Hidden Markov Models for Time Series

An Introduction Using R, Second Edition

Author: Walter Zucchini,Iain L. MacDonald,Roland Langrock

Publisher: CRC Press

ISBN: 1482253844

Category: Mathematics

Page: 370

View: 9814

Hidden Markov Models for Time Series: An Introduction Using R, Second Edition illustrates the great flexibility of hidden Markov models (HMMs) as general-purpose models for time series data. The book provides a broad understanding of the models and their uses. After presenting the basic model formulation, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference for HMMs. Through examples and applications, the authors describe how to extend and generalize the basic model so that it can be applied in a rich variety of situations. The book demonstrates how HMMs can be applied to a wide range of types of time series: continuous-valued, circular, multivariate, binary, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out the computations. Features Presents an accessible overview of HMMs Explores a variety of applications in ecology, finance, epidemiology, climatology, and sociology Includes numerous theoretical and programming exercises Provides most of the analysed data sets online New to the second edition A total of five chapters on extensions, including HMMs for longitudinal data, hidden semi-Markov models and models with continuous-valued state process New case studies on animal movement, rainfall occurrence and capture–recapture data

Nonparametric Models for Longitudinal Data

With Implementation in R

Author: Colin O. Wu,Xin Tian

Publisher: CRC Press

ISBN: 0429939086

Category: Mathematics

Page: 552

View: 9475

Nonparametric Models for Longitudinal Data with Implementations in R presents a comprehensive summary of major advances in nonparametric models and smoothing methods with longitudinal data. It covers methods, theories, and applications that are particularly useful for biomedical studies in the era of big data and precision medicine. It also provides flexible tools to describe the temporal trends, covariate effects and correlation structures of repeated measurements in longitudinal data. This book is intended for graduate students in statistics, data scientists and statisticians in biomedical sciences and public health. As experts in this area, the authors present extensive materials that are balanced between theoretical and practical topics. The statistical applications in real-life examples lead into meaningful interpretations and inferences. Features: Provides an overview of parametric and semiparametric methods Shows smoothing methods for unstructured nonparametric models Covers structured nonparametric models with time-varying coefficients Discusses nonparametric shared-parameter and mixed-effects models Presents nonparametric models for conditional distributions and functionals Illustrates implementations using R software packages Includes datasets and code in the authors’ website Contains asymptotic results and theoretical derivations Both authors are mathematical statisticians at the National Institutes of Health (NIH) and have published extensively in statistical and biomedical journals. Colin O. Wu earned his Ph.D. in statistics from the University of California, Berkeley (1990), and is also Adjunct Professor at the Georgetown University School of Medicine. He served as Associate Editor for Biometrics and Statistics in Medicine, and reviewer for National Science Foundation, NIH, and the U.S. Department of Veterans Affairs. Xin Tian earned her Ph.D. in statistics from Rutgers, the State University of New Jersey (2003). She has served on various NIH committees and collaborated extensively with clinical researchers.

Probabilistic Foundations of Statistical Network Analysis

Author: Harry Crane

Publisher: CRC Press

ISBN: 1351807331

Category: Business & Economics

Page: 236

View: 788

Probabilistic Foundations of Statistical Network Analysis presents a fresh and insightful perspective on the fundamental tenets and major challenges of modern network analysis. Its lucid exposition provides necessary background for understanding the essential ideas behind exchangeable and dynamic network models, network sampling, and network statistics such as sparsity and power law, all of which play a central role in contemporary data science and machine learning applications. The book rewards readers with a clear and intuitive understanding of the subtle interplay between basic principles of statistical inference, empirical properties of network data, and technical concepts from probability theory. Its mathematically rigorous, yet non-technical, exposition makes the book accessible to professional data scientists, statisticians, and computer scientists as well as practitioners and researchers in substantive fields. Newcomers and non-quantitative researchers will find its conceptual approach invaluable for developing intuition about technical ideas from statistics and probability, while experts and graduate students will find the book a handy reference for a wide range of new topics, including edge exchangeability, relative exchangeability, graphon and graphex models, and graph-valued Levy process and rewiring models for dynamic networks. The author’s incisive commentary supplements these core concepts, challenging the reader to push beyond the current limitations of this emerging discipline. With an approachable exposition and more than 50 open research problems and exercises with solutions, this book is ideal for advanced undergraduate and graduate students interested in modern network analysis, data science, machine learning, and statistics. Harry Crane is Associate Professor and Co-Director of the Graduate Program in Statistics and Biostatistics and an Associate Member of the Graduate Faculty in Philosophy at Rutgers University. Professor Crane’s research interests cover a range of mathematical and applied topics in network science, probability theory, statistical inference, and mathematical logic. In addition to his technical work on edge and relational exchangeability, relative exchangeability, and graph-valued Markov processes, Prof. Crane’s methods have been applied to domain-specific cybersecurity and counterterrorism problems at the Foreign Policy Research Institute and RAND’s Project AIR FORCE. ? ? ? ? ? ?

