Format: Paperback / softback, 187 pages, height x width: 235x155 mm, weight: 314 g, 50 Tables, color;
50 Tables, black and white; 5 Illustrations, color; 17 Illustrations, black and white; XII, 187 p. 22 illus., 5 illus. in color.
Series: Springer Texts in Statistics
Pub. Date: 01-Nov-2023
ISBN-13: 9783031098413
Bayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data sets, this book features an operational perspective, practical relevance, and applicabilitykeeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics:
Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence.
Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law.
Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context.
Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new informationscientific evidenceought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty.
This book would be relevant to students, practitioners, and applied statisticians interested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes
Format: Paperback / softback, 924 pages, height x width: 235x155 mm, weight: 1430 g, 20 Illustrations, color;
24 Illustrations, black and white; XXVIII, 924 p. 44 illus., 20 illus. in color.,
Series: Developments in Mathematics 72
Pub. Date: 06-Nov-2023
ISBN-13: 9783031059520
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations.
Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense.
Prefacing this Series.- Statement of Main Results Concerning the
Divergence Theorem.- Examples, Counterexamples, and Additional Perspectives.-
Measure Theoretical and Topological Rudiments.- Sets of Locally Finite
Perimeter and Other Categories of Euclidean Sets.- Tools from Harmonic
Analysis.- Quasi-Metric Spaces and Spaces of Homogenous Type.- Open Sets with
Locally Finite Surface Measures and Boundary Behavior.- Proofs of Main
Results Pertaining to the Divergence Theorem.- II: Function Spaces Measuring
Size and Smoothness on Rough Sets.- Preliminary Functional Analytic Matters.-
Selected Topics in Distribution Theory.- Hardy Spaces on Ahlfors Regular
Sets.- Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors
Regular Sets.- Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets.-
Boundary Traces from Weighted Sobolev Spaces in Besov Spaces.- Besov and
Triebel-Lizorkin Spaces in Open Sets.- Strong and Weak Normal Boundary Traces
of Vector Fields in Hardy and Morney Spaces.- Sobolev Spaces on the Geometric
Measure Theoretic boundary of Sets of Locally Finite Perimeter.- III:
Integral Representations Calderon-Zygmund Theory, Fatou Theorems, and
Applications to Scattering.- Integral Representations and Integral
Identities.- Calderon-Zygmund Theory on Uniformly Rectifiable Sets.-
Quantitative Fatou-Type Theorems in Arbitrary UR Domains.- Scattering by
Rough Obstacles.- IV: Boundary Layer Potentials on Uniformly Rectifiable
Domains, and Applications to Complex Analysis.- Layer Potential Operators on
Lebesgue and Sobolev Spaces.- Layer Potential Operators on Hardy, BMO, VMO,
and Holder Spaces.- Layer Potential Operators on Calderon, Morrey-Campanato,
and Morrey Spaces.- Layer Potential Operators Acting from Boundary Besov and
Triebel-Lizorkin Spaces.- Generalized double Layers in Uniformly Rectifiable
Domains.- Green Formulas and Layer Potential Operators for the Stokes
System.- Applications to Analysis in Several Complex Variables.- V: Fredholm
Theory and Finer Estimates for Integral Operators, with Applications to
Boundary Problems.- Abstract Fredholm Theory.- Distinguished Coefficient
Tensors.- Failure of Fredholm Solvability for Weakly Elliptic Systems.-
Quantifying Global and Infinitesimal Flatness.- Norm Estimates and
Invertibility Results for SIO's on Unbounded Boundaries.- Estimating
Chord-Dot-Normal SIO's on Domains with Compact Boundaries.- The
Radon-Carleman Problem.- Fredholmness and Invertibility of Layer Potentials
on Compact Boundaries.- Green Functions and Uniqueness for Boundary Problems
for Second-Order Systems.- Green Functions and Poisson Kernels for the
Laplacian.- Boundary Value Problems for Elliptic Systems in Rough Domains.
