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 vii
... rules 24 2.1 The product rule 24 2.2 The sum rule 30 2.3 Qualitative properties 35 2.4 Numerical values 37 2.5 Notation and finite-sets policy 43 2.6 Comments 44 2.6.1 'Subjective' vs. 'objective' 44 2.6.2 Godel's theorem 45 2.6.3 Venn ...
... rules 24 2.1 The product rule 24 2.2 The sum rule 30 2.3 Qualitative properties 35 2.4 Numerical values 37 2.5 Notation and finite-sets policy 43 2.6 Comments 44 2.6.1 'Subjective' vs. 'objective' 44 2.6.2 Godel's theorem 45 2.6.3 Venn ...
الصفحة 24
... rules for inference which follow from these desiderata. The resulting rules have a long, complicated, and astonishing ... rule We first seek a consistent rule relating the plausibility of the logical product AB to the plausibilities of A ...
... rules for inference which follow from these desiderata. The resulting rules have a long, complicated, and astonishing ... rule We first seek a consistent rule relating the plausibility of the logical product AB to the plausibilities of A ...
الصفحة 29
... product thus require that the relation sought must take the functional form w(AB\C) = w(A\BC)w(B\C) = w(B\AC)w(A\C), (2.28) which we shall call henceforth the product rule. By its construction (2.24), w(x) must be a positive continuous ...
... product thus require that the relation sought must take the functional form w(AB\C) = w(A\BC)w(B\C) = w(B\AC)w(A\C), (2.28) which we shall call henceforth the product rule. By its construction (2.24), w(x) must be a positive continuous ...
الصفحة 30
... product A A is always false, the logical sum A + A always true. The plausibility that A is false must depend in some ... product rule can be written for either AB or AB: w(AB\C) = w(A\C)w(B\AC) (2.37) w(A~B\C) = w(A\C)w(B\AC). (2.38) ...
... product A A is always false, the logical sum A + A always true. The plausibility that A is false must depend in some ... product rule can be written for either AB or AB: w(AB\C) = w(A\C)w(B\AC) (2.37) w(A~B\C) = w(A\C)w(B\AC). (2.38) ...
الصفحة 31
... product rule. In the special case y = 1 , this reduces to S[S(.v)]=*, (2.46) which states that S(x) is a self-reciprocal function; S(x) = S~l(x). Thus, from (2.36) it follows also that u — S(v). But this expresses only the evident fact ...
... product rule. In the special case y = 1 , this reduces to S[S(.v)]=*, (2.46) which states that S(x) is a self-reciprocal function; S(x) = S~l(x). Thus, from (2.36) it follows also that u — S(v). But this expresses only the evident fact ...
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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