Author: A. W. F. Edwards

Publisher: CUP Archive

ISBN: 9780521318716

Category: Mathematics

Page: 235

View: 6489

Dr Edwards' stimulating and provocative book advances the thesis that the appropriate axiomatic basis for inductive inference is not that of probability, with its addition axiom, but rather likelihood - the concept introduced by Fisher as a measure of relative support amongst different hypotheses. Starting from the simplest considerations and assuming no more than a modest acquaintance with probability theory, the author sets out to reconstruct nothing less than a consistent theory of statistical inference in science.

Statistical Inference Based on the likelihood

Author: Adelchi Azzalini

Publisher: Routledge

ISBN: 1351414461

Category: Mathematics

Page: 352

View: 8267

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.

Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics

Author: Daniel Sorensen,Daniel Gianola

Publisher: Springer Science & Business Media

ISBN: 0387954406

Category: Science

Page: 740

View: 5288

This book, suitable for numerate biologists and for applied statisticians, provides the foundations of likelihood, Bayesian and MCMC methods in the context of genetic analysis of quantitative traits. Although a number of excellent texts in these areas have become available in recent years, the basic ideas and tools are typically described in a technically demanding style and contain much more detail than necessary. Here, an effort has been made to relate biological to statistical parameters throughout, and the book includes extensive examples that illustrate the developing argument.

Maximum Likelihood Estimation and Inference

With Examples in R, SAS and ADMB

Author: Russell B. Millar

Publisher: John Wiley & Sons

ISBN: 1119977711

Category: Mathematics

Page: 384

View: 8851

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 Estimation

Logic and Practice

Author: Scott R. Eliason

Publisher: SAGE

ISBN: 9780803941076

Category: Mathematics

Page: 87

View: 6717

In this volume the underlying logic and practice of maximum likelihood (ML) estimation is made clear by providing a general modeling framework that utilizes the tools of ML methods. This framework offers readers a flexible modeling strategy since it accommodates cases from the simplest linear models to the most complex nonlinear models that link a system of endogenous and exogenous variables with non-normal distributions. Using examples to illustrate the techniques of finding ML estimators and estimates, Eliason discusses: what properties are desirable in an estimator; basic techniques for finding ML solutions; the general form of the covariance matrix for ML estimates; the sampling distribution of ML estimators; the application of ML in the normal distribution as well as in other useful distributions; and some helpful illustrations of likelihoods.

Applied Statistical Inference

Likelihood and Bayes

Author: Leonhard Held,Daniel Sabanés Bové

Publisher: Springer Science & Business Media

ISBN: 3642378870

Category: Mathematics

Page: 376

View: 953

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.

Introductory Statistical Inference with the Likelihood Function

Author: Charles A. Rohde

Publisher: Springer

ISBN: 3319104616

Category: Medical

Page: 332

View: 1578

This textbook covers the fundamentals of statistical inference and statistical theory including Bayesian and frequentist approaches and methodology possible without excessive emphasis on the underlying mathematics. This book is about some of the basic principles of statistics that are necessary to understand and evaluate methods for analyzing complex data sets. The likelihood function is used for pure likelihood inference throughout the book. There is also coverage of severity and finite population sampling. The material was developed from an introductory statistical theory course taught by the author at the Johns Hopkins University’s Department of Biostatistics. Students and instructors in public health programs will benefit from the likelihood modeling approach that is used throughout the text. This will also appeal to epidemiologists and psychometricians. After a brief introduction, there are chapters on estimation, hypothesis testing, and maximum likelihood modeling. The book concludes with sections on Bayesian computation and inference. An appendix contains unique coverage of the interpretation of probability, and coverage of probability and mathematical concepts.

Econometric Modeling

A Likelihood Approach

Author: David F. Hendry,Bent Nielsen

Publisher: Princeton University Press

ISBN: 1400845653

Category: Business & Economics

Page: 384

View: 3369

Econometric Modeling provides a new and stimulating introduction to econometrics, focusing on modeling. The key issue confronting empirical economics is to establish sustainable relationships that are both supported by data and interpretable from economic theory. The unified likelihood-based approach of this book gives students the required statistical foundations of estimation and inference, and leads to a thorough understanding of econometric techniques. David Hendry and Bent Nielsen introduce modeling for a range of situations, including binary data sets, multiple regression, and cointegrated systems. In each setting, a statistical model is constructed to explain the observed variation in the data, with estimation and inference based on the likelihood function. Substantive issues are always addressed, showing how both statistical and economic assumptions can be tested and empirical results interpreted. Important empirical problems such as structural breaks, forecasting, and model selection are covered, and Monte Carlo simulation is explained and applied. Econometric Modeling is a self-contained introduction for advanced undergraduate or graduate students. Throughout, data illustrate and motivate the approach, and are available for computer-based teaching. Technical issues from probability theory and statistical theory are introduced only as needed. Nevertheless, the approach is rigorous, emphasizing the coherent formulation, estimation, and evaluation of econometric models relevant for empirical research.

