Hardcover
ISBN: 9780691273891
Jun 3, 2025
Jul 29, 2025
Pages: 456
Size: 7 x 10 in. 98 b/w illus. 3 tables.
Paperback
An accessible guide to understanding statistics using simulations, with examples from a range of scientific disciplines
Real-world challenges such as small sample sizes, skewed distributions of data, biased sampling designs, and more predictors than data points are pushing the limits of classical statistical analysis. This textbook provides a new tool for the statistical toolkit: data simulations. It shows that using simulation and data-generating models is an excellent way to validate statistical reasoning and to augment study design and statistical analysis with planning and visualization. Although data simulations are not new to professional statisticians, Statistics by Simulation makes the approach accessible to a broader audience, with examples from many fields. It introduces the reasoning behind data simulation and then shows how to apply it in planning experiments or observational studies, developing analytical workflows, deploying model diagnostics, and developing new indices and statistical methods.
? Covers all steps of statistical practice, from planning projects to post-hoc analysis and model checking
? Provides examples from disciplines including sociology, psychology, ecology, economics, physics, and medicine
? Includes R code for all examples, with data and code freely available online
? Offers bullet-point outlines and summaries of each chapter
? Minimizes the use of jargon and requires only basic statistical background and skills
Preface
Acknowledgments
Part I: Propositi: Why and how to simulate
1. General Introduction
1.1 What are simulated data?
1.2 Simulated data are specific
1.3 Yes, scientists really simulate data
1.4 There are many good reasons to simulate data
1.5 Useful background knowledge to use this book most effectively
1.6 Notational conventions
1.7 Structure, organisation, and flow
1.8 Summary
2. The basics of simulating data and the need for computational competence
2.1 A road map for simulation in statistics
2.2 Two simple examples
2.3 More complex examples
2.4 Simulating autocorrelated data
2.5 Simulation versus randomisation techniques
2.6 Summary
Part II: Ante mensuram: Prospective simulations of study designs and their power
3. Think before you act
3.1 The illusion of truth: A case study
3.2 The question comes first
3.3 Setting expectations, defining hypotheses
3.4 Testing hypotheses and assessing their support
3.5 Pre-registration
3.6 Summary
4. Prospective simulation of statistical power
4.1 Simple group comparisons
4.2 How many data points do we need for a simple correlation?
4.3 Is “recruit until significant” problematic?
4.4 How long does a time series have to be?
4.5 Improving estimates: Is the experiment powerful enough?
4.6 Summary
Part III: Post mensuram: Simulations in statistical analysis
5. Assumptions: Is that one important?
5.1 Linear regression requires the data to be normally distributed
5.2 Regression models also assume that errors in predictor variables are negligible or unimportant
5.3 The intended, rather than the realised, manipulation is an admissible predictor variable
5.4 ANOVA requires homoscedasticity
5.5 Multiple testing and the inflation of false positives
5.6 Hyper-distributions in mixed-e?ect models are normal
5.7 Correlations among predictors are the same outside the range of the observed data
5.8 Summary
6. Folklore: Is that rule-of-thumb true or useful?
6.1 Model selection does not always improve interpretation
6.2 Selecting one of two correlated predictors does not mitigate collinearity in regression and machine learning
6.3 It is not OK to categorise continuous predictor variables
6.4 Use Monte Carlo simulation when data are heteroscedastic
6.5 Time series should not be detrended by default
6.6 Machine learning and Big Data do not obviate rules-of-thumb
6.7 Summary
7. Workflows and pipelines can introduce and propagate artefacts
7.1 What can we do about missing data?
7.2 Types of missing data
7.3 Imputation of missing predictors
7.4 Estimating values for censored observations
7.5 Pre-selecting predictors
7.6 Regression on residuals
7.7 Error propagation
7.8 Workflow: Stringing multiple statistical steps into an analytical pipeline
7.9 Summary
Part IV: Post exemplum: Diagnostic simulations
