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Maximum Likelihood Estimation and Inference

Maximum Likelihood Estimation and Inference PDF Author: Russell B. Millar
Publisher: John Wiley & Sons
ISBN: 1119977711
Category : Mathematics
Languages : en
Pages : 286

Book Description
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 and Inference

Maximum Likelihood Estimation and Inference PDF Author: Russell B. Millar
Publisher: John Wiley & Sons
ISBN: 1119977711
Category : Mathematics
Languages : en
Pages : 286

Book Description
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.

Algebraic Statistics

Algebraic Statistics PDF Author: Seth Sullivant
Publisher: American Mathematical Society
ISBN: 1470475103
Category : Mathematics
Languages : en
Pages : 506

Book Description
Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.

Stochastic Modeling of Scientific Data

Stochastic Modeling of Scientific Data PDF Author: Peter Guttorp
Publisher: CRC Press
ISBN: 135141366X
Category : Mathematics
Languages : en
Pages : 384

Book Description
Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.

Asymptotics, Nonparametrics, and Time Series

Asymptotics, Nonparametrics, and Time Series PDF Author: Subir Ghosh
Publisher: CRC Press
ISBN: 1482269775
Category : Mathematics
Languages : en
Pages : 858

Book Description
"Contains over 2500 equations and exhaustively covers not only nonparametrics but also parametric, semiparametric, frequentist, Bayesian, bootstrap, adaptive, univariate, and multivariate statistical methods, as well as practical uses of Markov chain models."

Markov-Switching Vector Autoregressions

Markov-Switching Vector Autoregressions PDF Author: Hans-Martin Krolzig
Publisher: Springer Science & Business Media
ISBN: 364251684X
Category : Business & Economics
Languages : en
Pages : 369

Book Description
This book contributes to re cent developments on the statistical analysis of multiple time series in the presence of regime shifts. Markov-switching models have become popular for modelling non-linearities and regime shifts, mainly, in univariate eco nomic time series. This study is intended to provide a systematic and operational ap proach to the econometric modelling of dynamic systems subject to shifts in regime, based on the Markov-switching vector autoregressive model. The study presents a comprehensive analysis of the theoretical properties of Markov-switching vector autoregressive processes and the related statistical methods. The statistical concepts are illustrated with applications to empirical business cyde research. This monograph is a revised version of my dissertation which has been accepted by the Economics Department of the Humboldt-University of Berlin in 1996. It con sists mainly of unpublished material which has been presented during the last years at conferences and in seminars. The major parts of this study were written while I was supported by the Deutsche Forschungsgemeinschajt (DFG), Berliner Graduier tenkolleg Angewandte Mikroökonomik and Sondeiforschungsbereich 373 at the Free University and Humboldt-University of Berlin. Work was finally completed in the project The Econometrics of Macroeconomic Forecasting founded by the Economic and Social Research Council (ESRC) at the Institute of Economies and Statistics, University of Oxford. It is a pleasure to record my thanks to these institutions for their support of my research embodied in this study.

Martingale Methods in Statistics

Martingale Methods in Statistics PDF Author: Yoichi Nishiyama
Publisher: CRC Press
ISBN: 1351644033
Category : Mathematics
Languages : en
Pages : 215

Book Description
Martingale Methods in Statistics provides a unique introduction to statistics of stochastic processes written with the author’s strong desire to present what is not available in other textbooks. While the author chooses to omit the well-known proofs of some of fundamental theorems in martingale theory by making clear citations instead, the author does his best to describe some intuitive interpretations or concrete usages of such theorems. On the other hand, the exposition of relatively new theorems in asymptotic statistics is presented in a completely self-contained way. Some simple, easy-to-understand proofs of martingale central limit theorems are included. The potential readers include those who hope to build up mathematical bases to deal with high-frequency data in mathematical finance and those who hope to learn the theoretical background for Cox’s regression model in survival analysis. A highlight of the monograph is Chapters 8-10 dealing with Z-estimators and related topics, such as the asymptotic representation of Z-estimators, the theory of asymptotically optimal inference based on the LAN concept and the unified approach to the change point problems via "Z-process method". Some new inequalities for maxima of finitely many martingales are presented in the Appendix. Readers will find many tips for solving concrete problems in modern statistics of stochastic processes as well as in more fundamental models such as i.i.d. and Markov chain models.

Optimal Estimation of Parameters

Optimal Estimation of Parameters PDF Author: Jorma Rissanen
Publisher: Cambridge University Press
ISBN: 1107004748
Category : Computers
Languages : en
Pages : 171

Book Description
A comprehensive and consistent theory of estimation, including a description of a powerful new tool, the generalized maximum capacity estimator.

Statistical Inferences for Stochasic Processes

Statistical Inferences for Stochasic Processes PDF Author: Ishwar V. Basawa
Publisher: Elsevier
ISBN: 1483296148
Category : Mathematics
Languages : en
Pages : 455

Book Description
Stats Inference Stochasic Process

Inference in Hidden Markov Models

Inference in Hidden Markov Models PDF Author: Olivier Cappé
Publisher: Springer Science & Business Media
ISBN: 0387289828
Category : Mathematics
Languages : en
Pages : 656

Book Description
This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Many examples illustrate the algorithms and theory. This book builds on recent developments to present a self-contained view.

Fundamentals of Bioinformatics and Computational Biology

Fundamentals of Bioinformatics and Computational Biology PDF Author: Gautam B. Singh
Publisher: Springer
ISBN: 3319114034
Category : Technology & Engineering
Languages : en
Pages : 345

Book Description
This book offers comprehensive coverage of all the core topics of bioinformatics, and includes practical examples completed using the MATLAB bioinformatics toolboxTM. It is primarily intended as a textbook for engineering and computer science students attending advanced undergraduate and graduate courses in bioinformatics and computational biology. The book develops bioinformatics concepts from the ground up, starting with an introductory chapter on molecular biology and genetics. This chapter will enable physical science students to fully understand and appreciate the ultimate goals of applying the principles of information technology to challenges in biological data management, sequence analysis, and systems biology. The first part of the book also includes a survey of existing biological databases, tools that have become essential in today’s biotechnology research. The second part of the book covers methodologies for retrieving biological information, including fundamental algorithms for sequence comparison, scoring, and determining evolutionary distance. The main focus of the third part is on modeling biological sequences and patterns as Markov chains. It presents key principles for analyzing and searching for sequences of significant motifs and biomarkers. The last part of the book, dedicated to systems biology, covers phylogenetic analysis and evolutionary tree computations, as well as gene expression analysis with microarrays. In brief, the book offers the ideal hands-on reference guide to the field of bioinformatics and computational biology.