Mixed Effects Models for the Population Approach

Models, Tasks, Methods and Tools

Author: Marc Lavielle

Publisher: CRC Press

ISBN: 1482226510

Category: Mathematics

Page: 383

View: 5847

Wide-Ranging Coverage of Parametric Modeling in Linear and Nonlinear Mixed Effects Models Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools presents a rigorous framework for describing, implementing, and using mixed effects models. With these models, readers can perform parameter estimation and modeling across a whole population of individuals at the same time. Easy-to-Use Techniques and Tools for Real-World Data Modeling The book first shows how the framework allows model representation for different data types, including continuous, categorical, count, and time-to-event data. This leads to the use of generic methods, such as the stochastic approximation of the EM algorithm (SAEM), for modeling these diverse data types. The book also covers other essential methods, including Markov chain Monte Carlo (MCMC) and importance sampling techniques. The author uses publicly available software tools to illustrate modeling tasks. Methods are implemented in Monolix, and models are visually explored using Mlxplore and simulated using Simulx. Careful Balance of Mathematical Representation and Practical Implementation This book takes readers through the whole modeling process, from defining/creating a parametric model to performing tasks on the model using various mathematical methods. Statisticians and mathematicians will appreciate the rigorous representation of the models and theoretical properties of the methods while modelers will welcome the practical capabilities of the tools. The book is also useful for training and teaching in any field where population modeling occurs.

Bayesian Essentials with R

Author: Jean-Michel Marin,Christian P. Robert

Publisher: Springer Science & Business Media

ISBN: 1461486874

Category: Computers

Page: 296

View: 6589

This Bayesian modeling book provides a self-contained entry to computational Bayesian statistics. Focusing on the most standard statistical models and backed up by real datasets and an all-inclusive R (CRAN) package called bayess, the book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical and philosophical justifications. Readers are empowered to participate in the real-life data analysis situations depicted here from the beginning. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. In particular, all R codes are discussed with enough detail to make them readily understandable and expandable. Bayesian Essentials with R can be used as a textbook at both undergraduate and graduate levels. It is particularly useful with students in professional degree programs and scientists to analyze data the Bayesian way. The text will also enhance introductory courses on Bayesian statistics. Prerequisites for the book are an undergraduate background in probability and statistics, if not in Bayesian statistics.

Diagnostic Checks in Time Series

Author: Wai Keung Li

Publisher: CRC Press

ISBN: 9780203485606

Category: Mathematics

Page: 216

View: 9557

Diagnostic checking is an important step in the modeling process. But while the literature on diagnostic checks is quite extensive and many texts on time series modeling are available, it still remains difficult to find a book that adequately covers methods for performing diagnostic checks. Diagnostic Checks in Time Series helps to fill that gap. Author Wai Keung Li--one of the world's top authorities in time series modeling--concentrates on diagnostic checks for stationary time series and covers a range of different linear and nonlinear models, from various ARMA, threshold type, and bilinear models to conditional non-Gaussian and autoregressive heteroscedasticity (ARCH) models. Because of its broad applicability, the portmanteau goodness-of-fit test receives particular attention, as does the score test. Unlike most treatments, the author's approach is a practical one, and he looks at each topic through the eyes of a model builder rather than a mathematical statistician. This book brings together the widely scattered literature on the subject, and with clear explanations and focus on applications, it guides readers through the final stages of their modeling efforts. With Diagnostic Checks in Time Series, you will understand the relative merits of the models discussed, know how to estimate these models, and often find ways to improve a model.