8. Evaluating models: How well do they really fit?
8.1 Learning from the prior
8.2 What does a model tell us, and what does it not tell us?
8.3 Visualising more complex effects: conditional, marginal, and partial plots
8.4 Model diagnostics
8.5 Predicting with confidence is not the same as confidence in prediction
8.6 Iterative learning: New priors from old posteriors
8.7 Outlook
8.8 Summary
9. Post hoc alternatives to retrospective power analysis
9.1 Reprise: Prospective power analysis
9.2 What is retrospective power analysis?
9.3 Post hoc alternatives to retrospective power analysis
9.4 Summary: Most retrospective analyses should be avoided
9.5 Coda: What would a Bayesian do instead?
Part V: In posterum: Simulations for new methods
10. Combining studies: Meta-analysis and federated analysis
10.1 Whence the data?
10.2 From meta-analysis through federated analysis to complete analysis
10.3 Meta-analysis
10.4 Individual participant-level meta-analysis
10.5 One-step federated analysis
10.6 Multi-step federated analysis
10.7 Complete data analysis
10.8 Conclusions and outlook
10.9 Summary
11. Putting it through its paces: Does this new method work?
11.1 Unit testing
11.2 Dimensional analysis
11.3 Comparisons
11.4 Intellectual advancement
11.5 Intuitive understanding
11.6 Model-agnostic number of parameters: Generalised degrees of freedom
11.7 Know your limits
11.8 Summary
12. Outroduction: How far should we push simulations?
12.1 Stochastic weather forecasting
12.2 Infusing fake signals to test the workflow at LIGO
12.3 Virtual LIDAR scanning
12.4 Advanced simulation may be neither possible nor desirable
A: Useful R functions for data simulations
A.1 Drawing random values from a distribution
A.2 Doing things repeatedly: for-loops and replicate
A.3 Shuffling, resampling, and bootstrapping: sample()
A.4 Little helpers
A.5 Dedicated simulation packages
Format: Hardback, 841 pages, height x width: 235x155 mm, 28 Illustrations, color;
6 Illustrations, black and white; X, 841 p. 34 illus., 28 illus. in color., 1 Hardback
Series: Forum for Interdisciplinary Mathematics
Pub. Date: 24-Jul-2025
ISBN-13: 9783031890024
This book is a systematic and comprehensive exposition of the state-of-the-art research results in the literature on equilibrium problems. The book describes the highest-level research and reflects a current picture of results in the literature on the three topics in a very central place of the general theory of equilibrium problems: existence, stability, and approximation, together with their particular cases, and numerous applications. It is intended to serve as both introductory and deep courses for graduate students; or as useful materials for researchers studying aspects of optimization and equilibrium problems or, more generally, working on inter-discipline such as mathematical economics, operations research and management, or even in various areas of science and technology. In providing profound knowledge of recent research, this book has advantages over existing recent books focused on equilibrium problems and variational relation problems and may also be suitable for readers preparing deep and comprehensive graduate courses.
1 Solution Existence for Scalar Equilibrium Problems.- 2 Existence of
Solutions to Scalar Quasiequilibrium Problems.- 3 Solution Existence for
Vector Equilibrium Problems.- 4 Stability of Scalar Equilibrium Problems.- 5
Stability of Scalar Quasiequilibrium Problems.- 6 Stability of Vector
Equilibrium Problems.- 7 Variational Convergence of Bifunctions and
Approximations of Equilibrium Problems.- 8 Approximations of Quasiequilibrium
Problems.- 9 Approximations of Vector Quasiequilibrium Problems.- 10
Variational Inclusion Problems and Variational Relation Problems.
Format: Hardback, 191 pages, height x width: 235x155 mm, 13 Illustrations, color; VII, 191 p. 13 illus. in color., 1 Hardback
Series: Trends in Mathematics
Pub. Date: 13-Jul-2025
ISBN-13: 9783031902390
This book is a collection of recent developments in spectral and approximation theory. The results collected here were presented at the International Conference on Spectral and Approximation Theory (ICSAT-2023) which took place at Cochin University of Science and Technology in Kerala, India. The conference ICSAT-2023 focuses on two significant areas in mathematics: spectral theory and approximation theory.
