In All Likelihood
In All Likelihood

Author: Yudi Pawitan

Publisher: OUP Oxford

Published: 2013-01-17

Total Pages: 626

ISBN-13: 0191650587

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Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood.

Maximum Likelihood Estimation and Inference
Maximum Likelihood Estimation and Inference

Author: Russell B. Millar

Publisher: John Wiley & Sons

Published: 2011-07-26

Total Pages: 286

ISBN-13: 1119977711

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This book takes a fresh look at the popular and well-established method of maximum likelihood for statistical estimation and inference. It begins with an intuitive introduction to the concepts and background of likelihood, and moves through to the latest developments in maximum likelihood methodology, including general latent variable models and new material for the practical implementation of integrated likelihood using the free ADMB software. Fundamental issues of statistical inference are also examined, with a presentation of some of the philosophical debates underlying the choice of statistical paradigm. Key features: Provides an accessible introduction to pragmatic maximum likelihood modelling. Covers more advanced topics, including general forms of latent variable models (including non-linear and non-normal mixed-effects and state-space models) and the use of maximum likelihood variants, such as estimating equations, conditional likelihood, restricted likelihood and integrated likelihood. Adopts a practical approach, with a focus on providing the relevant tools required by researchers and practitioners who collect and analyze real data. Presents numerous examples and case studies across a wide range of applications including medicine, biology and ecology. Features applications from a range of disciplines, with implementation in R, SAS and/or ADMB. Provides all program code and software extensions on a supporting website. Confines supporting theory to the final chapters to maintain a readable and pragmatic focus of the preceding chapters. This book is not just an accessible and practical text about maximum likelihood, it is a comprehensive guide to modern maximum likelihood estimation and inference. It will be of interest to readers of all levels, from novice to expert. It will be of great benefit to researchers, and to students of statistics from senior undergraduate to graduate level. For use as a course text, exercises are provided at the end of each chapter.

Maximum Likelihood for Social Science
Maximum Likelihood for Social Science

Author: Michael D. Ward

Publisher: Cambridge University Press

Published: 2018-11-22

Total Pages: 327

ISBN-13: 1107185823

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Practical, example-driven introduction to maximum likelihood for the social sciences. Emphasizes computation in R, model selection and interpretation.

Statistical Inference Based on the likelihood
Statistical Inference Based on the likelihood

Author: Adelchi Azzalini

Publisher: Routledge

Published: 2017-11-13

Total Pages: 356

ISBN-13: 1351414461

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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.

Empirical Likelihood
Empirical Likelihood

Author: Art B. Owen

Publisher: CRC Press

Published: 2001-05-18

Total Pages: 322

ISBN-13: 1420036157

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Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It al

Statistical Evidence
Statistical Evidence

Author: Richard Royall

Publisher: Routledge

Published: 2017-11-22

Total Pages: 191

ISBN-13: 1351414569

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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.

Confidence, Likelihood, Probability
Confidence, Likelihood, Probability

Author: Tore Schweder

Publisher: Cambridge University Press

Published: 2016-02-24

Total Pages: 521

ISBN-13: 1316445054

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This lively book lays out a methodology of confidence distributions and puts them through their paces. Among other merits, they lead to optimal combinations of confidence from different sources of information, and they can make complex models amenable to objective and indeed prior-free analysis for less subjectively inclined statisticians. The generous mixture of theory, illustrations, applications and exercises is suitable for statisticians at all levels of experience, as well as for data-oriented scientists. Some confidence distributions are less dispersed than their competitors. This concept leads to a theory of risk functions and comparisons for distributions of confidence. Neyman–Pearson type theorems leading to optimal confidence are developed and richly illustrated. Exact and optimal confidence distribution is the gold standard for inferred epistemic distributions. Confidence distributions and likelihood functions are intertwined, allowing prior distributions to be made part of the likelihood. Meta-analysis in likelihood terms is developed and taken beyond traditional methods, suiting it in particular to combining information across diverse data sources.

Likeness and Likelihood in the Presocratics and Plato
Likeness and Likelihood in the Presocratics and Plato

Author: Jenny Bryan

Publisher: Cambridge University Press

Published: 2012

Total Pages: 219

ISBN-13: 0521762944

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Studies the philosophical development of the meaning of the Greek word eoikos, which can be used to describe similarity, plausibility or even suitability. It focuses on Xenophanes, Parmenides and Plato's Timaeus and shows how such a study serves to enhance our understanding of their epistemology and methodology.