The principal focus here is on autoregressive moving average models and analogous random fields, with probabilistic and statistical questions also being discussed. The book contrasts Gaussian models with noncausal or noninvertible (nonminimum phase) non-Gaussian models and deals with problems of prediction and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. Intended as a text for gradutes in statistics, mathematics, engineering, the natural sciences and economics, the only recommendation is an initial background in probability theory and statistics. Notes on background, history and open problems are given at the end of the book.
Published by: Springer | Publication date: 09/27/2012Kindle book details: Kindle Edition, 247 pages
Here we present numerical analysis to advanced undergraduate and master degree level grad students. This is to be done in one semester. The programming language is Mathematica. The mathematical foundation and technique is included. The emphasis is geared toward the two major developing areas of applied mathematics, mathematical finance and mathematical biology.Contents:
- Linear Systems and Optimization
- Interpolating and Fitting
- Numerical Differentiation
- Numerical Integration
- Numerical Ordinary Differential Equations
- Monte Carlo Method
- Develops the topic with Mathematica. Beginning students in numerical analysis need a textbook that uses the programming language they will be using. Many universities use the programming language but few if any textbooks use it
- Includes much biologically based material, examples and exercises. Mathematical biology is currently the hottest area in Math
- Includes Monte Carlo method, FDM and numerical ODE methods. Hence suitable for a numerical analysis course in a Financial Math program, another hot topic for mathematics
- In one semester, it prepares students to take graduate level numerical analysis classes
Published by: World Scientific Publishing Company | Publication date: 08/23/2017Kindle book details: Kindle Edition, 163 pages
First derived within the context of life-testing, inverse Gaussian distribution has become one of the most important and widely employed distributions, and is often used to model the lifetimes of components. It is also used as a model in many varied applications, including fatigue analysis, economic prediction analysis, and the analysis of extreme events such as rainfall and flood levels. The interesting features and properties of this distribution make it an important and realistic model in a variety of problems across numerous disciplines.Because of the broad range of applications, this handbook will be useful not only to members of the statistical community but will also appeal to applied scientists, engineers, econometricians, and anyone who desires a thorough evaluation of this important topic.
Published by: Routledge | Publication date: 11/22/2017Kindle book details: Kindle Edition, 704 pages
Physical Sciences Data, Volume 16: Gaussian Basis Sets for Molecular Calculations provides information pertinent to the Gaussian basis sets, with emphasis on lithium, radon, and important ions. This book discusses the polarization functions prepared for lithium through radon for further improvement of the basis sets.Organized into three chapters, this volume begins with an overview of the basis set for the most stable negative and positive ions. This text then explores the total atomic energies given by the basis sets. Other chapters consider the distinction between diffuse functions and polarization function. This book presents as well the exponents of polarization function. The final chapter deals with the Gaussian basis sets.This book is a valuable resource for chemists, scientists, and research workers.
Published by: Elsevier Science | Publication date: 12/02/2012Kindle book details: Kindle Edition, 434 pages
The Gaussian Approximation Potential: An Interatomic Potential Derived from First Principles Quantum Mechanics (Springer Theses)
Simulation of materials at the atomistic level is an important tool in studying microscopic structures and processes. The atomic interactions necessary for the simulations are correctly described by Quantum Mechanics, but the size of systems and the length of processes that can be modelled are still limited. The framework of Gaussian Approximation Potentials that is developed in this thesis allows us to generate interatomic potentials automatically, based on quantum mechanical data. The resulting potentials offer several orders of magnitude faster computations, while maintaining quantum mechanical accuracy. The method has already been successfully applied for semiconductors and metals.
Published by: Springer | Publication date: 07/27/2010Kindle book details: Kindle Edition, 102 pages
Multilevel and Longitudinal Modeling Using Stata, Third Edition, by Sophia Rabe-Hesketh and Anders Skrondal, looks specifically at Stata’s treatment of generalized linear mixed models, also known as multilevel or hierarchical models. These models are “mixed” because they allow fixed and random effects, and they are “generalized” because they are appropriate for continuous Gaussian responses as well as binary, count, and other types of limited dependent variables.Volume I is devoted to continuous Gaussian linear mixed models and has nine chapters organized into four parts. The first part reviews the methods of linear regression. The second part provides in-depth coverage of two-level models, the simplest extensions of a linear regression model.Volume II is devoted to generalized linear mixed models for binary, categorical, count, and survival outcomes. The second volume has seven chapters also organized into four parts. The first three parts in volume II cover models for categorical responses, including binary, ordinal, and nominal (a new chapter); models for count data; and models for survival data, including discrete-time and continuous-time (a new chapter) survival responses. The fourth and final part in volume II describes models with nested and crossed-random effects with an emphasis on binary outcomes.