The life and work of M. N. N. Namboodiri.- On the asymptotic eigenvalue
distribution of matrices.- Singular value decomposition of unbounded
absolutely minimum attaining operators.- A note on eigenvalues and singular
values of variable Toeplitz matrices and matrix-sequences, with application
to variable two-step BDF approximations to parabolic equations.- Operators in
the Fock-Toeplitz algebra.- Wavelets on the interval: a short survey.- A
survey of collectively compact sets of operators and compact operator version
of Nayaks theorem.- Survey on the convexity of the Berezin range.- Novel
fractional wavelet frame.- On multilinear extensions of mid p-summing
operators.
Format: Hardback, 404 pages, height x width: 235x155 mm, 354 Illustrations,
color; 3 Illustrations, black and white; XX, 404 p. 357 illus., 354 illus. in color., 1
Series: Springer Series in Statistics
Pub. Date: 28-Jun-2025
ISBN-13: 9783031883644
This open access book presents robust statistical methods and procedures through the monitoring approach, with an emphasis on applications to linear regression. Illustrating the theory, it explores both large and small-sample properties. The performance of the forward search and of the monitoring of static robust estimators for regression data are illuminated through numerous data analyses using MATLAB and R.
The book describes the results of many years’ work of the authors in the development of powerful methods of robust regression analysis. Robust methods are designed to analyse contaminated data. The well-established static robust methods estimate model features, such as parameter estimates, assuming the amount of contamination in the data is known. These methods are described in detail in Chapter 2 for estimation in a simple sample. The extension to regression is presented in Chapter 3, with an emphasis on S-estimation and related procedures as well as on least trimmed squares. The monitoring methods of Chapter 4, including the forward search, find the appropriate level of robustness for each data set and so avoid biased estimation from the inclusion of outliers and inefficiency due to the deletion of uncontaminated observations. This analysis is followed by examples which illustrate the use of the interactive graphical analyses associated with the authors’ FSDA toolbox. Numerical comparisons of the size and power of outlier tests appear in Chapter 5. Later chapters illustrate applications to response transformation in regression and to non-parametric regression. Extensions of the robust multiple regression model include Bayesian, heteroskedastic, time series and compositional regression, together with the clustering of regression models. Finally, several approaches to model selection are investigated and robust analyses of regression data are presented that illustrate the use of the techniques introduced earlier.
Exercises are given at the end of each chapter, with solutions at the end of the book. The MATLAB code can be reproduced using MATLAB Online, without the need for a license, or via the language-agnostic Jupyter notebook environment, after installing the MATLAB kernel. Online computer code is available for all examples and exercises, together with a series of YouTube videos.
Aimed at professional statisticians and researchers concerned with insightful data analysis, as well as postgraduate students, the book may also serve as a text for a modern interactive robust regression course.
Preface.- Introduction and the Grand Plan.- Introduction to M-Estimation
for Univariate Samples.- Robust Estimators in Multiple Regression.- The
Monitoring Approach in Multiple Regression.- Practical Comparison of the
Different Estimators.- Transformations.- Non-parametric Regression.-
Extensions of the Multiple Regression Model.- Model selection.- Some Robust
Data Analyses.- Software and Datasets.- Solutions.- References.- Author Index.
Format: Hardback, 259 pages, height x width: 235x155 mm, 6 Illustrations,
color; 2 Illustrations, black and white; XI, 259 p. 8 illus., 6 illus. in color.,
Series: Infosys Science Foundation Series
Pub. Date: 24-Jul-2025
ISBN-13: 9789819650729
This book, Differential Geometry: Advanced Topics in CR and Pseudohermitian Geometry (Book I-D), is the fourth in a series of four books presenting a choice of advanced topics in Cauchy?Riemann (CR) and pseudohermitian geometry, such as Fefferman metrics, global behavior of tangential CR equations, Rossi spheres, the CR Yamabe problem on a CR manifold-with-boundary, Jacobi fields of the Tanaka?Webster connection, the theory of CR immersions versus Lorentzian geometry. The book also discusses boundary values of proper holomorphic maps of balls, Beltrami equations on Rossi spheres within the Koranyi?Reimann theory of quasiconformal mappings of CR manifolds, and pseudohermitian analogs to the Gauss?Ricci?Codazzi equations in the study of CR immersions between strictly pseudoconvex CR manifolds. The other three books of the series are:
Differential Geometry: Manifolds, Bundles, Characteristic Classes (Book I-A)
Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B)
Differential Geometry: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C)
The four books belong to an ampler book project, “Differential Geometry, Partial Differential Equations, and Mathematical Physics”, by the same authors and aim to demonstrate how certain portions of differential geometry (DG) and the theory of partial differential equations (PDEs) apply to general relativity and (quantum) gravity theory.