Format: Paperback / softback, 626 pages, height x width: 235x155 mm, weight: 973 g, 1 Tables,
color; 1 Illustrations, black and white; XVI, 626 p. 1 illus.,
Pub. Date: 23-Nov-2023
ISBN-13: 9783031144615
This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis.
The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group.
The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.
- 1. Partial Sums of Vilenkin-Fourier Series in Lebesgue Spaces. -
2. Martingales and Almost Everywhere Convergence of Partial Sums of
Vilenkin-Fourier Series. - 3. Vilenkin-Fejer Means and an Approximate
Identityin Lebesgue Spaces. - 4. Norlund and T Means of Vilenkin-Fourier
Series in Lebesgue Spaces. - 5. Theory of Martingale Hardy Spaces. -
6. Vilenkin-Fourier Coefficients and Partial Sums in Martingale Hardy Spaces.
-
7. Vilenkin-Fejer Means in Martingale Hardy Spaces. - 8. Norlund and T
Means of Vilenkin-Fourier Series in Martingale Hardy Spaces. - 9. Convergence
of Vilenkin-Fourier Series in Variable Martingale Hardy Spaces. -
10. Appendix: Dyadic Group and Walsh and Kaczmarz Systems.
Format: Hardback, 108 pages, height x width: 279x210 mm, weight: 602 g, 6 Tables, color; 1 Illustrations, black and white; IX, 108 p. 1 illus.
Pub. Date: 17-Nov-2023
ISBN-13: 9783031453526
This study guide is designed for students taking a Calculus II course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes applications of integration, sequences and series and their applications, polar coordinate systems, and complex numbers. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve studentsf problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based courses
Chapter 1: Problems: Applications of integration.- Chapter 2: Solutions
of Problems: Applications of integration.- Chapter 3: Problems: Sequences and
series and their applications.- Chapter 4: Solutions of Problems: Sequences
and series and their applications.- Chapter 5: Problems: Polar coordinate
system.- Chapter 6: Solutions of Problems: Polar coordinate system.- Chapter
7: Problems: Complex numbers.- Chapter 8: Solutions of Problems: Complex
numbers.
Format: Paperback / softback, 638 pages, height x width: 235x155 mm, weight: 1015 g, XXXI, 638 p.,
Series: Bocconi & Springer Series 11
Pub. Date: 17-Nov-2023
ISBN-13: 9783031094484
The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the other hand it focuses on the techniques of stochastic integration and calculus via regularization initiated by the authors. The definitions relies on a smoothing procedure of the integrator process, they generalize the usual It? and Stratonovich integrals for Brownian motion but the integrator could also not be a semimartingale and the integrand is allowed to be anticipating. The resulting calculus requires a simple formalism: nevertheless it entails pathwise techniques even though it takes into account randomness. It allows connecting different types of pathwise and non pathwise integrals such as Young, fractional, Skorohod integrals, enlargement of filtration and rough paths. The covariation, but also high order variations, play a fundamental role in the calculus via regularization, which can also be applied for irregular integrators. A large class of Gaussian processes, various generalizations of semimartingales such that Dirichlet and weak Dirichlet processes are revisited. Stochastic calculus via regularization has been successfully used in applications, for instance in robust finance and on modeling vortex filaments in turbulence. The book is addressed to PhD students and researchers in stochastic analysis and applications to various fields.
- 1. Review on Basic Probability Theory. - 2. Processes, Brownian Motion
and Martingales. - 3. Fractional Brownian Motion and Related Processes. -
4. Stochastic Integration via Regularization. - 5. It? Integrals. -
6. Stability of the Covariation and It?s Formula. - 7. Change of probability
and martingale representation. - 8. About finite quadratic variation:
examples. - 9. Hermite Polynomials and Wiener Chaos. - 10. Elements of Wiener
Analysis. - 11. Elements of Non-causal Calculus. -
12. It? Classical
Stochastic Differential Equations. - 13. It? SDEs with Non-Lipschitz
Coefficients. - 14. FollmerDirichlet Processes. - 15. Weak Dirichlet
Processes. - Stochastic Calculus with n-Covariations. - Calculus via
Regularization and Rough Paths.