Statistikübungen für Bachelor- und Masterstudenten

Ein Arbeitsbuch mit einer Einführung in R

Author: Fred Böker,Stefan Sperlich,Walter Zucchini

Publisher: Springer-Verlag

ISBN: 3642347886

Category: Business & Economics

Page: 378

View: 9002

Das Übungsbuch stellt eine ausgesuchte Sammlung von Problemstellungen und Lösungen bereit, die durch eine Formelsammlung mit den wichtigsten im Buch verwendeten Formeln abgerundet wird. Zusätzlich wird ein umfangreiches Set von Programmen in R zur Verfügung gestellt, die zur Aufgabenstellung und Lösung geschrieben wurden. Der Anhang des Buches beinhaltet daher auch eine kurze Einführung in die Statistik-Software R. Der Inhalt, Organisation inklusive Kapitelaufteilung orientiert sich an dem bei Springer erschienenem Werk "Statistik für Bachelor- und Masterstudenten: Eine Einführung für Wirtschafts- und Sozialwissenschaftler"


Twentieth National Conference on Artificial Intelligence (AAAI-05) : Seventeenth Innovative Applications of Artificial Intelligence Conference (IAAI-05).

Author: N.A

Publisher: N.A


Category: Artificial intelligence

Page: 1759

View: 5552

Statistik für Bachelor- und Masterstudenten

Eine Einführung für Wirtschafts- und Sozialwissenschaftler

Author: Walter Zucchini,Andreas Schlegel,Oleg Nenadic,Stefan Sperlich

Publisher: Springer-Verlag

ISBN: 3540889876

Category: Science

Page: 453

View: 9045

Das Buch führt in die wesentlichen statistischen Konzepte und Ideen ein und erläutert anhand von Beispielen detailliert deren Umsetzung. Der Stil ist, anders als bei den meisten Konkurrenzwerken, betont locker gehalten - ohne dabei auf eine exakte Darstellung zu verzichten. Das Buch ist speziell auf die Bedürfnisse von Anfängern im Fach Statistik zugeschnitten und für Bachelor- und Masterstudenten aller Disziplinen geeignet – auch zum Selbststudium.

Computational Social Network Analysis

Trends, Tools and Research Advances

Author: Kai Subel,Michel Schultz

Publisher: GRIN Verlag

ISBN: 3640733061

Category: Computers

Page: 21

View: 9697

Studienarbeit aus dem Jahr 2010 im Fachbereich Informatik - Internet, neue Technologien, Universität Hamburg, Sprache: Deutsch, Abstract: Diese Ausarbeitung befasst sich mit dem Thema Computational Soical Network Analysis. Ziel ist es, dem Leser einen Einblick in diese Thematik zu verschaffen. Dabei werden Hintergründe, anwendbare Methoden und Tools vorgestellt, die hierbei Verwendung finden. Zunächst wird dabei näher auf den Hintergrund, also warum dieses Gebiet als Forschungsgegenstand so interessant ist, eingegangen. Anschließend werden verschiedene Aspekte, die man im Rahmen der Analyse sozialer Netzwerke untersuchen kann benannt. In diesem Zusammenhang werden auch zwei verschiedene Kategorien zur formalen Analyse benannt. Zur Verdeutlichung wird die Verwendung dieser am Ende des Kapitels auch noch einmal anhand eines Praxisbeispiels gezeigt. Das nächste Kapitel befasst sich mit der Fragstellung, wie Schlüsselfiguren in Netzwerken ermittelt werden können und was für Rollen diese spielen. Dabei werden auch die verschiedenen Arten von Schlüsselfiguren benannt. Eine weitere zentrale Rolle in der Analyse sozialer Netzwerke nehmen Gruppen ein. Die Bedeutung von Gruppen und wie man sie ermitteln kann wird im nächsten Kapitel erläutert. Aufbauend auf den Gruppen sollen Interaktionen innerhalb von Netzwerken untersucht werden. Hierfür werden zunächst die nötigen Werkzeuge, wie die SCAN oder DISSECT Methode vorgestellt und anschließend die Einsatzgebiete anhand von Beispielen verdeutlicht. Im 7. Kapitel wird eine eLearning Plattform näher betrachtet. Hierbei werden zunächst die Eigenschaften und Besonderheiten von eLearning Plattformen beschrieben und anschießend anhand eines Praxisbeispiels verschiedene Methoden zur Analyse sozialer Netzwerke angewendet.

