Published December 18, 2019
Textbook - 538 Pages
ISBN 9781138492561 - CAT# K350148
Series: Chapman & Hall/CRC Texts in Statistical Science
Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research.
This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection.
The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book.
Published January 8, 2020
Textbook - 543 Pages - 204 Color Illustrations
ISBN 9780367415426 - CAT# 335692
Series: Chapman & Hall/CRC Texts in Statistical Science
Surrogates: a graduate textbook, or professional handbook, on topics at the interface between machine learning, spatial statistics, computer simulation, meta-modeling (i.e., emulation), design of experiments, and optimization. Experimentation through simulation, "human out-of-the-loop" statistical support (focusing on the science), management of dynamic processes, online and real-time analysis, automation, and practical application are at the forefront.
Gaussian process (GP) regression for flexible nonparametric and nonlinear modeling.
Applications to uncertainty quantification, sensitivity analysis, calibration of computer models to field data, sequential design/active learning and (blackbox/Bayesian) optimization under uncertainty.
Advanced topics include treed partitioning, local GP approximation, modeling of simulation experiments (e.g., agent-based models) with coupled nonlinear mean and variance (heteroskedastic) models.
Treatment appreciates historical response surface methodology (RSM) and canonical examples, but emphasizes contemporary methods and implementation in R at modern scale.
Rmarkdown facilitates a fully reproducible tour, complete with motivation from, application to, and illustration with, compelling real-data examples.
Presentation targets numerically competent practitioners in engineering, physical, and biological sciences. Writing is statistical in form, but the subjects are not about statistics. Rather, they’re about prediction and synthesis under uncertainty; about visualization and information, design and decision making, computing and clean code.
1 Historical Perspective
2 Four Motivating Datasets
3 Steepest Ascent and Ridge Analysis
4 Space-filling Design
5 Gaussian process regression
6 Model-Based Design for GPs
7 Optimization
8 Calibration and Sensitivity
9 GP Fidelity and Scale
10 Heteroskedasticity
Appendix A Numerical Linear Algebra for Fast GPs
Appendix B An Experiment Game
April 1, 2020 Forthcoming
Textbook - 576 Pages - 58 B/W Illustrations
ISBN 9781138055025 - CAT# K33231
Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists.
This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth.
Can be used as a traditional textbook as well as for self-study
Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction
Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
I. Introduction. II. Understanding Smoothness. 2. Proving Propositions. 3. Sequences of Real Numbers. 4. BolzanoWeierstrass Results. 5. Topological Compactness. 6. Function Limits. 7. Continuity. 8. Consequences of continuity of intervals. 9. Lower Semicontinuous and Convex Functions. 10. Basic Differentiability. 11. The Properties of Derivatives. 12. Consequences of Derivatives. 13. Exponential and Logarithm Functions. 14. Extremal Theory for One Variable. 15. Differentiation in R2 and R3.16. Multivariable Extremal Theory. III. Integration and Sequences of Functions. 17. Uniform Continuity. 18. Cauchy Sequences of Real Numbers. 19. Series of Real Numbers. 20. Series in Gerenal. 21. Integration Theiry. 22. Existence of Reimann Integral Theories. 23. The Fundamental Theorem of Calculus (FTOC). 24. Convergence of sequences of functions. 25. Series of Functions and Power Series. 26. Riemann Integration: Discontinuities and Compositions. 27. Fourier Series. 28. Application. IV. Summing it All Up . 29. Summary. V. References. VI. Detailed References.
April 15, 2020 Forthcoming
Textbook - 515 Pages - 56 B/W Illustrations
ISBN 9781138055056 - CAT# K33232
Basic Analysis II: A Modern Calculus in Many Variables focuses on differentiation in Rn and important concepts about mappings from Rn to Rm, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These topics converge nicely with many other important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a minimal grounding in analysis.
Can be used as a traditional textbook as well as for self-study
Suitable for undergraduates in mathematics and associated disciplines
Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
1. Beginning Remarks 2.Preliminaries 3.Vector Spaces 4.Linear Transformations 5.Symmetric Matrices 6.Continuity and Topology 7.Abstract Symmetric Matrices 8.Rotations and Orbital Mechanics 9.Determinants and Matrix Manipulations 10.Differentiability 11.Multivariable Extremal Theory 12.The Inverse and Implicit Function Theorems 13.Linear Approximation Applications 14.Integration in Multiple Dimensions 15.Change of Variables and Fubini’s Theorem 16.Line Integrals 17.Differential Forms 18.The Exponential Matrix 19.Nonlinear Parametric Optimization Theory 20.Summing It All Up. References. Index
April 21, 2020 Forthcoming
Textbook - 454 Pages - 8 B/W Illustrations
ISBN 9781138055087 - CAT# K33234
Basic Analysis III: Mappings on Infinite Dimensional Spaces is intended as a first course in abstract linear analysis. This textbook cover metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist.
Can be used as a traditional textbook as well as for self-study
Suitable for undergraduates in mathematics and associated disciplines
Emphasizes learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
I. Introduction II. Metric Spaces. 2. Metric Spaces. 3. Completing a Metric Space. III. Normed Linear Spaces. 4. Vector Spaces. 5. Normed Linear Spaces. 6. Linear Operators on Normed Spaces. IV. Inner Product Spaces. 7. Inner Product Spaces. 8. Hilbert Spaces. 9. Dual Spaces. 10. Hahn - Banach Results. 11. More About Dual Spaces. 12. Some Classical Results. V. Operators. 13. Sturm?Liouville Operators. 14. Self Adjoint Operators. VI. Topics in Applied Modeling. 15. Fields and Charges on a Set. 16. Games. VII. Summing It All Up. VIII. References. IX. Detailed Indices.
May 1, 2020 Forthcoming
Textbook - 328 Pages - 16 Color Illustrations
ISBN 9780367235994 - CAT# K422596
The first text to introduce modern topics in dynamical systems at the undergraduate level, the book integrates both theory and computer experiments into its coverage of contemporary ideas. A classic, it offers a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton's method, symbolic dynamics, the Julia set, and the Mandelbrot set. It includes biographies of some of the leading researchers in the field. The new edition offers a heavily revised chapter on chaos and an emphasis on encouraging student research and experiment. The book is accessible to readers with only a background in calculus. Many new examples and exercises and updated references.