Chapman and Hall/CRC 2015 352 pages
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
Hardback:
978-1-43-989880-2
25th December 2015
This book describes statistical methods for analyzing uncertainty in complex mathematical or computational models of physical systems. Such models are widely used in science and engineering?for example, climate models or cost-effectiveness models in health economics?and almost always have uncertainty in their predictions. Model users may not have all the information they need to specify values of various quantities required by the model, and models usually cannot be expected to represent the real world perfectly. This book presents methods for analyzing uncertainty within the statistical frameworks of Bayesian and Bayes linear analysis. The core of this book is the problem of analyzing uncertainty for computationally expensive models. The book uses simple examples to illustrate the methods and includes substantive case studies to highlight applications.
Introduction. Univariate Emulators. Multivariate Emulators. Design. Analysis with Univariate Emulators. Linking Models to Reality. Using Observational Data. Emulators for Stochastic Models. Case Study 1: Sensitivity Analysis in Epidemic Modelling. Case Study 2: Climate Modelling. Case Study 3: History Matching an Oil Reservoir Model.
Chapman and Hall/CRC 2015 300 pages
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
Hardback:
978-1-46-659228-5
15th December 2015
This book provides a good balance of propensity score modeling theory (particularly semiparametric methods) and applications through worked examples and software, including R and Stata code. Key topics covered include longitudinal data, survival data, survey sampling, model selection, and Bayesian aspects. The book is suitable for graduate students and researchers in statistics as well as practitioners in applied areas, such as the health, social, and behavioral sciences, and econometrics.
Introduction. Semiparametric Theory of Efficient Estimation. Propensity Score Adjustments. Inverse Probability of Treatment Weighting. Longitudinal Data. Survival Models. Bayesian Formulation.
Chapman and Hall/CRC 2016 400 pages
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
Hardback:
978-1-46-651600-7
15th January 2016
This book covers the recent advancement of statistical methods for the analysis of longitudinal data. Real datasets from four large NIH-supported longitudinal clinical trials and epidemiological studies illustrate the practical applications of the statistical methods. This book focuses on the nonparametric approaches, which have gained tremendous popularity in biomedical studies. These approaches have the flexibility to answer many scientific questions that cannot be properly addressed by the existing parametric approaches, such as the linear and nonlinear mixed effects models.
Overview of Longitudinal Analysis. Parametric and Semiparametric Methods. Nonparametric Models for Conditional-Means. Nonparametric Models with Missing. Functional Linear Models. Nonparametric Joint-Models with Survival Data. Methods for Time-Dependent and Outcome-Adaptive Covariate. Nonparametric Models for Distribution Functions. Structural Nonparametric Methods for Quantile Regression. Appendices.
This research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions.
This monograph is a sequel to the book Rational Homotopy Theory [RHT], published by Springer in 2001, but is self-contained except only that some results from [RHT] are simply quoted without proof.
Basic Definitions and Constructions
Homotopy Lie Algebras and Sullivan Lie Algebras
Fibrations and Λ-Extensions
Holonomy
The Model of the Fibre is the Fibre of the Model
Loop Spaces and Loop Space Actions
Sullivan Spaces
Examples
Lusternik-Schnirelmann Category
Depth of a Sullivan Algebra and of a Sullivan Lie Algebra
Depth of a Connected Graded Lie Algebra of Finite Type
Trichotomy
Exponential Growth
Structure of a Graded Lie Algebra of Finite Depth
Weight Decompositions of a Sullivan Lie Algebra
Problems
Readership: Researchers in algebraic topology and Lie algebra theory.
This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1?26 April 2013. It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge ? where interactions are rare between researchers from these two areas ? by highlighting the latest developments, suggesting potential new research problems, and promoting new collaborations.
It is perhaps one of the few volumes, if not only, which treats such a juxtaposition of diverse topics, emphasizing their common core at the heart of Lie theory.
Modular Representations of Finite Reductive Groups (Marc Cabanes)
?-Modular Representations of p-Adic Groups (? ≠ p) (Vincent Secherre)
p-Modular Representations of p-Adic Groups (Florian Herzig)
Representation Theory and Cohomology of Khovanov?Lauda?Rouquier Algebras (Alexander S Kleshchev)
Cyclotomic Quiver Hecke Algebras of Type A (Andrew Mathas)
Readership: Graduate students and professional mathematicians interested in modular representation theory.