STATISTICAL SIMULATION POWER METHOD POLYNOMIALS AND OTHER TRANSFORMATIONS

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Statistical Simulation

Author : Todd C. Headrick
ISBN : 1420064916
Genre : Mathematics
File Size : 52.30 MB
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Although power method polynomials based on the standard normal distributions have been used in many different contexts for the past 30 years, it was not until recently that the probability density function (pdf) and cumulative distribution function (cdf) were derived and made available. Focusing on both univariate and multivariate nonnormal data generation, Statistical Simulation: Power Method Polynomials and Other Transformations presents techniques for conducting a Monte Carlo simulation study. It shows how to use power method polynomials for simulating univariate and multivariate nonnormal distributions with specified cumulants and correlation matrices. The book first explores the methodology underlying the power method, before demonstrating this method through examples of standard normal, logistic, and uniform power method pdfs. It also discusses methods for improving the performance of a simulation based on power method polynomials. The book then develops simulation procedures for systems of linear statistical models, intraclass correlation coefficients, and correlated continuous variates and ranks. Numerical examples and results from Monte Carlo simulations illustrate these procedures. The final chapter describes how the g-and-h and generalized lambda distribution (GLD) transformations are special applications of the more general multivariate nonnormal data generation approach. Throughout the text, the author employs Mathematica® in a range of procedures and offers the source code for download online. Written by a longtime researcher of the power method, this book explains how to simulate nonnormal distributions via easy-to-use power method polynomials. By using the methodology and techniques developed in the text, readers can evaluate different transformations in terms of comparing percentiles, measures of central tendency, goodness-of-fit tests, and more.
Category: Mathematics

Monte Carlo Simulation Based Statistical Modeling

Author : Ding-Geng (Din) Chen
ISBN : 9789811033070
Genre : Medical
File Size : 46.39 MB
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This book brings together expert researchers engaged in Monte-Carlo simulation-based statistical modeling, offering them a forum to present and discuss recent issues in methodological development as well as public health applications. It is divided into three parts, with the first providing an overview of Monte-Carlo techniques, the second focusing on missing data Monte-Carlo methods, and the third addressing Bayesian and general statistical modeling using Monte-Carlo simulations. The data and computer programs used here will also be made publicly available, allowing readers to replicate the model development and data analysis presented in each chapter, and to readily apply them in their own research. Featuring highly topical content, the book has the potential to impact model development and data analyses across a wide spectrum of fields, and to spark further research in this direction.
Category: Medical

Simulating Data With Sas

Author : Rick Wicklin
ISBN : 9781629592534
Genre : Mathematics
File Size : 90.37 MB
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Data simulation is a fundamental technique in statistical programming and research. Rick Wicklin's Simulating Data with SAS brings together the most useful algorithms and the best programming techniques for efficient data simulation in an accessible how-to book for practicing statisticians and statistical programmers. This book discusses in detail how to simulate data from common univariate and multivariate distributions, and how to use simulation to evaluate statistical techniques. It also covers simulating correlated data, data for regression models, spatial data, and data with given moments. It provides tips and techniques for beginning programmers, and offers libraries of functions for advanced practitioners. As the first book devoted to simulating data across a range of statistical applications, Simulating Data with SAS is an essential tool for programmers, analysts, researchers, and students who use SAS software. This book is part of the SAS Press program.
Category: Mathematics

Current Topics In The Theory And Application Of Latent Variable Models

Author : Michael C. Edwards
ISBN : 9781136699795
Genre : Psychology
File Size : 75.39 MB
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This book presents recent developments in the theory and application of latent variable models (LVMs) by some of the most prominent researchers in the field. Topics covered involve a range of LVM frameworks including item response theory, structural equation modeling, factor analysis, and latent curve modeling, as well as various non-standard data structures and innovative applications. The book is divided into two sections, although several chapters cross these content boundaries. Part one focuses on complexities which involve the adaptation of latent variables models in research problems where real-world conditions do not match conventional assumptions. Chapters in this section cover issues such as analysis of dyadic data and complex survey data, as well as analysis of categorical variables. Part two of the book focuses on drawing real-world meaning from results obtained in LVMs. In this section there are chapters examining issues involving assessment of model fit, the nature of uncertainty in parameter estimates, inferences, and the nature of latent variables and individual differences. This book appeals to researchers and graduate students interested in the theory and application of latent variable models. As such, it serves as a supplementary reading in graduate level courses on latent variable models. Prerequisites include basic knowledge of latent variable models.
Category: Psychology