Published by: Stata Press | Publication date: 04/02/2012Kindle book details: Kindle Edition, 2 pages
Copulae in Mathematical and Quantitative Finance: Proceedings of the Workshop Held in Cracow, 10-11 July 2012: 213 (Lecture Notes in Statistics)
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 1950s, copulas have gained considerable popularity in several fields of applied mathematics, especially finance and insurance. Today, copulas represent a well-recognized tool for market and credit models, aggregation of risks, and portfolio selection. Historically, the Gaussian copula model has been one of the most common models in credit risk. However, the recent financial crisis has underlined its limitations and drawbacks. In fact, despite their simplicity, Gaussian copula models severely underestimate the risk of the occurrence of joint extreme events. Recent theoretical investigations have put new tools for detecting and estimating dependence and risk (like tail dependence, time-varying models, etc) in the spotlight. All such investigations need to be further developed and promoted, a goal this book pursues. The book includes surveys that provide an up-to-date account of essential aspects of copula models in quantitative finance, as well as the extended versions of talks selected from papers presented at the workshop in Cracow.
Published by: Springer | Publication date: 06/18/2013Kindle book details: Kindle Edition, 294 pages
Modelling and Control of Dynamic Systems Using Gaussian Process Models (Advances in Industrial Control)
This monograph opens up new horizons for engineers and researchers inacademia and in industry dealing with or interested in new developments in thefield of system identification and control. It emphasizes guidelines forworking solutions and practical advice for their implementation rather than thetheoretical background of Gaussian process (GP) models. The book demonstratesthe potential of this recent development in probabilistic machine-learningmethods and gives the reader an intuitive understanding of the topic. Thecurrent state of the art is treated along with possible future directions forresearch.Systems control design relies on mathematical models and these may bedeveloped from measurement data. This process of system identification, whenbased on GP models, can play an integral part of control design in data-basedcontrol and its description as such is an essential aspect of the text. Thebackground of GP regression is introduced first with system identification andincorporation of prior knowledge then leading into full-blown control. The bookis illustrated by extensive use of examples, line drawings, and graphicalpresentation of computer-simulation results and plant measurements. Theresearch results presented are applied in real-life case studies drawn fromsuccessful applications including:
- a gas–liquid separator control;
- urban-traffic signal modelling and reconstruction; and
- prediction of atmospheric ozone concentration.
Published by: Springer | Publication date: 11/21/2015Kindle book details: Kindle Edition, 267 pages
The fourth edition of Numerical Methods Using MATLAB® provides a clear and rigorous introduction to a wide range of numerical methods that have practical applications. The authors’ approach is to integrate MATLAB® with numerical analysis in a way which adds clarity to the numerical analysis and develops familiarity with MATLAB®. MATLAB® graphics and numerical output are used extensively to clarify complex problems and give a deeper understanding of their nature. The text provides an extensive reference providing numerous useful and important numerical algorithms that are implemented in MATLAB® to help researchers analyze a particular outcome. By using MATLAB® it is possible for the readers to tackle some large and difficult problems and deepen and consolidate their understanding of problem solving using numerical methods. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization and many other fields. The text will be a valuable aid to people working in a wide range of fields, such as engineering, science and economics.
- Features many numerical algorithms, their fundamental principles, and applications
- Includes new sections introducing Simulink, Kalman Filter, Discrete Transforms and Wavelet Analysis
- Contains some new problems and examples
- Is user-friendly and is written in a conversational and approachable style
- Contains over 60 algorithms implemented as MATLAB® functions, and over 100 MATLAB® scripts applying numerical algorithms to specific examples.
Published by: Academic Press | Publication date: 10/10/2018Kindle book details: Kindle Edition, 608 pages
JMP 14 Predictive and Specialized Modeling provides details about modeling techniques such as partitioning, neural networks, nonlinear regression, and time series analysis. Topics include the Gaussian platform, which is useful in analyzing computer simulation experiments. The book also covers the Response Screening platform, which is useful in testing the effect of a predictor when you have many responses.
Published by: SAS Institute | Publication date: 08/21/2018Kindle book details: Kindle Edition, 456 pages