Modes of Parametric Statistical InferenceJohn Wiley & Sons, 27 січ. 2006 р. - 192 стор. A fascinating investigation into the foundations of statistical inference This publication examines the distinct philosophical foundations of different statistical modes of parametric inference. Unlike many other texts that focus on methodology and applications, this book focuses on a rather unique combination of theoretical and foundational aspects that underlie the field of statistical inference. Readers gain a deeper understanding of the evolution and underlying logic of each mode as well as each mode's strengths and weaknesses. The book begins with fascinating highlights from the history of statistical inference. Readers are given historical examples of statistical reasoning used to address practical problems that arose throughout the centuries. Next, the book goes on to scrutinize four major modes of statistical inference: * Frequentist * Likelihood * Fiducial * Bayesian The author provides readers with specific examples and counterexamples of situations and datasets where the modes yield both similar and dissimilar results, including a violation of the likelihood principle in which Bayesian and likelihood methods differ from frequentist methods. Each example is followed by a detailed discussion of why the results may have varied from one mode to another, helping the reader to gain a greater understanding of each mode and how it works. Moreover, the author provides considerable mathematical detail on certain points to highlight key aspects of theoretical development. The author's writing style and use of examples make the text clear and engaging. This book is fundamental reading for graduate-level students in statistics as well as anyone with an interest in the foundations of statistics and the principles underlying statistical inference, including students in mathematics and the philosophy of science. Readers with a background in theoretical statistics will find the text both accessible and absorbing. |
Зміст
1 A Forerunner | 1 |
2 Frequentist Analysis | 3 |
3 Likelihood | 7 |
4 Testing Hypotheses | 25 |
5 Unbiased and Invariant Tests | 45 |
6 Elements of Bayesianism | 81 |
7 Theories of Estimation | 105 |
8 Set and Interval Estimation | 137 |
183 | |
187 | |
Інші видання - Показати все
Modes of Parametric Statistical Inference Seymour Geisser,Wesley O. Johnson Попередній перегляд недоступний - 2006 |
Modes of Parametric Statistical Inference Seymour Geisser,Wesley O. Johnson Попередній перегляд недоступний - 2006 |
Загальні терміни та фрази
Analysis ancillary statistic Applications assume B’s Gain Bayesian Bayesian inference binomial condition Consider defined degrees of freedom density distribution Example exponential family f(Dju F(tju f(xju fiducial find first Fisher FISHER INFORMATION fixed frequentist given Hence hypothesis implies independent invariant tests KOTZ L(ujD level a test likelihood principle likelihood ratio likelihood test Linear lower priced paperback Mathematical minimum variance Models Modes of Parametric monotone Multivariate N-P theory Neyman non-secretor Note null observed P(reject parameter Parametric Statistical Parametric Statistical Inference posterior probability priced paperback edition prior probability probability function problem Proof random variables Regression reject H0 rejection region sample space satisfies scalar Second Edition Seymour Geisser similar test Statistical Inference Statistical Methods Stochastic subset sufficient statistic Suppose Table Theorem Third Edition transformation trial true value UMPI UMPU unbiased estimator unbiased tests var(T versus