Numerical Methods of Statistics
Numerical Methods of Statistics

Author: John F. Monahan

Publisher: Cambridge University Press

Published: 2011-04-18

Total Pages: 465

ISBN-13: 1139498002

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This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.

Numerical Analysis for Statisticians
Numerical Analysis for Statisticians

Author: Kenneth Lange

Publisher: Springer Science & Business Media

Published: 2010-05-17

Total Pages: 606

ISBN-13: 1441959459

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Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.

Numerical Methods for Nonlinear Estimating Equations
Numerical Methods for Nonlinear Estimating Equations

Author: Christopher G. Small

Publisher: Oxford University Press

Published: 2003

Total Pages: 330

ISBN-13: 9780198506881

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Non linearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators, and the use of root search algorithms, or one-step estimators, is a standard method of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihood's for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms, which when started at points of nonconcavity often have very poor convergence properties, and for additional flexibility proposes a number of modification to the standard methods for solving these algorithms. The book also extends beyond simple root search algorithms to include a discussion of the testing of roots for consistency, and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student.

Pattern Recognition, Tracking and Vertex Reconstruction in Particle Detectors
Pattern Recognition, Tracking and Vertex Reconstruction in Particle Detectors

Author: Rudolf Frühwirth

Publisher: Springer Nature

Published: 2021

Total Pages: 208

ISBN-13: 303065771X

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This open access book is a comprehensive review of the methods and algorithms that are used in the reconstruction of events recorded by past, running and planned experiments at particle accelerators such as the LHC, SuperKEKB and FAIR. The main topics are pattern recognition for track and vertex finding, solving the equations of motion by analytical or numerical methods, treatment of material effects such as multiple Coulomb scattering and energy loss, and the estimation of track and vertex parameters by statistical algorithms. The material covers both established methods and recent developments in these fields and illustrates them by outlining exemplary solutions developed by selected experiments. The clear presentation enables readers to easily implement the material in a high-level programming language. It also highlights software solutions that are in the public domain whenever possible. It is a valuable resource for PhD students and researchers working on online or offline reconstruction for their experiments.

Computational Methods for Numerical Analysis with R
Computational Methods for Numerical Analysis with R

Author: James P Howard, II

Publisher: CRC Press

Published: 2017-07-12

Total Pages: 257

ISBN-13: 1498723640

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Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

A Handbook of Numerical and Statistical Techniques
A Handbook of Numerical and Statistical Techniques

Author: J. H. Pollard

Publisher: CUP Archive

Published: 1977

Total Pages: 372

ISBN-13: 9780521297509

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This handbook is designed for experimental scientists, particularly those in the life sciences. It is for the non-specialist, and although it assumes only a little knowledge of statistics and mathematics, those with a deeper understanding will also find it useful. The book is directed at the scientist who wishes to solve his numerical and statistical problems on a programmable calculator, mini-computer or interactive terminal. The volume is also useful for the user of full-scale computer systems in that it describes how the large computer solves numerical and statistical problems. The book is divided into three parts. Part I deals with numerical techniques and Part II with statistical techniques. Part III is devoted to the method of least squares which can be regarded as both a statistical and numerical method. The handbook shows clearly how each calculation is performed. Each technique is illustrated by at least one example and there are worked examples and exercises throughout the volume.

Numerical Issues in Statistical Computing for the Social Scientist
Numerical Issues in Statistical Computing for the Social Scientist

Author: Micah Altman

Publisher: John Wiley & Sons

Published: 2004-02-15

Total Pages: 349

ISBN-13: 0471475742

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At last—a social scientist's guide through the pitfalls of modern statistical computing Addressing the current deficiency in the literature on statistical methods as they apply to the social and behavioral sciences, Numerical Issues in Statistical Computing for the Social Scientist seeks to provide readers with a unique practical guidebook to the numerical methods underlying computerized statistical calculations specific to these fields. The authors demonstrate that knowledge of these numerical methods and how they are used in statistical packages is essential for making accurate inferences. With the aid of key contributors from both the social and behavioral sciences, the authors have assembled a rich set of interrelated chapters designed to guide empirical social scientists through the potential minefield of modern statistical computing. Uniquely accessible and abounding in modern-day tools, tricks, and advice, the text successfully bridges the gap between the current level of social science methodology and the more sophisticated technical coverage usually associated with the statistical field. Highlights include: A focus on problems occurring in maximum likelihood estimation Integrated examples of statistical computing (using software packages such as the SAS, Gauss, Splus, R, Stata, LIMDEP, SPSS, WinBUGS, and MATLAB®) A guide to choosing accurate statistical packages Discussions of a multitude of computationally intensive statistical approaches such as ecological inference, Markov chain Monte Carlo, and spatial regression analysis Emphasis on specific numerical problems, statistical procedures, and their applications in the field Replications and re-analysis of published social science research, using innovative numerical methods Key numerical estimation issues along with the means of avoiding common pitfalls A related Web site includes test data for use in demonstrating numerical problems, code for applying the original methods described in the book, and an online bibliography of Web resources for the statistical computation Designed as an independent research tool, a professional reference, or a classroom supplement, the book presents a well-thought-out treatment of a complex and multifaceted field.

Assessment of Treatment Plant Performance and Water Quality Data: A Guide for Students, Researchers and Practitioners
Assessment of Treatment Plant Performance and Water Quality Data: A Guide for Students, Researchers and Practitioners

Author: Marcos von Sperling

Publisher: IWA Publishing

Published: 2020-01-15

Total Pages: 668

ISBN-13: 1780409311

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This book presents the basic principles for evaluating water quality and treatment plant performance in a clear, innovative and didactic way, using a combined approach that involves the interpretation of monitoring data associated with (i) the basic processes that take place in water bodies and in water and wastewater treatment plants and (ii) data management and statistical calculations to allow a deep interpretation of the data. This book is problem-oriented and works from practice to theory, covering most of the information you will need, such as (a) obtaining flow data and working with the concept of loading, (b) organizing sampling programmes and measurements, (c) connecting laboratory analysis to data management, (e) using numerical and graphical methods for describing monitoring data (descriptive statistics), (f) understanding and reporting removal efficiencies, (g) recognizing symmetry and asymmetry in monitoring data (normal and log-normal distributions), (h) evaluating compliance with targets and regulatory standards for effluents and water bodies, (i) making comparisons with the monitoring data (tests of hypothesis), (j) understanding the relationship between monitoring variables (correlation and regression analysis), (k) making water and mass balances, (l) understanding the different loading rates applied to treatment units, (m) learning the principles of reaction kinetics and reactor hydraulics and (n) performing calibration and verification of models. The major concepts are illustrated by 92 fully worked-out examples, which are supported by 75 freely-downloadable Excel spreadsheets. Each chapter concludes with a checklist for your report. If you are a student, researcher or practitioner planning to use or already using treatment plant and water quality monitoring data, then this book is for you! 75 Excel spreadsheets are available to download.