Mathematisches Denken

Vom Vergnügen am Umgang mit Zahlen

Author: T.W. Körner

Publisher: Springer-Verlag

ISBN: 3034850018

Category: Science

Page: 719

View: 7735

Dieses Buch wendet sich zuallererst an intelligente Schüler ab 14 Jahren sowie an Studienanfänger, die sich für Mathematik interessieren und etwas mehr als die Anfangsgründe dieser Wissenschaft kennenlernen möchten. Es gibt inzwischen mehrere Bücher, die eine ähnliche Zielstellung verfolgen. Besonders gern erinnere ich mich an das Werk Vom Einmaleins zum Integral von Colerus, das ich in meiner Kindheit las. Es beginnt mit der folgenden entschiedenen Feststellung: Die Mathematik ist eine Mausefalle. Wer einmal in dieser Falle gefangen sitzt, findet selten den Ausgang, der zurück in seinen vormathematischen Seelenzustand leitet. ([49], S. 7) Einige dieser Bücher sind im Anhang zusammengestellt und kommen tiert. Tatsächlich ist das Unternehmen aber so lohnenswert und die Anzahl der schon vorhandenen Bücher doch so begrenzt, daß ich mich nicht scheue, ihnen ein weiteres hinzuzufügen. An zahlreichen amerikanischen Universitäten gibt es Vorlesungen, die gemeinhin oder auch offiziell als ,,Mathematik für Schöngeister'' firmieren. Dieser Kategorie ist das vorliegende Buch nicht zuzuordnen. Statt dessen soll es sich um eine ,,Mathematik für Mathematiker'' handeln, für Mathema tiker freilich, die noch sehr wenig von der Mathematik verstehen. Weshalb aber sollte nicht der eine oder andere von ihnen eines Tages den Autor dieses 1 Buches durch seine Vorlesungen in Staunen versetzen? Ich hoffe, daß auch meine Mathematikerkollegen Freude an dem Werk haben werden, und ich würde mir wünschen, daß auch andere Leser, bei denen die Wertschätzung für die Mathematik stärker als die Furcht vor ihr ist, Gefallen an ihm finden mögen.

Dirichlet Forms and Analysis on Wiener Space

Author: Nicolas Bouleau,Francis Hirsch

Publisher: Walter de Gruyter

ISBN: 311085838X

Category: Mathematics

Page: 335

View: 2877

The subject of this book is analysis on Wiener space by means of Dirichlet forms and Malliavin calculus. There are already several literature on this topic, but this book has some different viewpoints. First the authors review the theory of Dirichlet forms, but they observe only functional analytic, potential theoretical and algebraic properties. They do not mention the relation with Markov processes or stochastic calculus as discussed in usual books (e.g. Fukushima’s book). Even on analytic properties, instead of mentioning the Beuring-Deny formula, they discuss “carré du champ” operators introduced by Meyer and Bakry very carefully. Although they discuss when this “carré du champ” operator exists in general situation, the conditions they gave are rather hard to verify, and so they verify them in the case of Ornstein-Uhlenbeck operator in Wiener space later. (It should be noticed that one can easily show the existence of “carré du champ” operator in this case by using Shigekawa’s H-derivative.) In the part on Malliavin calculus, the authors mainly discuss the absolute continuity of the probability law of Wiener functionals. The Dirichlet form corresponds to the first derivative only, and so it is not easy to consider higher order derivatives in this framework. This is the reason why they discuss only the first step of Malliavin calculus. On the other hand, they succeeded to deal with some delicate problems (the absolute continuity of the probability law of the solution to stochastic differential equations with Lipschitz continuous coefficients, the domain of stochastic integrals (Itô-Ramer-Skorokhod integrals), etc.). This book focuses on the abstract structure of Dirichlet forms and Malliavin calculus rather than their applications. However, the authors give a lot of exercises and references and they may help the reader to study other topics which are not discussed in this book. Zentralblatt Math, Reviewer: S.Kusuoka (Hongo)