Series: Interdisciplinary Statistics
ISBN: 9781584886303
Publication Date: 3/27/2008
Number of Pages: 208
Explores alternatives to the profile likelihood method, including approximated likelihood and multilevel models
Shows how the nonparametric profile maximum likelihood estimator can be computed via the EM algorithm with a gradient function update
Explains how to test for and determine the amount of heterogeneity in an MAIPD
Highlights the application of the software program CAMAP for analyzing an MAIPD and offers the software for free online
Illustrates the use of meta-analysis in many real-world trial examples, such as nicotine replacement therapy, cholesterol lowering, cancer treatments, respiratory tract infections, diseased cows, beta-blockers, hypertension, and tuberculosis prevention
Providing reliable information on an intervention effect, meta-analysis is a powerful statistical tool for analyzing and combining results from individual studies. Meta-Analysis of Binary Data Using Profile Likelihood focuses on the analysis and modeling of a meta-analysis with individually pooled data (MAIPD). It presents a unifying approach to modeling a treatment effect in a meta-analysis of clinical trials with binary outcomes.
After illustrating the meta-analytic situation of an MAIPD with several examples, the authors introduce the profile likelihood model and extend it to cope with unobserved heterogeneity. They describe elements of log-linear modeling, ways for finding the profile maximum likelihood estimator, and alternative approaches to the profile likelihood method. The authors also discuss how to model covariate information and unobserved heterogeneity simultaneously and use the profile likelihood method to estimate odds ratios. The final chapters look at quantifying heterogeneity in an MAIPD and show how meta-analysis can be applied to the surveillance of scrapie.
Containing new developments not available in the current literature, along with easy-to-follow inferences and algorithms, this book enables clinicians to efficiently analyze MAIPDs.
(hardback)
ISBN-13: 978-0-19-533472-2
Publication date: 24 April 2008
320 pages, 16 ht,
Series: Math Applications Series
Description
First monograph treating this subject
Proofs contain enough detail to be useful as a textbook or for personal study
Rigorous treatment with clearly present arguments
This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. There are carefully analyzed logistic type equations with boundary blow-up solutions and generalized Lane-Emden-Fowler equations or Gierer-Meinhardt systems with singular nonlinearity in anisotropic media. These nonlinear problems appear as mathematical models in various branches of Physics, Mechanics, Genetics, Economics, Engineering, and they are also relevant in Quantum Physics and Differential Geometry.
One of the main purposes of this volume is to deduce decay rates for general classes of solutions in terms of estimates of particular problems. Much of the material included in this volume is devoted to the asymptotic analysis of solutions and to the qualitative study of related bifurcation problems. Numerical approximations illustrate many abstract results of this volume. A systematic description of the most relevant singular phenomena described in these lecture notes includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity.
The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear singular phenomena
Contents
II BLOW-UP SOLUTIONS
2. Blow-up solutions for semilinear elliptic equations
3. Entire solutions blowing-up at infinity for elliptic systems
III ELLIPTIC PROBLEMS WITH SINGULAR NONLINEARITIES
4. Sublinear perturbations of singular elliptic problems
5. Bifurcation and asymptotic analysis. The monotone case
6. Bifurcation and asymptotic analysis. The nonmonotone case
7. Superlinear perturbations of singular elliptic problems
8. Stability of the solution of a singular problem
9. The influence of a nonlinear convection term in singular elliptic problems
10. Singular Gierer-Meinhardt systems
A Spectral theory for differential operators
B Implicit function theorem
C Ekeland's variational principle
D Mountain pass theorem
References
Index
Audience
Graduate students and academics in mathematics
Contents
1. Semilinear elliptic systems: existence, multiplicity, symmetry of solutions (D.G. De Figueiredo) 2. Nonlinear variational problems via the fibering method (S. Pohozaev) 3. Superlinear elliptic equations and systems (B. Ruf) 4. Nonlinear eigenvalue problem with quantization (T. Suzuki and F. Takahashi) 5. Stationary problem of Boltzmann equation (S. Ukai and T Yang) 6. Existence and stability of spikes for the Gierer-Meinhardt system (J. Wei)
Hardbound, ISBN-13: 978-0-444-53217-6, 620 pages, publication date: FEB-2008
8 Paperback books (ISBN-13: 9780521720540)
Size: 460 x 360 mm
Weight: 12.5 kg
This is a complete edition in eight volumes of all the known mathematical papers of Isaac Newton ? edited, annotated and translated by D. T. Whiteside. Papers originally in Latin are provided with accurate English translations which face the original text or in a footnote. Some of the manuscript folios are reproduced in facsimile. The commentary clarifies the peculiarities of seventeenth-century idiom and illuminates the contemporary significance of the text. Notes are printed on the page-openings to which they refer, so far as possible, and give more specific help with points of idiom and mathematical usage, recast Newtonfs arguments into modern notation, and provide references to secondary works. Paraphrases have been added to papers that are excessively abrupt. For his work on this edition, Professor Whiteside was awarded both the Alexandre Koyre Medal of the International Academy of the History of Science and the George Sarton Medal of the American History of Science Society.