Description
This volume describes how to develop Bayesian thinking, modelling
and computation both from philosophical, methodological and
application point of view. It further describes parametric and
nonparametric Bayesian methods for modelling and how to use
modern computational methods to summarize inferences using
simulation. The book covers wide range of topics including
objective and subjective Bayesian inferences with a variety of
applications in modelling categorical, survival, spatial,
spatiotemporal, Epidemiological, software reliability, small area
and micro array data. The book concludes with a chapter on how to
teach Bayesian thoughts to nonstatisticians.
Contents
Preface Contributors 1. Bayesian Inference for Casual Effects (Donald
B. Rubin) 2. Reference Analysis (Jose M. Bernardo) 3. Probability
Matching Priors (Gauri Sankar Datta and Trevor J. Sweeting) 4.
Model Selection and Hypothesis Testing Based on Objective
Probabilities and Bayes Factors (Luis Raul Pericchi) 5. Role of P-values
and other measures of evidence in Bayesian Analysis (Jayanta
Ghosh, Sumitra Purkayastha and Tapas Samanta) 6. Bayesian Model
Checking and Model Diagnostics (Hal S. Stern and Sandip Sinharay)
7. The Elimination of Nuisance Parameters (Brunero Liseo) 8.
Bayesian Estimation of Multivariate Location Parameters (Ann
Cohen Brandwein and William E. Strawdermann) 9. Bayesian
Nonparametric Modeling and Data Analysis: An Introduction (Timothy
E. Hanson, Adam J. Branscum and Wesley O. Johnson) 10. Some
Bayesian Nonparametric Models (Paul Damien) 11. Bayesian Modeling
in the Wavelet Domain (Fabrizio Ruggeri and Brani Vidakovic) 12.
Bayesian Nonparametric Inference (Stephen Walker) 13. Bayesian
Methods for Function Estimation (Nidhan Choudhuri, Subhashis
Ghosal and Anindya Roy) 14. MCMC Methods to Estimate Bayesian
Parametric Models (Antonietta Mira) 15. Bayesian Computation:
From Posterior Densities to Bayes Factors, Marginal Likelihoods,
and Posterior Model Probabilities (Ming-Hui Chen) 16. Bayesian
Modelling and Inference on Mixtures of Distributions (Jean-Michel
Marin, Kerrie Mengersen and Christian P. Robert) 17. Simulation
Based Optimal Design (Peter Muller) 18. Variable Selection and
Covariance Selection in Multivariate Regression Models (Edward
Cripps, Chris Carter and Robert Kohn) 19. Dynamic Models (Helio S.
Mignon, Dani Gamerman, Hedibert F. Lopes and Marco A.R. Ferreira)
20. Bayesian Thinking in Spatial Statistics (Lance A. Waller) 21.
Robust Bayesian Analysis (Fabrizio Ruggeri, David Rios Insua and
Jacinto Martin) 22. Elliptical Measurement Error Models - A
Bayesian Approach (Heleno Bolfarine and R.B. Arellano-Valle) 23.
Bayesian Sensitivity Analysis in Skew-elliptical Models (Ignacio
Vidal, Pilar Iglesias and Marcia Branco) 24. Bayesian Methods for
DNA Microarray Data Analysis (Veerabhadran Baladandyuthapani,
Shubhankar Ray and Bani Mallick) 25. Bayesian Biostatistics (David
B. Dunson) 26. Innovative Bayesian Methods for Biostatistics and
Epidemiology (Paul Gustafson, Shahadut Hossain and Lawrence
McCandless) 27. Bayesian Analysis of Case-Control Studies (Bhramar
Mukherjee, Samiran Sinha and Malay Ghosh) 28. Bayesian Analysis
of ROC Data (Valen E. Johnson and Timothy D. Johnson) 29.
Modeling and Analysis for Categorical Response Data (Siddhartha
Chib) 30. Bayesian Methods and Simulation-Based Computation for
Contingency Tables (James H. Albert) 31. Multiple Events Time
Data: A Bayesian Recourse (Debajyoti Sinha and Sujit K. Ghosh) 32.
Bayesian Survival Analysis for Discrete Data with Left-Truncation
and Interval Censoring (Chong Z. He and Dongchu Sun) 33. Software
Reliability (Lynn Kuo) 34. Bayesian Aspects of Small Area
Estimation (Tapabrata Maiti) 35. Teaching Bayesian Thought to
Nonstatisticians (Dalene K. Stangl) Colour Figures Subject Index
Contents of Previous Volumes
Hardbound, ISBN: 0-444-51539-9, 1062 pages, publication date:
2005
Cloth | 2005 | ISBN: 0-691-12309-8
280 pp. | 6 x 9 | 32 line illus.
A student in class asks the math teacher: "Shouldn't minus
times minus make minus?" Teachers soon convince most
students that it does not. Yet the innocent question brings with
it a germ of mathematical creativity. What happens if we
encourage that thought, odd and ungrounded though it may seem?
Few books in the field of mathematics encourage such creative
thinking. Fewer still are engagingly written and fun to read.
This book succeeds on both counts. Alberto Martinez shows us how
many of the mathematical concepts that we take for granted were
once considered contrived, imaginary, absurd, or just plain wrong.
Even today, he writes, not all parts of math correspond to
things, relations, or operations that we can actually observe or
carry out in everyday life.
Negative Math ponders such issues by exploring controversies in
the history of numbers, especially the so-called negative and
"impossible" numbers. It uses history, puzzles, and
lively debates to demonstrate how it is still possible to devise
new artificial systems of mathematical rules. In fact, the book
contends, departures from traditional rules can even be the basis
for new applications. For example, by using an algebra in which
minus times minus makes minus, mathematicians can describe curves
or trajectories that are not represented by traditional
coordinate geometry.
Clear and accessible, Negative Math expects from its readers only
a passing acquaintance with basic high school algebra. It will
prove pleasurable reading not only for those who enjoy popular
math, but also for historians, philosophers, and educators.
Table of Contents:
Figures ix
Chapter 1: Introduction 1
Chapter 2: The Problem 10
Chapter 3: History: Much Ado About Less than Nothing 18
The Search for Evident Meaning 36
Chapter 4: History: Meaningful and Meaningless Expressions 43
Impossible Numbers? 66
Chapter 5: History: Making Radically New Mathematics 80
From Hindsight to Creativity 104
Chapter 6: Math Is Rather Flexible 110
Sometimes -1 Is Greater than Zero 112
Traditional Complications 115
Can Minus Times Minus Be Minus? 131
Unity in Mathematics 166
Chapter 7: Making a Meaningful Math 174
Finding Meaning 175
Designing Numbers and Operations 186
Physical Mathematics? 220
Notes 235
Further Reading 249
Acknowledgments 259
Index 261
Series: Monographs in Mathematics, Vol. 99
2006, XII, 264 p., Hardcover
ISBN: 3-7643-2430-9
About this book
This book presents a self-contained introduction to the analytic foundation of a level set method for various surface evolution equations including curvature flow equations. These equations are important for many fields of applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set method.
Table of contents
Series: Advanced Courses in Mathematics - CRM Barcelona
2006, VI, 163 p., Softcover
ISBN: 3-7643-2182-2
About this textbook
Free loop spaces play a central role in both string topology and topological cyclic
homology, a topological version of Connes' cyclic homology.
The first part focuses on string topology and discusses the loop product from different
points of view. The second part is devoted to the construction of algebraic models for computing topological cyclic homology and starts with the study of free loop spaces.
Table of contents