assignment probability distribution probability theory problem product rule propositions random experiment reasoning relevant result robot rules of probability sampling distribution solution specified statement sufficient statistic suppose tell theorem theory as logic toss trials true widgets