Likeness and Likelihood in the Presocratics and Plato

Author: Jenny Bryan

Publisher: Cambridge University Press

ISBN: 0521762944

Category: History

Page: 210

View: 7449

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.

Maximum-Likelihood Deconvolution

A Journey into Model-Based Signal Processing

Author: Jerry M. Mendel

Publisher: Springer Science & Business Media

ISBN: 1461233704

Category: Technology & Engineering

Page: 227

View: 883

Convolution is the most important operation that describes the behavior of a linear time-invariant dynamical system. Deconvolution is the unraveling of convolution. It is the inverse problem of generating the system's input from knowledge about the system's output and dynamics. Deconvolution requires a careful balancing of bandwidth and signal-to-noise ratio effects. Maximum-likelihood deconvolution (MLD) is a design procedure that handles both effects. It draws upon ideas from Maximum Likelihood, when unknown parameters are random. It leads to linear and nonlinear signal processors that provide high-resolution estimates of a system's input. All aspects of MLD are described, from first principles in this book. The purpose of this volume is to explain MLD as simply as possible. To do this, the entire theory of MLD is presented in terms of a convolutional signal generating model and some relatively simple ideas from optimization theory. Earlier approaches to MLD, which are couched in the language of state-variable models and estimation theory, are unnecessary to understand the essence of MLD. MLD is a model-based signal processing procedure, because it is based on a signal model, namely the convolutional model. The book focuses on three aspects of MLD: (1) specification of a probability model for the system's measured output; (2) determination of an appropriate likelihood function; and (3) maximization of that likelihood function. Many practical algorithms are obtained. Computational aspects of MLD are described in great detail. Extensive simulations are provided, including real data applications.


Author: Anthony William Fairbank Edwards

Publisher: JHU Press

ISBN: 9780801844454

Category: Mathematics

Page: 275

View: 6414

"The book is indeed a classic. Virtually every philosopher of science now writing about probabilistic inference has been influenced by Edwards' book, and his ideas are now as alive and relevant as they were when the book first appeared. Edwards is an absolutely seminal thinker in the foundations of statistics and scientific inference."--Elliott Sober, University of Wisconsin-Madison. "Full of appropriate examples (especially from genetics) and historical commentary, this monograph offers a rare simultaneous treatment of both mathematical and philosophical foundations."--American Mathematical Monthly. This new and expanded edition of A. W. F. Edwards' classic volume on scientific inference presents his most important published articles on the subject. Edwards argues that the appropriate axiomatic basis for inductive inference is not that of probability, with its addition axiom, but that of likelihood, the concept introduced by Fisher as a measure of relative support among different hypotheses. Starting from the simplest considerations and assuming no more than a basic acquaintancewith probability theory, the author sets out to reconstruct a consistent theory of statistical inference in science. Using the likelihood approach, he explores estimation, tests of significance, randomization, experimental design, and other statistical topics. Likelihood is important reading for students and professionals in biology, mathematical sciences, and philosophy. "This book is commended to all philosophers of science who are interested in the problems of scientific inference."--Search. "This book, by a well-known geneticist, will do much to publicize the generality of the likelihood method asa foundation for statistical procedure. It is both smoothly written and persuasive."--Operations Research. "Likelihood is an important text and, in addition, is a joy to read, being a paragon of lucid and witty exposition."--Mathematical Gazette

Econometric Applications of Maximum Likelihood Methods

Author: J. S. Cramer

Publisher: CUP Archive

ISBN: 9780521378574

Category: Business & Economics

Page: 224

View: 6134

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric research papers, or with the literature on the mathematical basis of Maximum Likelihood theory. They can also try their hand at some advanced econometric research of their own.

Maximum Likelihood Estimation for Sample Surveys

Author: Raymond L. Chambers,David G. Steel,Suojin Wang,Alan Welsh

Publisher: CRC Press

ISBN: 1420011359

Category: Mathematics

Page: 391

View: 3554

Sample surveys provide data used by researchers in a large range of disciplines to analyze important relationships using well-established and widely used likelihood methods. The methods used to select samples often result in the sample differing in important ways from the target population and standard application of likelihood methods can lead to biased and inefficient estimates. Maximum Likelihood Estimation for Sample Surveys presents an overview of likelihood methods for the analysis of sample survey data that account for the selection methods used, and includes all necessary background material on likelihood inference. It covers a range of data types, including multilevel data, and is illustrated by many worked examples using tractable and widely used models. It also discusses more advanced topics, such as combining data, non-response, and informative sampling. The book presents and develops a likelihood approach for fitting models to sample survey data. It explores and explains how the approach works in tractable though widely used models for which we can make considerable analytic progress. For less tractable models numerical methods are ultimately needed to compute the score and information functions and to compute the maximum likelihood estimates of the model parameters. For these models, the book shows what has to be done conceptually to develop analyses to the point that numerical methods can be applied. Designed for statisticians who are interested in the general theory of statistics, Maximum Likelihood Estimation for Sample Surveys is also aimed at statisticians focused on fitting models to sample survey data, as well as researchers who study relationships among variables and whose sources of data include surveys.

