1st Edition - February 1, 2024
Hardback ISBN: 9780443136511
Hardback
Longitudinal Data Analysis, Volume 50 in the Handbook of Statistics series covers how data consists of a series of repeated observations of the same subjects over an extended time frame and is thus useful for measuring change. Such studies and the data arise in a variety of fields, such as health sciences, genomic studies, experimental physics, sociology, sports and student enrollment in universities. For example, in health studies, intra-subject correlation of responses must be accounted for, covariates vary with time, and bias can arise if patients drop out of the study.
Contributors in this volume include: Patrick Heagerty Peter Song Geert Verbeke Ziyue Liu Bernard Roy Frieden Damla Senturk Brian Tom You-Gan Wang Babatunde Gbadamosi Christian Geiser Bonnie Spring James Robert Carey
Product details
No. of pages: 420
Language: English
Published: February 1, 2024
IHardback ISBN: 9780443136511
Part of Cambridge Series in Statistical and Probabilistic Mathematics
Not yet published - available from January 2024
FORMAT: Hardback ISBN: 9781009305112
Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering.
Covers a wide spectrum of essential techniques and key examples in discrete probability and its applications
Largely self-contained (including an appendix on measure-theoretic foundations and a background section in each chapter) to cater for readers with different probability backgrounds
Introduces many applications in the theoretical foundations of data science, including community recovery, multi-armed bandit problems, MCMC and statistical phylogenetics
Preface
Notation
1. Introduction
2. Moments and tails
3. Martingales and potentials
4. Coupling
5. Spectral methods
6. Branching processes
A. Useful combinatorial formulas
B. Measure-theoretic foundations
Bibliography
Index.
Part of Cambridge Series in Statistical and Probabilistic Mathematics
available from February 2024
FORMAT: Hardback
ISBN: 9781009410069
An emerging field in statistics, distributional regression facilitates the modelling of the complete conditional distribution, rather than just the mean. This book introduces generalized additive models for location, scale and shape (GAMLSS) ? one of the most important classes of distributional regression. Taking a broad perspective, the authors consider penalized likelihood inference, Bayesian inference, and boosting as potential ways of estimating models and illustrate their usage in complex applications. Written by the international team who developed GAMLSS, the text's focus on practical questions and problems sets it apart. Case studies demonstrate how researchers in statistics and other data-rich disciplines can use the model in their work, exploring examples ranging from fetal ultrasounds to social media performance metrics. The R code and data sets for the case studies are available on the book's companion website, allowing for replication and further study.
Provides a comprehensive overview of the current state of Generalized Additive Models for Location, Scale and Shape (GAMLSS)
Demonstrates how GAMLSS works in practice including challenging case studies
Supplemented by a companion website with R code and case study data
Gives an integrated perspective on different inferential approaches for GAMLSS
Preface
Notation and Termanology
Part I. Introduction and Basics:
1. Distributional Regression Models
2. Distributions
3. Additive Model Terms
Part II. Statistical Inference in GAMLSS:
4. Inferential Methods
5. Penalized Maximum Likelihood Inference
6. Bayesian Inference
7. Statistical Boosting for GAMLSS
Part. III Applications and Case Studies:
8. Fetal Ultrasound
9. Speech Intelligibility Testing
10. Social Media Post Performance
11. Childhood Undernutrition in India
12. Socioeconomic Determinants of Federal Election Outcomes in Germany
13. Variable Selection for Gene Expression Data
Appendix A. Continuous Distributions
Appendix B. Discrete Distributions
Bibliography
Index.
Copyright 2024
Paperback
Hardback ISBN 9781032583396
324 Pages 43 B/W Illustrations
February 6, 2024 by Chapman & Hall
The aim of this book is to lead the reader out from the ordinary routine of computing and calculating by engaging in a more dynamic process of learning. This Learning-by-Doing Approach can be traced back to Aristotle, who wrote in his Nicomachean Ethics that gFor the things we have to learn before we can do them, we learn by doing themh.
The theory is illustrated through many relevant examples, followed by a large number of exercises whose requirements are rendered by action verbs: find, show, verify, check and construct. Readers are compelled to analyze and organize analytical skills.
Rather than placing the exercises in bulk at the end of each chapter, sets of practice questions after each theoretical concept are included. The reader has the possibility to check their understanding, work on the new topics and gain confidence during the learning activity. As the theory unfolds, the exercises become more complex ? sometimes they span over several topics. Hints have been added in order to guide the reader in the process.
This book stems from the Differential Calculus course which the author taught for many years. The goal of this book is to immerse the reader in the subtleties of Differential Calculus through an active perspective. Particular attention was paid to continuity and differentiability topics, presented in a new course of action.
Copyright 2024
Hardback ISBN 9781032666365
272 Pages
February 27, 2024 by Chapman & Hall
This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space).
The theory of normal families is more than 100 years old. It has played a seminal role in the function theory of complex variables. It was used in the first rigorous proof of the Riemann mapping theorem. It is used to study automorphism groups of domains, geometric analysis, and partial differential equations.
The theory of normal families led to the idea, in 1957, of normal functions as developed by Lehto and Virtanen. This is the natural class of functions for treating the Lindelof principle. The latter is a key idea in the boundary behavior of holomorphic functions.
This book treats normal families, normal functions, the Lindelof principle, and other related ideas. Both the analytic and the geometric approaches to the subject area are offered. The authors include many incisive examples.
The book could be used as the text for a graduate research seminar. It would also be useful reading for established researchers and for budding complex analysts.
Copyright 2024
Hardback ISBN 9780367321987
392 Pages 30 Color & 31 B/W Illustrations
February 26, 2024 by Chapman & Hall
The emergence of data science, in recent decades, has magnified the need for efficient methodology for analyzing data and highlighted the importance of statistical inference. Despite the tremendous progress that has been made, statistical science is still a young discipline and continues to have several different and competing paths in its approaches and its foundations. While the emergence of competing approaches is a natural progression of any scientific discipline, differences in the foundations of statistical inference can sometimes lead to different interpretations and conclusions from the same dataset. The increased interest in the foundations of statistical inference has led to many publications, and recent vibrant research activities in statistics, applied mathematics, philosophy and other fields of science reflect the importance of this development. The BFF approaches not only bridge foundations and scientific learning, but also facilitate objective and replicable scientific research, and provide scalable computing methodologies for the analysis of big data. Most of the published work typically focusses on a single topic or theme, and the body of work is scattered in different journals. This handbook provides a comprehensive introduction and broad overview of the key developments in the BFF schools of inference. It is intended for researchers and students who wish for an overview of foundations of inference from the BFF perspective and provides a general reference for BFF inference.
Provides a comprehensive introduction to the key developments in the BFF schools of inference.
Gives an overview of modern inferential methods, allowing scientists in other fields to expand their knowledge.
Is accessible for readers with different perspectives and backgrounds.