Principles Of Statistical Inference

Author : D. R. Cox
Publisher : Cambridge University Press
Page : 227 pages
File Size : 48,5 Mb
Release : 2006-08-10
Category : Mathematics
ISBN : 9781139459136

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Principles of Statistical Inference by D. R. Cox Pdf

In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The mathematics is kept as elementary as feasible, though previous knowledge of statistics is assumed. The book will be valued by every user or student of statistics who is serious about understanding the uncertainty inherent in conclusions from statistical analyses.

Author : Miltiadis C. Mavrakakis,Jeremy Penzer
Publisher : CRC Press
Page : 444 pages
File Size : 52,8 Mb
Release : 2021-03-28
Category : Mathematics
ISBN : 9781315362045

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Probability and Statistical Inference by Miltiadis C. Mavrakakis,Jeremy Penzer Pdf

Probability and Statistical Inference: From Basic Principles to Advanced Models covers aspects of probability, distribution theory, and inference that are fundamental to a proper understanding of data analysis and statistical modelling. It presents these topics in an accessible manner without sacrificing mathematical rigour, bridging the gap between the many excellent introductory books and the more advanced, graduate-level texts. The book introduces and explores techniques that are relevant to modern practitioners, while being respectful to the history of statistical inference. It seeks to provide a thorough grounding in both the theory and application of statistics, with even the more abstract parts placed in the context of a practical setting. Features: •Complete introduction to mathematical probability, random variables, and distribution theory. •Concise but broad account of statistical modelling, covering topics such as generalised linear models, survival analysis, time series, and random processes. •Extensive discussion of the key concepts in classical statistics (point estimation, interval estimation, hypothesis testing) and the main techniques in likelihood-based inference. •Detailed introduction to Bayesian statistics and associated topics. •Practical illustration of some of the main computational methods used in modern statistical inference (simulation, boostrap, MCMC). This book is for students who have already completed a first course in probability and statistics, and now wish to deepen and broaden their understanding of the subject. It can serve as a foundation for advanced undergraduate or postgraduate courses. Our aim is to challenge and excite the more mathematically able students, while providing explanations of statistical concepts that are more detailed and approachable than those in advanced texts. This book is also useful for data scientists, researchers, and other applied practitioners who want to understand the theory behind the statistical methods used in their fields.

Author : David Roxbee Cox
Publisher : Unknown
Page : 219 pages
File Size : 50,5 Mb
Release : 2008
Category : Electronic
ISBN : OCLC:717646933

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Principles of Statistical Inference by David Roxbee Cox Pdf

Author : George Casella,Roger Berger
Publisher : CRC Press
Page : 1746 pages
File Size : 52,7 Mb
Release : 2024-05-23
Category : Mathematics
ISBN : 9781040024027

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Statistical Inference by George Casella,Roger Berger Pdf

This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation. Features The classic graduate-level textbook on statistical inference Develops elements of statistical theory from first principles of probability Written in a lucid style accessible to anyone with some background in calculus Covers all key topics of a standard course in inference Hundreds of examples throughout to aid understanding Each chapter includes an extensive set of graduated exercises Statistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations. This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001.

Author : Ian Hacking
Publisher : Cambridge University Press
Page : 229 pages
File Size : 48,7 Mb
Release : 2016-08-26
Category : Mathematics
ISBN : 9781107144958

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Logic of Statistical Inference by Ian Hacking Pdf

This book showcases Ian Hacking's early ideas on the central issues surrounding statistical reasoning. Presented in a fresh twenty-first-century series livery, and with a specially commissioned new preface, this influential work is now available for a new generation of readers in statistics, philosophy of science and philosophy of maths.

Author : Henry E. Kyburg Jr.
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401021753

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The Logical Foundations of Statistical Inference by Henry E. Kyburg Jr. Pdf

Everyone knows it is easy to lie with statistics. It is important then to be able to tell a statistical lie from a valid statistical inference. It is a relatively widely accepted commonplace that our scientific knowledge is not certain and incorrigible, but merely probable, subject to refinement, modifi cation, and even overthrow. The rankest beginner at a gambling table understands that his decisions must be based on mathematical ex pectations - that is, on utilities weighted by probabilities. It is widely held that the same principles apply almost all the time in the game of life. If we turn to philosophers, or to mathematical statisticians, or to probability theorists for criteria of validity in statistical inference, for the general principles that distinguish well grounded from ill grounded generalizations and laws, or for the interpretation of that probability we must, like the gambler, take as our guide in life, we find disagreement, confusion, and frustration. We might be prepared to find disagreements on a philosophical and theoretical level (although we do not find them in the case of deductive logic) but we do not expect, and we may be surprised to find, that these theoretical disagreements lead to differences in the conclusions that are regarded as 'acceptable' in the practice of science and public affairs, and in the conduct of business.

Author : Deborah G. Mayo
Publisher : Cambridge University Press
Page : 503 pages
File Size : 40,7 Mb
Release : 2018-09-20
Category : Mathematics
ISBN : 9781107054134

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Statistical Inference as Severe Testing by Deborah G. Mayo Pdf

Unlock today's statistical controversies and irreproducible results by viewing statistics as probing and controlling errors.