Introduction To Scientific Programming And Simulation Using R Second Edition

Author : Owen Jones
ISBN : 9781466570016
Genre : Mathematics
File Size : 56.39 MB
Format : PDF
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Learn How to Program Stochastic Models Highly recommended, the best-selling first edition of Introduction to Scientific Programming and Simulation Using R was lauded as an excellent, easy-to-read introduction with extensive examples and exercises. This second edition continues to introduce scientific programming and stochastic modelling in a clear, practical, and thorough way. Readers learn programming by experimenting with the provided R code and data. The book’s four parts teach: Core knowledge of R and programming concepts How to think about mathematics from a numerical point of view, including the application of these concepts to root finding, numerical integration, and optimisation Essentials of probability, random variables, and expectation required to understand simulation Stochastic modelling and simulation, including random number generation and Monte Carlo integration In a new chapter on systems of ordinary differential equations (ODEs), the authors cover the Euler, midpoint, and fourth-order Runge-Kutta (RK4) schemes for solving systems of first-order ODEs. They compare the numerical efficiency of the different schemes experimentally and show how to improve the RK4 scheme by using an adaptive step size. Another new chapter focuses on both discrete- and continuous-time Markov chains. It describes transition and rate matrices, classification of states, limiting behaviour, Kolmogorov forward and backward equations, finite absorbing chains, and expected hitting times. It also presents methods for simulating discrete- and continuous-time chains as well as techniques for defining the state space, including lumping states and supplementary variables. Building readers’ statistical intuition, Introduction to Scientific Programming and Simulation Using R, Second Edition shows how to turn algorithms into code. It is designed for those who want to make tools, not just use them. The code and data are available for download from CRAN.
Category: Mathematics

Monte Carlo

Author : George Fishman
ISBN : 9781475725537
Genre : Mathematics
File Size : 75.31 MB
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Apart from a thorough exploration of all the important concepts, this volume includes over 75 algorithms, ready for putting into practice. The book also contains numerous hands-on implementations of selected algorithms to demonstrate applications in realistic settings. Readers are assumed to have a sound understanding of calculus, introductory matrix analysis, and intermediate statistics, but otherwise the book is self-contained. Suitable for graduates and undergraduates in mathematics and engineering, in particular operations research, statistics, and computer science.
Category: Mathematics

Engineering Risk Assessment With Subset Simulation

Author : Siu-Kui Au
ISBN : 9781118398074
Genre : Technology & Engineering
File Size : 61.59 MB
Format : PDF, Kindle
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This book starts with the basic ideas in uncertainty propagation using Monte Carlo methods and the generation of random variables and stochastic processes for some common distributions encountered in engineering applications. It then introduces a class of powerful simulation techniques called Markov Chain Monte Carlo method (MCMC), an important machinery behind Subset Simulation that allows one to generate samples for investigating rare scenarios in a probabilistically consistent manner. The theory of Subset Simulation is then presented, addressing related practical issues encountered in the actual implementation. The book also introduces the reader to probabilistic failure analysis and reliability-based sensitivity analysis, which are laid out in a context that can be efficiently tackled with Subset Simulation or Monte Carlo simulation in general. The book is supplemented with an Excel VBA code that provides a user-friendly tool for the reader to gain hands-on experience with Monte Carlo simulation. Presents a powerful simulation method called Subset Simulation for efficient engineering risk assessment and failure and sensitivity analysis Illustrates examples with MS Excel spreadsheets, allowing readers to gain hands-on experience with Monte Carlo simulation Covers theoretical fundamentals as well as advanced implementation issues A companion website is available to include the developments of the software ideas This book is essential reading for graduate students, researchers and engineers interested in applying Monte Carlo methods for risk assessment and reliability based design in various fields such as civil engineering, mechanical engineering, aerospace engineering, electrical engineering and nuclear engineering. Project managers, risk managers and financial engineers dealing with uncertainty effects may also find it useful.
Category: Technology & Engineering

Introduction To Statistics And Data Analysis

Author : Roxy Peck
ISBN : 9781305445963
Genre : Mathematics
File Size : 40.87 MB
Format : PDF, Kindle
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Roxy Peck, Chris Olsen, and Jay Devore's new edition uses real data and attention-grabbing examples to introduce students to the study of statistics and data analysis. Traditional in structure yet modern in approach, this text guides students through an intuition-based learning process that stresses interpretation and communication of statistical information. Simple notation--including frequent substitution of words for symbols--helps students grasp concepts and cement their comprehension. Hands-on activities and interactive applets allow students to practice statistics firsthand. INTRODUCTION TO STATISTICS AND DATA ANALYSIS includes updated coverage of most major technologies, as well as expanded coverage of probability. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Category: Mathematics

Computer Vision

Author : Richard Szeliski
ISBN : 1848829469
Genre : Computers
File Size : 66.34 MB
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Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.
Category: Computers