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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النتائج 1-5 من 88
الصفحة xii
... example 432 14.5 How would our robot do it? 437 14.6 Historical remarks 438 14.6.1 The classical matched filter 439 14.7 The widget problem 440 14.7.1 Solution for Stage 2 443 14.7.2 Solution for Stage 3 445 14.7.3 Solution for Stage 4 ...
... example 432 14.5 How would our robot do it? 437 14.6 Historical remarks 438 14.6.1 The classical matched filter 439 14.7 The widget problem 440 14.7.1 Solution for Stage 2 443 14.7.2 Solution for Stage 3 445 14.7.3 Solution for Stage 4 ...
الصفحة xxi
... example, our system of probability could hardly be more different from that of Kolmogorov, in style, philosophy, and purpose. What we consider to be fully half of probability theory as it is needed in current applications - the ...
... example, our system of probability could hardly be more different from that of Kolmogorov, in style, philosophy, and purpose. What we consider to be fully half of probability theory as it is needed in current applications - the ...
الصفحة xxii
... example, the question: 'What is the probability that an integer is even?' can have any answer we please in (0, 1) ... Examples appear in almost every chapter. Comparisons For many years, there has been controversy over 'frequentist ...
... example, the question: 'What is the probability that an integer is even?' can have any answer we please in (0, 1) ... Examples appear in almost every chapter. Comparisons For many years, there has been controversy over 'frequentist ...
الصفحة xxiv
... example, is included in this, as are the highly successful Maximum Entropy spectrum analysis and image reconstruction algorithms in current use. However, we think that in the future the latter two applications will evolve into the ...
... example, is included in this, as are the highly successful Maximum Entropy spectrum analysis and image reconstruction algorithms in current use. However, we think that in the future the latter two applications will evolve into the ...
الصفحة xxvi
... example, to tell us that a sugar substitute can produce a barely detectable incidence of cancer in doses 1000 times greater than would ever be encountered in practice, is hardly an argument against using the substitute; indeed, the fact ...
... example, to tell us that a sugar substitute can produce a barely detectable incidence of cancer in doses 1000 times greater than would ever be encountered in practice, is hardly an argument against using the substitute; indeed, the 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