Format: Paperback / softback, 318 pages, height x width: 235x155 mm, weight: 504 g,
103 Illustrations, color; 108 Illustrations, black and white; IX, 318 p. 211 illus., 103 illus. in color.,
Series: Foundations for Undergraduate Research in Mathematics
Pub. Date: 25-Nov-2023
ISBN-13: 9783031085628
Mathematics research opportunities for undergraduate students have grown significantly in recent years, but accessible research topics for first- and second-year students with minimal experience beyond high school mathematics are still hard to find. To address this need, this volume provides beginning students with specific research projects and the tools required to tackle them. Most of these projects are accessible to students who have not yet taken Calculus, but students who know some Calculus will find plenty to do here as well. Chapters are self-contained, presenting projects students can pursue, along with essential background material and suggestions for further reading. Suggested prerequisites are noted at the beginning of each chapter. Some topics covered include:
games on graphs
modeling of biological systems
mosaics and virtual knots
mathematics for sustainable humanity
mathematical epidemiology
Mathematics Research for the Beginning Student, Volume 1 will appeal to undergraduate students at two- and four-year colleges who are interested in pursuing mathematics research projects. Faculty members interested in serving as advisors to these students will find ideas and guidance as well. This volume will also be of interest to advanced high school students interested in exploring mathematics research for the first time. A separate volume with research projects for students who have already studied calculus is also available.
Games on Graphs.- Mathematics for Sustainable Humanity--Population, Climate, Energy, Economy, Policy, and Social Justice.- Mosaics and Virtual Knots.- Graph Labelings: A Prime Area to Explore.- Acrobatics in a Parametric Arena.- But Who Should Have Won? Simulating Outcomes of Judging Protocols and Ranking Systems.- Modeling of biological systems: from algebra to calculus and computer simulations.- Population Dynamics of Infectious Diseases.- Playing with Knots.
Format: Paperback / softback, 308 pages, height x width: 235x155 mm, weight: 492 g, 1 Illustrations, black and white; IX, 308 p. 1 illus.,
Series: Foundations for Undergraduate Research in Mathematics
Pub. Date: 18-Nov-2023
ISBN-13: 9783031085666
Mathematics research opportunities for undergraduate students have grown significantly in recent years, but accessible research topics for first- and second-year students are still hard to find. To address this need, this volume provides beginning students who have already had some exposure to calculus with specific research projects and the tools required to tackle them. Chapters are self-contained, presenting projects students can pursue, along with essential background material and suggestions for further reading. In addition to calculus, some of the later chapters require prerequisites such as linear algebra and statistics. Suggested prerequisites are noted at the beginning of each chapter. Some topics covered include:
lattice walks in the plane
statistical modeling of survival data
building blocks and geometry
modeling of weather and climate change
mathematics of risk and insurance
Mathematics Research for the Beginning Student, Volume 2 will appeal to undergraduate students at two- and four-year colleges who are interested in pursuing mathematics research projects. Faculty members interested in serving as advisors to these students will find ideas and guidance as well. This volume will also be of interest to advanced high school students interested in exploring mathematics research for the first time. A separate volume with research projects for students who have not yet studied calculus is also available.
Constructible Pi and other block-based adventures in geometry.- Numerical Simulation of Arterial Blood Flow.- Statistical tools and techniques in modeling survival data.- So you want to price and invest in options?.- The Spiking Neuron.- Counting lattice walks in the plane.- The Mathematics of Host-Parasitoid Population Dynamics.- Mathematical Modeling of Weather and Climate Change.- Beyond Trends and Patterns: Importance of the Reproduction Number from Narratives to the Dynamics of Mathematical Models.- Application of Mathematics to Risk and Insurance.