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Entropy and the quantum II : Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona
The goal of the Entropy and the Quantum schools has been to introduce young researchers to some of the exciting current topics in mathematical physics. These topics often involve analytic techniques that can easily be understood with a dose of physical intuition. In March of 2010, four beautiful lectures were delivered on the campus of the University of Arizona. They included Isoperimetric Inequalities for Eigenvalues of the Laplacian by Rafael Benguria, Universality of Wigner Random Matrices by Laszlo Erdos, Kinetic Theory and the Kac Master Equation by Michael Loss, and Localization in Disordered Media by Gunter Stolz. Additionally, there were talks by other senior scientists and a number of interesting presentations by junior participants. The range of the subjects and the enthusiasm of the young speakers are testimony to the great vitality of this field, and the lecture notes in this volume reflect well the diversity of this school.
eBook
Practical applications of Bayesian reliability
Demonstrates how to solve reliability problems using practical applications of Bayesian models This self-contained reference provides fundamental knowledge of Bayesian reliability and utilizes numerous examples to show how Bayesian models can solve real life reliability problems. It teaches engineers and scientists exactly what Bayesian analysis is, what its benefits are, and how they can apply the methods to solve their own problems. To help readers get started quickly, the book presents many Bayesian models that use JAGS and which require fewer than 10 lines of command. It also offers a number of short R scripts consisting of simple functions to help them become familiar with R coding. Practical Applications of Bayesian Reliability starts by introducing basic concepts of reliability engineering, including random variables, discrete and continuous probability distributions, hazard function, and censored data. Basic concepts of Bayesian statistics, models, reasons, and theory are presented in the following chapter. Coverage of Bayesian computation, Metropolis-Hastings algorithm, and Gibbs Sampling comes next. The book then goes on to teach the concepts of design capability and design for reliability; introduce Bayesian models for estimating system reliability; discuss Bayesian Hierarchical Models and their applications; present linear and logistic regression models in Bayesian Perspective; and more.-Provides a step-by-step approach for developing advanced reliability models to solve complex problems, and does not require in-depth understanding of statistical methodology -Educates managers on the potential of Bayesian reliability models and associated impact -Introduces commonly used predictive reliability models and advanced Bayesian models based on real life applications -Includes practical guidelines to construct Bayesian reliability models along with computer codes for all of the case studies -JAGS and R codes are provided on an accompanying website to enable practitioners to easily copy them and tailor them to their own applications Practical Applications of Bayesian Reliability is a helpful book for industry practitioners such as reliability engineers, mechanical engineers, electrical engineers, product engineers, system engineers, and materials scientists whose work includes predicting design or product performance.
Book
The Theory That Would Not Die
Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.
In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years-at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.
Drawing on primary source material and interviews with statisticians and other scientists,The Theory That Would Not Dieis the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.
eBook
Bayesian statistics the fun way : understanding statistics and probability with Star Wars, LEGO, and Rubber Ducks
\"An introduction to Bayesian statistics with simple and pop culture-based explanations. Topics covered include measuring your own uncertainty in a belief, applying Bayes' theorem, and calculating distributions\"-- Provided by publisher.
Book
MetaBayesDTA: codeless Bayesian meta-analysis of test accuracy, with or without a gold standard
Background
The statistical models developed for meta-analysis of diagnostic test accuracy studies require specialised knowledge to implement. This is especially true since recent guidelines, such as those in Version 2 of the Cochrane Handbook of Systematic Reviews of Diagnostic Test Accuracy, advocate more sophisticated methods than previously. This paper describes a web-based application - MetaBayesDTA - that makes many advanced analysis methods in this area more accessible.
Results
We created the app using R, the Shiny package and Stan. It allows for a broad array of analyses based on the bivariate model including extensions for subgroup analysis, meta-regression and comparative test accuracy evaluation. It also conducts analyses not assuming a perfect reference standard, including allowing for the use of different reference tests.
Conclusions
Due to its user-friendliness and broad array of features, MetaBayesDTA should appeal to researchers with varying levels of expertise. We anticipate that the application will encourage higher levels of uptake of more advanced methods, which ultimately should improve the quality of test accuracy reviews.
Journal Article
Bayesian inference on complicated data
Due to great applications in various fields, such as social science, biomedicine, genomics, and signal processing, and the improvement of computing ability, Bayesian inference has made substantial developments for analyzing complicated data. This book introduces key ideas of Bayesian sampling methods, Bayesian estimation, and selection of the prior.
Book
A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria
We analyze a class of nonlinear partial differential equations (PDEs) defined on
eBook