Data Analysis And Approximate Models
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Data Analysis And Approximate Models
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Author : Patrick Laurie Davies
language : en
Publisher: CRC Press
Release Date : 2014-07-07
Data Analysis And Approximate Models written by Patrick Laurie Davies and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-07 with Mathematics categories.
The First Detailed Account of Statistical Analysis That Treats Models as ApproximationsThe idea of truth plays a role in both Bayesian and frequentist statistics. The Bayesian concept of coherence is based on the fact that two different models or parameter values cannot both be true. Frequentist statistics is formulated as the problem of estimating
Mathematics Of Epidemics On Networks
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Author : István Z. Kiss
language : en
Publisher: Springer
Release Date : 2017-06-08
Mathematics Of Epidemics On Networks written by István Z. Kiss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-08 with Mathematics categories.
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve differential equation models or directly simulate epidemics on networks. Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike.
Low Rank Approximation
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Author : Ivan Markovsky
language : en
Publisher: Springer
Release Date : 2019-01-10
Low Rank Approximation written by Ivan Markovsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-10 with Technology & Engineering categories.
This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory with a range of applications from systems and control theory to psychometrics being described. Special knowledge of the application fields is not required. The second edition of /Low-Rank Approximation/ is a thoroughly edited and extensively rewritten revision. It contains new chapters and sections that introduce the topics of: • variable projection for structured low-rank approximation;• missing data estimation;• data-driven filtering and control;• stochastic model representation and identification;• identification of polynomial time-invariant systems; and• blind identification with deterministic input model. The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB^® /Octave examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis. “Each chapter is completed with a new section of exercises to which complete solutions are provided.” Low-Rank Approximation (second edition) is a broad survey of the Low-Rank Approximation theory and applications of its field which will be of direct interest to researchers in system identification, control and systems theory, numerical linear algebra and optimization. The supplementary problems and solutions render it suitable for use in teaching graduate courses in those subjects as well.
Bayesian Data Analysis Third Edition
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Author : Andrew Gelman
language : en
Publisher: CRC Press
Release Date : 2013-11-01
Bayesian Data Analysis Third Edition written by Andrew Gelman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-01 with Mathematics categories.
Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Multi State Survival Models For Interval Censored Data
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Author : Ardo van den Hout
language : en
Publisher: CRC Press
Release Date : 2016-11-25
Multi State Survival Models For Interval Censored Data written by Ardo van den Hout and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-25 with Mathematics categories.
Multi-State Survival Models for Interval-Censored Data introduces methods to describe stochastic processes that consist of transitions between states over time. It is targeted at researchers in medical statistics, epidemiology, demography, and social statistics. One of the applications in the book is a three-state process for dementia and survival in the older population. This process is described by an illness-death model with a dementia-free state, a dementia state, and a dead state. Statistical modelling of a multi-state process can investigate potential associations between the risk of moving to the next state and variables such as age, gender, or education. A model can also be used to predict the multi-state process. The methods are for longitudinal data subject to interval censoring. Depending on the definition of a state, it is possible that the time of the transition into a state is not observed exactly. However, when longitudinal data are available the transition time may be known to lie in the time interval defined by two successive observations. Such an interval-censored observation scheme can be taken into account in the statistical inference. Multi-state modelling is an elegant combination of statistical inference and the theory of stochastic processes. Multi-State Survival Models for Interval-Censored Data shows that the statistical modelling is versatile and allows for a wide range of applications.
Joint Modeling Of Longitudinal And Time To Event Data
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Author : Robert Elashoff
language : en
Publisher: CRC Press
Release Date : 2016-10-04
Joint Modeling Of Longitudinal And Time To Event Data written by Robert Elashoff and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-04 with Mathematics categories.
Longitudinal studies often incur several problems that challenge standard statistical methods for data analysis. These problems include non-ignorable missing data in longitudinal measurements of one or more response variables, informative observation times of longitudinal data, and survival analysis with intermittently measured time-dependent covariates that are subject to measurement error and/or substantial biological variation. Joint modeling of longitudinal and time-to-event data has emerged as a novel approach to handle these issues. Joint Modeling of Longitudinal and Time-to-Event Data provides a systematic introduction and review of state-of-the-art statistical methodology in this active research field. The methods are illustrated by real data examples from a wide range of clinical research topics. A collection of data sets and software for practical implementation of the joint modeling methodologies are available through the book website. This book serves as a reference book for scientific investigators who need to analyze longitudinal and/or survival data, as well as researchers developing methodology in this field. It may also be used as a textbook for a graduate level course in biostatistics or statistics.
Proceedings Of The 2nd International Conference On Mechanical System Dynamics
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Author : Xiaoting Rui
language : en
Publisher: Springer Nature
Release Date : 2024-06-18
Proceedings Of The 2nd International Conference On Mechanical System Dynamics written by Xiaoting Rui and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-18 with Science categories.
The 2nd International Conference of Mechanical System Dynamics (ICMSD2023) is devoted to “Technology Innovations by Understanding Mechanical Dynamics”, with 18 sessions to promote research in dynamic theories on complex structures, multidisciplinary integration, and advanced technologies for applications. It is held on September 1–5 in Peking University, Beijing, China. The conference is expected to provide a platform for academic researchers and engineers in the field of mechanical system dynamics to exchange scientific and technical ideas.
Dependence Modeling With Copulas
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Author : Harry Joe
language : en
Publisher: CRC Press
Release Date : 2014-06-26
Dependence Modeling With Copulas written by Harry Joe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-26 with Mathematics categories.
Dependence Modeling with Copulas covers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured facto
Missing And Modified Data In Nonparametric Estimation
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Author : Sam Efromovich
language : en
Publisher: CRC Press
Release Date : 2018-03-12
Missing And Modified Data In Nonparametric Estimation written by Sam Efromovich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-12 with Mathematics categories.
This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.
Semialgebraic Statistics And Latent Tree Models
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Author : Piotr Zwiernik
language : en
Publisher: CRC Press
Release Date : 2015-08-21
Semialgebraic Statistics And Latent Tree Models written by Piotr Zwiernik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Mathematics categories.
The first part of the book gives a general introduction to key concepts in algebraic statistics, focusing on methods that are helpful in the study of models with hidden variables. The author uses tensor geometry as a natural language to deal with multivariate probability distributions, develops new combinatorial tools to study models with hidden data, and describes the semialgebraic structure of statistical models. The second part illustrates important examples of tree models with hidden variables. The book discusses the underlying models and related combinatorial concepts of phylogenetic trees as well as the local and global geometry of latent tree models. It also extends previous results to Gaussian latent tree models. This book shows you how both combinatorics and algebraic geometry enable a better understanding of latent tree models. It contains many results on the geometry of the models, including a detailed analysis of identifiability and the defining polynomial constraints