Series: Springer Texts in Statistics
2014, XII, 324 p. 67 illus., 30 illus. in color.
Hardcover
ISBN 978-1-4614-8686-2
Due: November 29, 2013
No prior knowledge of R required to learn the essentials for using it with Bayesian statistics
Each chapter includes exercises that are both methodology and data-based
Important textbook for students, practitioners, and applied statisticians
This Bayesian modeling book provides a self-contained entry to computational Bayesian statistics. Focusing on the most standard statistical models and backed up by real datasets and an all-inclusive R (CRAN) package called bayess, the book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical and philosophical justifications. Readers are empowered to participate in the real-life data analysis situations depicted here from the beginning. The stakes are high and the reader determines the outcome. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. In particular, all R codes are discussed with enough detail to make them readily understandable and expandable. This works in conjunction with the bayess package.
Bayesian Essentials with R can be used as a textbook at both undergraduate and graduate levels, as exemplified by courses given at Universite Paris Dauphine (France), University of Canterbury (New Zealand), and University of British Columbia (Canada). It is particularly useful with students in professional degree programs and scientists to analyze data the Bayesian way. The text will also enhance introductory courses on Bayesian statistics. Prerequisites for the book are an undergraduate background in probability and statistics, if not in Bayesian statistics. A strength of the text is the noteworthy emphasis on the role of models in statistical analysis.
This is the new, fully-revised edition to the book Bayesian Core: A Practical Approach to Computational Bayesian Statistics.
User's Manual.- Normal Models.- Regression and Variable Selection.- Generalized Linear Models.- Capture-Recapture Experiments.- Mixture Models.- Time Series.- Image Analysis.- References.- Index
Series: Undergraduate Texts in Mathematics
2013, X, 640 p.
Hardcover
ISBN 978-3-319-02098-3
Due: November 29, 2013
Many interesting examples and exercises that are connected to real world problems balanced with well explained theory
Provides an excellent reading course for undergraduate partial differential equations
Treats both linear and nonlinear partial differential equations?
This textbook is designed for a one year course covering the fundamentals of partial differential equations, aimed towards advanced undergraduates and beginning graduate students in mathematics, science and engineering. Exercises appear at the end of almost every subsection, and come in a variety of flavors. Most exercise sets start with some straightforward computational problems to develop and reinforce the principal new techniques and ideas.?
Content Level ≫ Upper undergraduate
Keywords ≫ Complex Analysis - Dynamics of Planar Media - Eigenvalues and Eigenvectors - Finite Elements and Weak Solutions - Fourier Transforms - Linear and Nonlinear Evolution Equations
Related subjects ≫ Analysis - Dynamical Systems & Differential Equations
What are Partial Differential Equations?.- Linear and Nonlinear Waves.- Fourier Series.- Separation of Variables.- Finite Differences.- Generalized Functions and Green’s Functions.- Complex Analysis and Conformal Mapping.- Fourier Transforms.- Linear and Nonlinear Evolution Equations.- A General Framework for Linear Partial Differential Equations?.- Finite Elements and Weak Solutions.- Dynamics of Planar Media.- Partial Differential Equations in Space?.-
Series: Trends in Mathematics
2014, IV, 324 p. 47 illus., 11 illus. in color.
Hardcover I
ISBN 978-3-319-01805-8
Due: November 30, 2013
Representative collection of modern developments in the subject written by leading specialists and members of the Steering Committee of the HCAA network which united 27 universities and 51 senior researchers across the European Research Area
Acessible for both senior researchers and Ph.D. students
Highlights the results and perspectives of the future development created within the network and in collaboration with other analogous organizations
This volume highlights the main results of the research performed within the network “Harmonic and Complex Analysis and its Applications” (HCAA), which was a five-year (2007?2012) European Science Foundation Programme intended to explore and to strengthen the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. It coordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings, potential theory, Banach spaces of analytic functions and their applications to the problems of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveys written as a result of activities of the Programme and will be interesting and useful for professionals and novices in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader will undoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme.
L.D. Abreu, H.G. Feichtinger: Function spaces of polyanalytic functions.- F. Bracci, M.D. Contreras, S. Diaz-Madrigal,A. Vasil'ev: Classical and stochastic Lowner-Kufarev equations.- M. Elin, F. Jacobzon, M. Levenshtein, D. Shoikhet: The Schwarz Lemma. Rigidity and Dynamics.- H.G. Feichtinger, M. Pap: Coorbit theory and Bergman spaces.- S.J. Gardiner, T. Sjodin: Quadrature domains and their two-phase counterparts.- B. Gustafsson: Exponential transforms, resultants and moments.- M. Schlichenmaier: From the Virasoro Algebra to Krichever?Novikov Type Algebras and Beyond.
Series: Applied Mathematical Sciences, Vol. 188
2014, VIII, 287 p. 15 illus.
Hardcover
ISBN 978-1-4614-8826-2
Due: November 30, 2013
Provides a basic introduction to direct and inverse scattering theory
Introduces the main themes of the new qualitative approach to inverse scattering theory
Provides a systematic approach to the theory of transmission eigenvalues which at this time is an extremely active area of research in inverse scattering theory
Offers a basic introduction to the advanced mathematics needed to understand current research papers in inverse scattering theory
Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to the inverse scattering problem which avoids the incorrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques. These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties without making any weak scattering assumption and using essentially no a priori information on the nature of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on the use of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posed problems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an earlier book by the authors published by Springer titled Qualitative Methods in Inverse Scattering Theory
Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized and easy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to the field as well as those who could benefit from such a nice codified collection of profitable results combined in one bound volume. SIAM Review, 2006
1. Functional Analysis and Sobolev Spaces.- 2. Ill-Posed Problems.- 3. Scattering by Imperfect Conductors.- 4. Inverse Scattering Problems for Imperfect Conductors.- 5. Scattering by Orthotropic Media.- 6. Inverse Scattering Problems for Orthotropic Media.- 7. Factorization Methods.- 8. Mixed Boundary Value Problems.- 9. Inverse Spectral Problems for Transmission Eigenvalues.- 10. A Glimpse at Maxwell's Equations.
Series: Lecture Notes in Mathematics, Vol. 2098
2014, Approx. 350 p. 27 illus.
Softcover
ISBN 978-3-319-02584-1
Due: December 31, 2013
Fundamental contributions to multistatic imaging
New dictionary-matching techniques for imaging
Matlab codes for the main algorithms described in the book are provided
This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data.
In this book the trade-off between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that high-order polarization tensors provide an accurate representation of the target. Moreover, a dictionary-matching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.
Mathematical and Probabilistic Tools.- Small Volume Expansions and Concept of Generalized Polarization Tensors.- Multistatic Configuration.- Localization and Detection Algorithms.- Dictionary Matching and Tracking Algorithms.- Imaging of Extended Targets.- Invisibility.- Numerical Implementations and Results.- References.- Index.