Statistical Information And Likelihood

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Statistical Information and Likelihood

Author : D. Basu
Publisher : Springer Science & Business Media
ISBN 13 : 1461238943
Total Pages : 386 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Statistical Information and Likelihood by : D. Basu

Download or read book Statistical Information and Likelihood written by D. Basu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is an honor to be asked to write a foreword to this book, for I believe that it and other books to follow will eventually lead to a dramatic change in the current statistics curriculum in our universities. I spent the 1975-76 academic year at Florida State University in Tallahassee. My purpose was to complete a book on Statistical Reliability Theory with Frank Proschan. At the time, I was working on total time on test processes. At the same time, I started attending lectures by Dev Basu on statistical inference. It was Lehmann's hypothesis testing course and Lehmann's book was the text. However, I noticed something strange - Basu never opened the book. He was obviously not following it. Instead, he was giving a very elegant, measure theoretic treatment of the concepts of sufficiency, ancillarity, and invariance. He was interested in the concept of information - what it meant. - how it fitted in with contemporary statistics. As he looked at the fundamental ideas, the logic behind their use seemed to evaporate. I was shocked. I didn't like priors. I didn't like Bayesian statistics. But after the smoke had cleared, that was all that was left. Basu loves counterexamples. He is like an art critic in the field of statistical inference. He would find a counterexample to the Bayesian approach if he could. So far, he has failed in this respect.

Statistical Evidence

Author : Richard Royall
Publisher : Routledge
ISBN 13 : 1351414550
Total Pages : 212 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Statistical Evidence by : Richard Royall

Download or read book Statistical Evidence written by Richard Royall and published by Routledge. This book was released on 2017-11-22 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.

Applied Statistical Inference

Author : Leonhard Held
Publisher : Springer Science & Business Media
ISBN 13 : 3642378870
Total Pages : 381 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Applied Statistical Inference by : Leonhard Held

Download or read book Applied Statistical Inference written by Leonhard Held and published by Springer Science & Business Media. This book was released on 2013-11-12 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers modern statistical inference based on likelihood with applications in medicine, epidemiology and biology. Two introductory chapters discuss the importance of statistical models in applied quantitative research and the central role of the likelihood function. The rest of the book is divided into three parts. The first describes likelihood-based inference from a frequentist viewpoint. Properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic are discussed in detail. In the second part, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. Modern numerical techniques for Bayesian inference are described in a separate chapter. Finally two more advanced topics, model choice and prediction, are discussed both from a frequentist and a Bayesian perspective. A comprehensive appendix covers the necessary prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis.

Mathematical Statistics

Author : Richard J. Rossi
Publisher : John Wiley & Sons
ISBN 13 : 1118771168
Total Pages : 611 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Mathematical Statistics by : Richard J. Rossi

Download or read book Mathematical Statistics written by Richard J. Rossi and published by John Wiley & Sons. This book was released on 2018-06-14 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function This book addresses mathematical statistics for upper-undergraduates and first year graduate students, tying chapters on estimation, confidence intervals, hypothesis testing, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as sufficiency, exponential family distributions, and large sample properties. Mathematical Statistics: An Introduction to Likelihood Based Inference makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous examples, case studies, a large number of exercises ranging from drill and skill to extremely difficult problems, and many of the important theorems of mathematical statistics along with their proofs. In addition to the connected chapters mentioned above, Mathematical Statistics covers likelihood-based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE's and bootstrap confidence intervals. There’s also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. Prepares students with the tools needed to be successful in their future work in statistics data science Includes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage Emphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties Includes sections on Bayesian estimation and credible intervals Features examples, problems, and solutions Mathematical Statistics: An Introduction to Likelihood Based Inference is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and/or statistical inference.

The Likelihood Principle

Author : James O. Berger
Publisher : IMS
ISBN 13 : 9780940600133
Total Pages : 266 pages
Book Rating : 4.6/5 (1 download)

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Book Synopsis The Likelihood Principle by : James O. Berger

Download or read book The Likelihood Principle written by James O. Berger and published by IMS. This book was released on 1988 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tools for Statistical Inference

Author : Martin A. Tanner
Publisher : Springer Science & Business Media
ISBN 13 : 1468401920
Total Pages : 166 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Tools for Statistical Inference by : Martin A. Tanner

Download or read book Tools for Statistical Inference written by Martin A. Tanner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. In this second edition, I have attempted to expand the treatment of many of the techniques dis cussed, as well as include important topics such as the Metropolis algorithm and methods for assessing the convergence of a Markov chain algorithm. Prerequisites for this book include an understanding of mathematical statistics at the level of Bickel and Doksum (1977), some understanding of the Bayesian approach as in Box and Tiao (1973), experience with condi tional inference at the level of Cox and Snell (1989) and exposure to statistical models as found in McCullagh and Neider (1989). I have chosen not to present the proofs of convergence or rates of convergence since these proofs may require substantial background in Markov chain theory which is beyond the scope ofthis book. However, references to these proofs are given. There has been an explosion of papers in the area of Markov chain Monte Carlo in the last five years. I have attempted to identify key references - though due to the volatility of the field some work may have been missed.

Probability, Statistics, and Truth

Author : Richard Von Mises
Publisher : Courier Corporation
ISBN 13 : 0486242145
Total Pages : 273 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Probability, Statistics, and Truth by : Richard Von Mises

Download or read book Probability, Statistics, and Truth written by Richard Von Mises and published by Courier Corporation. This book was released on 1981-01-01 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.

All of Statistics

Author : Larry Wasserman
Publisher : Springer Science & Business Media
ISBN 13 : 0387217363
Total Pages : 446 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis All of Statistics by : Larry Wasserman

Download or read book All of Statistics written by Larry Wasserman and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.

