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Multiscale Modeling : A Bayesian Perspective
The book is aimed at statisticians, applied mathematicians, and engineers working on problems dealing with multiscale processes in time and/or space, such as in engineering, finance, and environmetrics. The book will also be of interest to those working on multiscale computation research. The main prerequisites are knowledge of Bayesian statistics and basic Markov chain Monte Carlo methods. A number of real-world examples are thoroughly analyzed in order to demonstrate the methods and to assist the readers in applying these methods to their own work. To further assist readers, the authors are making source code (for R) available for many of the basic methods discussed herein.
Monte Carlo Methods in Fuzzy Optimization
This book is a concise and readable introduction to Monte Carlo methods to find good approximate solutions to fuzzy optimization problems. Various basic applications and illustrative examples are presented in an understandable way. The aim of the book is to convince the reader that Monte Carlo methods can be useful in generating approximate solutions to fuzzy optimization problems.
Monte Carlo and Quasi-Monte Carlo Methods 2006
This book represents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm (Germany) in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications, as well as providing information on current research in these very active areas. Besides covering theory, the book is an excellent resource work for practitioners as well.
Monte Carlo and Quasi-Monte Carlo Methods 2004
The proceedings include many aspects of Monte Carlo methods, quasi-Monte Carlo methods, and the numerical solution of partial differential equations.
Introduction to Bayesian Statistics
This is the second and translated edition of the German book “Einf ̈uhrung in die Bayes-Statistik, Springer-Verlag, Berlin Heidelberg New York, 2000”. It has been completely revised and numerous new developments are pointed out together with the relevant literature. The Chapter 5.2.4 is extended by the stochastic trace estimation for variance components. The new Chapter 5.2.6 presents the estimation of the regularization parameter of type Tykhonov regularization for inverse problems as the ratio of two variance components.The reconstruction and the smoothing of digital three-dimensional images is demonstrated in the new Chapter 5.3. The Chapter 6.2.1 on importance sampling for the Monte Carlo integration is rewritten to solve a more general integral. This chapter contains also the derivation of the SIR (sampling-importance-resampling) algorithm as an alternative to the rejection method for generating random samples. Markov Chain Monte Carlo methods are now frequently applied in Bayesian statistics.
Global Optimization ; Vol. # 84 : From Theory to Implementation
Global optimization describe the theory of the algorithms, whereas a given implementation’s quality never depends exclusively on the theoretical soundness of the algorithms that are implemented. The literature rarely discusses the tuning of algorithmic parameters, implementation tricks, software architectures, and the embedding of local solvers within global solvers. And yet, there are many good software implementations "out there” from which the entire community could learn something. The scope of this book is moving a few steps toward the systematization of the path that goes from the invention to the implementation and testing of a global optimization algorithm.
Finite Mixture and Markov Switching Models
The prominence of finite mixture modelling is greater than ever. Many important statistical topics like clustering data, outlier treatment, or dealing with unobserved heterogeneity involve finite mixture models in some way or other. The area of potential applications goes beyond simple data analysis and extends to regression analysis and to non-linear time series analysis using Markov switching models.It is the first time that the Bayesian perspective of finite mixture modelling is systematically presented in book form. It is argued that the Bayesian approach provides much insight in this context and is easily implemented in practice. Although the main focus is on Bayesian inference, the author reviews several frequentist techniques, especially selecting the number of components of a finite mixture model, and discusses some of their shortcomings compared to the Bayesian approach. The aim of this book is to impart the finite mixture and Markov switching approach to statistical modelling to a wide-ranging community. This includes not only statisticians, but also biologists, economists, engineers, financial agents, market researcher, medical researchers or any other frequent user of statistical models. This book should help newcomers to the field to understand how finite mixture and Markov switching models are formulated, what structures they imply on the data, what they could be used for, and how they are estimated.
Computer Algebra Recipes : An Introductory Guide to the Mathematical Models of Science
Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models. Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry.
Computational Methods in Transport ; Granlibakken 2004
Based on a series of lectures given in the Granlibakken workshop was devoted to providing a forum, where computational transport researchers could communicate their methods with their results. This book presents computational transport in mathematics, astrophysics, high energy density physics, atmospheric physics, oceanography, and plant canopies.
Computational Many-Particle Physics
Complicated many-particle problems abound in nature and in research alike. Plasma physics, statistical physics and condensed matter physics, as primary examples, are all heavily dependent on efficient methods for solving such problems. Addressing graduate students and young researchers, this book presents an overview and introduction to state-of-the-art numerical methods for studying interacting classical and quantum many-particle systems. A broad range of techniques and algorithms are covered, and emphasis is placed on their implementation on modern high-performance computers.
Le raisonnement bayésien : Modélisation et inférence = Bayesian reasoning : Modeling and inference
Describes in detail the practice of the Bayesian statistical approach using many examples chosen for their educational interest. The first part gives the general principles of statistical modeling making it possible to supervise but also to come to the aid of the imagination of the apprentice modeler. By examining examples of increasing difficulty, the reader forges the keys to building their own model. The second part presents the most useful calculation algorithms for estimating the unknowns of the model. Each inference method is presented and illustrated by numerous application cases.
Bayesian computation with R : Introduces Bayesian modeling by use of computation using the R language
R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry. Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language.
Advances in High Performance Computing and Computational Sciences ; The 1st Kazakh-German Advanced Research Workshop, Almaty, Kazakhstan, September 25 to October 1, 2005
The contributions range from computer science, mathematics and high performance computing to applications in computational fluid dynamics, combustion and industrial problems. They show a wealth of theoretical work and simulation experience with a potential of bringing together theoretical mathematical modelling and usage of high performance computing systems presenting the state of the art of computational technologies.