These books supply some of the ad hoc DG and PDEs machinery yet do not constitute a comprehensive treatise on DG or PDEs, but rather authors’ choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions?isometric, holomorphic, and CR?and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.
Pseudohermitian geometry.- CR manifolds with boundary.- Jacobi fields of
the Tanaka-Webster connection.- CR immersions and Lorentzian geometry.-
Proper holomorphic maps in harmonic map theory.- Beltrami equations on Rossi
sphere.- CR immersions.
Format: Hardback, 571 pages, height x width: 235x155 mm, 1 Illustrations,
color; 30 Illustrations, black and white; X, 571 p. 31 illus., 1 illus. in color., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 17-Jul-2025
ISBN-13: 9783031913020
This book, now in a revised and extended second edition, offers an in-depth account of Coxeter groups through the perspective of geometric group theory. It examines the connections between Coxeter groups and major open problems in topology related to aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer Conjectures. The book also discusses key topics in geometric group theory and topology, including Hopfs theory of ends, contractible manifolds and homology spheres, the Poincare Conjecture, and Gromovs theory of CAT(0) spaces and groups. In addition, this second edition includes new chapters on Artin groups and their Betti numbers. Written by a leading expert, the book is an authoritative reference on the subject.
Chapter 1. Introduction and preview.
Chapter 2. Some basic notions in geometric group theory.
Chapter 3. Coxeter groups.
Chapter 4. More combinatorics of Coxeter groups.
Chapter 5. The basic construction.
Chapter 6. Geometric reflection groups.
Chapter 7. The complex E.
Chapter 8. The algebraic topology of U and of E.
Chapter 9. The fundamental group and the fundamental group at infinity.
Chapter 10. Actions on manifolds.
Chapter 11. The reflection group trick.
Chapter 12. E is CAT(0).
Chapter 13. Rigidity.
Chapter 14. Free quotients and surface subgroups.
Chapter 15. Another look at (co)homology.
Chapter 16. The Euler characteristic.
Chapter 17. Growth series.
Chapter 18. Artin Groups.
Chapter 19. L2-Betti numbers of Artin groups.
Chapter 20. Buildings.
Chapter 21. Hecke - von Neumann algebras.
Chapter 22. Weighted L2- (co)homology.
Format: Hardback, 315 pages, height x width: 235x155 mm, X, 315 p., 1 Hardback
Series: Industrial and Applied Mathematics
Pub. Date: 18-Jul-2025
ISBN-13: 9789819653379
This book discusses various inverse problems for the time-fractional diffusion equation, such as inverse coefficient problems (nonlinear problems) and inverse problems for determining the right-hand sides of equations and initial functions (linear problems). The study of inverse problems requires a comprehensive investigation of direct problems (such as representation formulas, a priori estimates and differential properties of the solution). This is particularly evident in nonlinear problems, where obtaining solvability theorems necessitates careful tracking of the exact dependence of the differential properties of the solution to the direct problem on the smoothness of the coefficients and other problem data. Therefore, a significant portion of the book is devoted to direct problems, such as initial problems (Cauchy problems) and initial-boundary value problems with various boundary conditions.
Coeffcient Determination Problems with Local Boundary and
Overdetermination Conditions.- Inverse Coeffcient Problems with Nonlocal
Initial and Integral Overdetermination Conditions.- Coeffcient Determination
Problems with Cauchy and Overdetermination Conditions.- Carleman Estimate
Method in Inverse Problems for a Fractional Diffusion Equation.-
Determination of Source and Initial Functions.- Convolution Kernel
Determination Problems in Fractional Diffusion Equations.- Determining Two
Unknown Functions in a Fractional Diffusion Equation.