Statistical Inference Based on the likelihood

Author : Adelchi Azzalini
Publisher : Routledge
ISBN 13 : 1351414461
Total Pages : 356 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Statistical Inference Based on the likelihood by : Adelchi Azzalini

Download or read book Statistical Inference Based on the likelihood written by Adelchi Azzalini and published by Routledge. This book was released on 2017-11-13 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood. Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.

Parametric Statistical Models and Likelihood

Author : Ole E Barndorff-Nielsen
Publisher : Springer Science & Business Media
ISBN 13 : 1461239346
Total Pages : 285 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Parametric Statistical Models and Likelihood by : Ole E Barndorff-Nielsen

Download or read book Parametric Statistical Models and Likelihood written by Ole E Barndorff-Nielsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a slightly revised and expanded version of a set I I I of notes used for a lecture series given at the Ecole dlEte de I Probabilites at st. Flour in August 1986. In view of the statistical nature of the material discussed herein it was agreed to publish the material as a separate volume in the statistics series rather than, as is the tradition, in a joint volume in the Lecture Notes in Mathematics Series. It is a genuine pleasure to have this opportunity to thank I I I the organizers of Les Ecoles dlEte, and in particular Professor P. -L. Hennequin, for the excellent arrangements of these Summer Schools which form a very significant forum for the exchange of scientific ideas relating to probability. The efficient, careful and patient preparation of the typescript by Oddbj~rg Wethelund is also gratefully acknowledged. Aarhus, June 1988 O. E. Barndorff-Nielsen Parametric statistical Models and Likelihood O. E. Barndorff-Nielsen o. Introduction 0. 1. Outline of contents 1 0. 2. A few preliminaries 2 1. Likelihood and auxiliary statistics 1. 1. Likelihood 4 1. 2. Moments and cumulants of log likelihood derivatives 10 1. 3. Parametrization invariance 13 1. 4. Marginal and conditional likelihood 15 * 1. 5. Combinants, auxiliaries, and the p -model 19 1. 6. Orthogonal parameters 27 1. 7. Pseudo likelihood, profile likelihood and modified 30 profile likelihood 1. 8. Ancillarity and conditionality 33 41 1. 9. Partial sufficiency and partial ancillarity 1. 10.

Confidence, Likelihood, Probability

Author : Tore Schweder
Publisher : Cambridge University Press
ISBN 13 : 0521861608
Total Pages : 521 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Confidence, Likelihood, Probability by : Tore Schweder

Download or read book Confidence, Likelihood, Probability written by Tore Schweder and published by Cambridge University Press. This book was released on 2016-02-24 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to develop a methodology of confidence distributions, with a lively mix of theory, illustrations, applications and exercises.

Probability and Statistical Inference

Author : Nitis Mukhopadhyay
Publisher : CRC Press
ISBN 13 : 1000291553
Total Pages : 694 pages
Book Rating : 4.0/5 (2 download)

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Book Synopsis Probability and Statistical Inference by : Nitis Mukhopadhyay

Download or read book Probability and Statistical Inference written by Nitis Mukhopadhyay and published by CRC Press. This book was released on 2020-08-30 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Priced very competitively compared with other textbooks at this level! This gracefully organized textbook reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, numerous figures and tables, and computer simulations to develop and illustrate concepts. Beginning wi

Statistical Information and Likelihood

Author : Dev Basu
Publisher :
ISBN 13 : 9783540967514
Total Pages : 365 pages
Book Rating : 4.9/5 (675 download)

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Book Synopsis Statistical Information and Likelihood by : Dev Basu

Download or read book Statistical Information and Likelihood written by Dev Basu and published by . This book was released on 1988 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:

In All Likelihood

Author : Yudi Pawitan
Publisher : Oxford University Press, USA
ISBN 13 : 0199671222
Total Pages : 544 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis In All Likelihood by : Yudi Pawitan

Download or read book In All Likelihood written by Yudi Pawitan and published by Oxford University Press, USA. This book was released on 2013-01-17 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces likelihood as a unifying concept in statistical modelling and inference. The complete range of concepts and applications are covered, from very simple to very complex studies. It relies on realistic examples, and presents the main results using heuristic rather than formal mathematical arguments.

Likelihood and Bayesian Inference

Author : Leonhard Held
Publisher : Springer Nature
ISBN 13 : 3662607921
Total Pages : 409 pages
Book Rating : 4.6/5 (626 download)

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Book Synopsis Likelihood and Bayesian Inference by : Leonhard Held

Download or read book Likelihood and Bayesian Inference written by Leonhard Held and published by Springer Nature. This book was released on 2020-03-31 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.

Probability and Statistical Inference

Author : Miltiadis C. Mavrakakis
Publisher : CRC Press
ISBN 13 : 131536204X
Total Pages : 444 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Probability and Statistical Inference by : Miltiadis C. Mavrakakis

Download or read book Probability and Statistical Inference written by Miltiadis C. Mavrakakis and published by CRC Press. This book was released on 2021-03-28 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Meta-analysis of Binary Data Using Profile Likelihood

Author : Dankmar Bohning
Publisher : CRC Press
ISBN 13 : 1420011332
Total Pages : 207 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Meta-analysis of Binary Data Using Profile Likelihood by : Dankmar Bohning

Download or read book Meta-analysis of Binary Data Using Profile Likelihood written by Dankmar Bohning and published by CRC Press. This book was released on 2008-03-27 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing reliable information on an intervention effect, meta-analysis is a powerful statistical tool for analyzing and combining results from individual studies. Meta-Analysis of Binary Data Using Profile Likelihood focuses on the analysis and modeling of a meta-analysis with individually pooled data (MAIPD). It presents a unifying approac