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 x
... frequency 270 9.1 Physical experiments 271 9.2 The poorly informed robot 274 9.3 Induction 276 9.4 Are there general inductive rules? 277 9.5 Multiplicity factors 280 9.6 Partition function algorithms 281 9.6.1 Solution by inspection ...
... frequency 270 9.1 Physical experiments 271 9.2 The poorly informed robot 274 9.3 Induction 276 9.4 Are there general inductive rules? 277 9.5 Multiplicity factors 280 9.6 Partition function algorithms 281 9.6.1 Solution by inspection ...
الصفحة xiv
... frequency in exchangeable sequences 576 18.14 Prediction of frequencies 576 18.15 One-dimensional neutron multiplication 579 18.15.1 The frequentist solution 579 1 8. 1 5.2 The Laplace solution 58 1 18.16 The de Finetti theorem 586 ...
... frequency in exchangeable sequences 576 18.14 Prediction of frequencies 576 18.15 One-dimensional neutron multiplication 579 18.15.1 The frequentist solution 579 1 8. 1 5.2 The Laplace solution 58 1 18.16 The de Finetti theorem 586 ...
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المحتوى
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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