Stochastic Geometry

Likelihood and Computation

Author: Wilfrid S. Kendall,M.N.M. van Lieshout

Publisher: CRC Press

ISBN: 9780849303968

Category: Mathematics

Page: 408

View: 6602

Stochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including: o a "crash-course" introduction to key stochastic geometry themes o considerations of geometric sampling bias issues o tesselations o shape o random sets o image analysis o spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo

The Likelihood Principle

Author: James O. Berger,Robert L. Wolpert

Publisher: IMS

ISBN: 9780940600133

Category: Mathematics

Page: 208

View: 332


Maximum Likelihood Estimation with Stata, Third Edition

Author: William Gould,Jeffrey Pitblado,William Sribney

Publisher: Stata Press

ISBN: 1597180122

Category: Computers

Page: 290

View: 3949

Maximum Likelihood Estimation with Stata, Fourth Edition is written for researchers in all disciplines who need to compute maximum likelihood estimators that are not available as prepackaged routines. Readers are presumed to be familiar with Stata, but no special programming skills are assumed except in the last few chapters, which detail how to add a new estimation command to Stata. The book begins with an introduction to the theory of maximum likelihood estimation with particular attention on the practical implications for applied work. Individual chapters then describe in detail each of the four types of likelihood evaluator programs and provide numerous examples, such as logit and probit regression, Weibull regression, random-effects linear regression, and the Cox proportional hazards model. Later chapters and appendixes provide additional details about the ml command, provide checklists to follow when writing evaluators, and show how to write your own estimation commands.

Quasi-Likelihood And Its Application

A General Approach to Optimal Parameter Estimation

Author: C. C. Heyde

Publisher: Springer Science & Business Media

ISBN: 9780387982250

Category: Mathematics

Page: 235

View: 6941

This is author-approved bcc: Quasi-likelihood is a very generally applicable estimating function based methodology for optimally estimating model parameters in systems subject to random effects. Only assumptions about means and covariances are required in contrast to the full distributional assumptions of ordinary likelihood based methodology. This monograph gives the first account in book form of all the essential features of the quasi-likelihood methodology,and stresses its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential princples rather than detailed proofs. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided. Readers are assumed to have a firm grounding in probability and statistics at the graduate level. Christopher Heyde is Professor of Statistics at both Columbia University in New York and the Australian National University in Canberra. He is also Director of the Center for Applied Probability at Columbia. He is a Fellow of the Australian Academy of Science and has been Foundation Dean of the School of Mathematical Sciences at the Australian National University and Foundation Director of the Key Centre for Statistical Sciences in Melbourne. He has served as President of the Bernoulli Society and Vice President of the International Statistical Institute and is Editor-in-Chief of the international probability journals "Journal of Applied Probability" and "Advances in Applied Probability". He has done considerable distinguished research in probability and statistics which has been honoured by the awards of the Pitman Medal (1988),Hannan Medal

Nonlinear Statistical Estimation with Numerical Maximum Likelihood

Author: Gerald Gerard Brown

Publisher: N.A


Category: Estimation theory

Page: 157

View: 9739

The topics of maximum likelihood estimation and nonlinear programming are developed thoroughly with emphasis on the numerical details of obtaining estimates from highly nonlinear models. Parametric estimation is discussed with the three parameter Weibull family of densities serving as an example. A general nonlinear programming method is discussed for both first and second order representations of the maximum likelihood estimaton, as well as a hybrid of both approaches. A new class of constrained parametric estimators is introduced with numerical methods for their determination. Structural estimation with maximum likelihood is examined, and a Bernoulli regression technique is presented.

Information Bounds and Nonparametric Maximum Likelihood Estimation

Author: P. Groeneboom,J.A. Wellner

Publisher: Springer Science & Business Media

ISBN: 9783764327941

Category: Mathematics

Page: 126

View: 4225

The book gives an account of recent developments in the theory of nonparametric and semiparametric estimation. The first part deals with information lower bounds and differentiable functionals. The second part focuses on nonparametric maximum likelihood estimators for interval censoring and deconvolution. The distribution theory of these estimators is developed and new algorithms for computing them are introduced. The models apply frequently in biostatistics and epidemiology and although they have been used as a data-analytic tool for a long time, their properties have been largely unknown. Contents: Part I. Information Bounds: 1. Models, scores, and tangent spaces • 2. Convolution and asymptotic minimax theorems • 3. Van der Vaart's Differentiability Theorem • PART II. Nonparametric Maximum Likelihood Estimation: 1. The interval censoring problem • 2. The deconvolution problem • 3. Algorithms • 4. Consistency • 5. Distribution theory • References.