Edited by: Dipak K. Dey, University of Connecticut, Storrs,
Sujit K. Ghosh, North Carolina State University, Raleigh,
and Bani K. Mallick, Texas A&M University, College StationGeneralized Linear Models A Bayesian Perspective
series: Biostatistics volume: 5
05/01/2000 In Press
Hardcover, 448 Pages, Illustrated
ISBN: 0-8247-9034-0
description:
Describes how to conceptualize, perform, and critique traditional generalized linear models (GLMs) from a Bayesian perspective and how to use modern
computational methods to summarize inferences using simulation. Describes random effects in generalized linear mixed models (GLMMs) with fully
explained examples. Advises on modeling using WinBUGS software.
Edited by: Tian-Xiao He, Illinois Wesleyan University, Bloomington, Illinois
Wavelet Analysis and Multiresolution Methods
series: Lecture Notes in Pure and Applied Mathematics volume: 212
05/01/2000 In Press
Softcover, 396 Pages, Illustrated
ISBN: 0-8247-0417-7
description:
Contains papers selected from the Wavelet Analysis and multiresolution Methods Session of the AMS meting held at the University of Illinois at
Urbana-Champaign. Covers construction, analysis, computation, and application of multiwavelets; scaling vectors; nonhomogeneous refinement;
multivariate orthogonal and biorthogonal wavelets; and more.
Charles F. Van Loan , Cornell University
Introduction to Scientific Computing: A Matrix-Vector
Approach Using MATLAB, 2/e
Published July 1999 by Engineering/Science/Mathematics
Copyright 2000, 367 pp.
Paper
ISBN 0-13-949157-0
For one-semester courses in Numerical Methods in computer science and engineering programs, and Numerical Analysis courses in mathematics programs.
Unique in content and approach, this text covers all the topics that are usually covered in an introduction to scientific computing ut folds in graphics and matrix-vector manipulation in a way that gets students to appreciate the connection between continuous mathematics and computing. Matlab 5 is used throughout to encourage experimentation, and each chapter focuses on a different important theorem llowing students to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a 塗ard・problem that involves ill-conditioning, high dimension, etc.; 2) at least one theorem with both a rigorous proof and a 菟roof by MATLAB・experiment to bolster intuition; 3) at least one recursive algorithm; and 4) at least one connection to a real-world application. The text is brief and clear enough for introductory numerical analysis students to 堵et their feet wet,・yet comprehensive enough in its treatment of problems and applications for higher-level students to develop a deeper grasp of numerical tools.
1. Power Tools of the Trade.
2. Polynomial Interpolation.
3. Piecewise Polynomial Interpolation.
4. Numerical Integration.
5. Matrix Computations.
6. Linear Systems.
7. The QR and Cholesky Factorizations.
8. Nonlinear Equations and Optimization.
9. The Initial Value Problem.
Bibliography.
Index.
James Munkres , Massachusetts Institute of Technology
Topology, 2/e
Published December 1999 by Engineering/Science/Mathematics
Copyright 2000, 537 pp.
Cloth
ISBN 0-13-181629-2
For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a
one-semester course on both general and algebraic topology or separate courses treating each topic separately.
This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses. Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences.
I. GENERAL TOPOLOGY.
1. Set Theory and Logic.
2. Topological Spaces and Continuous Functions.
3. Connectedness and Compactness.
4. Countability and Separation Axioms.
5. The Tychonoff Theorem.
6. Metrization Theorems and Paracompactness.
7. Complete Metric Spaces and Function Spaces.
8. Baire Spaces and Dimension Theory.
II. ALGEBRAIC TOPOLOGY.
9. The Fundamental Group.
10. Separation Theorems in the Plane.
11. The Seifert-van Kampen Theorem.
12. Classification of Surfaces.
13. Classification of Covering Spaces.
14. Applications to Group Theory.
Index.
G.A. Mikhailov
Parametric Estimates by the Monte Carlo Method
This monograph is devoted to the further development of parametric weight Monte Carlo estimates for solving linear and nonlinear integral equations, radiation transfer equations, and boundary value problems, including problems with random parameters. The use of these estimates leads to the construction of new, effective
Monte Carlo methods for calculating parametric multiple derivatives of solutions and for the main eigenvalues.
The book opens with an introduction on the theory of weight Monte Carlo methods. The following chapters contain new material on solving boundary value problems with complex parameters, mixed problems to parabolic equations, boundary value problems of the second and third kind, and some improved techniques
related to vector and nonlinear Helmholtz equations. Special attention is given to the foundation and optimization of the global `walk on grid' method for solving the Helmholtz difference equation. Additionally, new Monte Carlo methods for solving stochastic radiation transfer roblems are presented, including the estimation of probabilistic moments of corresponding critical parameters.
This monograph will be of value and interest to graduate and postgraduate researchers in the field of Monte Carlo methods, mathematical physics, radiation transfer theory, and statistical modelling, both in academia and industry.
Contents:
1. INTRODUCTION: WEIGHT UNBIASED MONTE CARLO ESTIMATES
Integral equations, linear functionals
Terminating Markov chains
Standard weight estimates in the Monte Carlo method, biasedness
Variances of the standard estimates
The main approaches to variance reduction
The use of recurrent representations
Randomization
Vector estimates related to the triangular system of integral equations
Calculation of parametric derivatives and the main eigenvalues of integral operators
Test integral equations and problems
The extensions of unbiasedness conditions
Approximate confidence intervals
2. PARAMETRIC ESTIMATES FOR SOLVING PROBLEMS OF MATHEMATICAL PHYSICS
Introductory information
Solving the Helmholtz equation with a complex parameter
Solution of boundary value problems of the second and third kinds
Solution of the Dirichlet problem for the vector and nonlinear Helmholtz equations
Estimating the main eigenvalue of the Laplace operator
Global algorithms of the Monte Carlo method for solving n-dimensional difference equations
3. PARAMETRIC ESTIMATES FOR STUDYING THE RADIATION TRANSFER IN INHOMOGENEOUS MEDIA
Introductory information
Calculation of parametric derivatives and critical values of parameters
Use of the averaged estimates by the Monte Carlo method for the study of the effects of medium stochasticity
- Modelling the homogeneous stochastic fields
- Partially averaged weight estimates
- Finiteness conditions for the variance of a partially averaged weight estimate
- Asymptotic estimation of the passage probability
- Test problem
- Additional remarks
Critical parameters of the particle transport process with multiplication in a stochastic medium
- Averaging the constants and the solution of the transfer equation
- Use of the diffusion approximation
- Estimation by the Monte Carlo method
- Use of the simplest mathematical models
- Use of the second order parametric derivatives
New approach to path estimates in the Monte Carlo method
Monte Carlo estimates for derivatives of polarized radiation
A. THE IMPROVEMENT OF RANDOM NUMBER GENERATORS BY MODULO 1 SUMMATION
Estimates of the nonuniformity of distributions of the congruent sums of random quantities
Congruent sums of grid random quantities
Improvement in the random number generators by congruent summation
B. ON MODELLING CHEMICAL REACTIONS BY THE MONTE CARLO METHOD
Introduction
General scheme of chemical reaction modelling by the Monte Carlo method
Conditions of coexistence of steady states in chemical systems
Calculation of quasi-potentials of dynamic systems
Examples
C. ONE UNSOLVED MINIMAX PROBLEM
References
1999; viii+188 pages
ISBN 90-6764-297-5