Author : Michael C. Acree
Publisher : Springer Nature
Page : 457 pages
File Size : 42,5 Mb
Release : 2021-07-05
Category : Psychology
ISBN : 9783030732578

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The Myth of Statistical Inference by Michael C. Acree Pdf

This book proposes and explores the idea that the forced union of the aleatory and epistemic aspects of probability is a sterile hybrid, inspired and nourished for 300 years by a false hope of formalizing inductive reasoning, making uncertainty the object of precise calculation. Because this is not really a possible goal, statistical inference is not, cannot be, doing for us today what we imagine it is doing for us. It is for these reasons that statistical inference can be characterized as a myth. The book is aimed primarily at social scientists, for whom statistics and statistical inference are a common concern and frustration. Because the historical development given here is not merely anecdotal, but makes clear the guiding ideas and ambitions that motivated the formulation of particular methods, this book offers an understanding of statistical inference which has not hitherto been available. It will also serve as a supplement to the standard statistics texts. Finally, general readers will find here an interesting study with implications far beyond statistics. The development of statistical inference, to its present position of prominence in the social sciences, epitomizes a number of trends in Western intellectual history of the last three centuries, and the 11th chapter, considering the function of statistical inference in light of our needs for structure, rules, authority, and consensus in general, develops some provocative parallels, especially between epistemology and politics.

Author : Luigi Pace,Alessandra Salvan
Publisher : World Scientific
Page : 584 pages
File Size : 41,6 Mb
Release : 1997-08-05
Category : Mathematics
ISBN : 9812386947

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Principles of Statistical Inference by Luigi Pace,Alessandra Salvan Pdf

In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term ?neo-Fisherian? highlights this.After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.

Author : Pierre Moulin,Venugopal V. Veeravalli
Publisher : Cambridge University Press
Page : 423 pages
File Size : 45,8 Mb
Release : 2019
Category : Mathematics
ISBN : 9781107185920

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Statistical Inference for Engineers and Data Scientists by Pierre Moulin,Venugopal V. Veeravalli Pdf

A mathematically accessible textbook introducing all the tools needed to address modern inference problems in engineering and data science.

Author : Walter T. Ambrosius
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 46,9 Mb
Release : 2007-07-06
Category : Medical
ISBN : 9781588295316

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Topics in Biostatistics by Walter T. Ambrosius Pdf

This book presents a multidisciplinary survey of biostatics methods, each illustrated with hands-on examples. It introduces advanced methods in statistics, including how to choose and work with statistical packages. Specific topics of interest include microarray analysis, missing data techniques, power and sample size, statistical methods in genetics. The book is an essential resource for researchers at every level of their career.

Author : Seymour Geisser,Wesley O. Johnson
Publisher : John Wiley & Sons
Page : 218 pages
File Size : 45,6 Mb
Release : 2006-01-27
Category : Mathematics
ISBN : 9780471743125

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Modes of Parametric Statistical Inference by Seymour Geisser,Wesley O. Johnson Pdf

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.

Author : Hannelore Liero,Silvelyn Zwanzig
Publisher : CRC Press
Page : 280 pages
File Size : 51,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781466503205

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Introduction to the Theory of Statistical Inference by Hannelore Liero,Silvelyn Zwanzig Pdf

Based on the authors' lecture notes, this text presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Unlike related textbooks, it combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models. Suitable for a second semester undergraduate course on statistical inference, the text offers proofs to support the mathematics and does not require any use of measure theory. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

Author : Ian C. Marschner
Publisher : CRC Press
Page : 272 pages
File Size : 50,5 Mb
Release : 2014-12-11
Category : Mathematics
ISBN : 9781482222241

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Inference Principles for Biostatisticians by Ian C. Marschner Pdf

Designed for students training to become biostatisticians as well as practicing biostatisticians, Inference Principles for Biostatisticians presents the theoretical and conceptual foundations of biostatistics. It covers the theoretical underpinnings essential to understanding subsequent core methodologies in the field.Drawing on his extensive exper

Author : Miltiadis C. Mavrakakis,Jeremy Penzer
Publisher : Chapman and Hall/CRC
Page : 608 pages
File Size : 49,9 Mb
Release : 2014-12-15
Category : Mathematics
ISBN : 158488939X

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Modelling, Inference and Data Analysis by Miltiadis C. Mavrakakis,Jeremy Penzer Pdf

Modelling, Inference and Data Analysis brings together key topics in mathematical statistics and presents them in a rigorous yet accessible manner. It covers aspects of probability, distribution theory and random processes that are fundamental to a proper understanding of inference. The book also discusses the properties of estimators constructed from a random sample of ends, with sections on methods for estimating parameters in time series models and computationally intensive inferential techniques. The text challenges and excites the more mathematically able students while providing an approachable explanation of advanced statistical concepts for students who struggle with existing texts.