Brani Vidakovic - Böcker

This volume provides a thorough introduction and reference for any researcher who is interested in Bayesian inference for wavelet-based models, but is not necessarily an expert in either. To achieve this goal the book starts with an extensive introductory chapter providing a self-contained introduction to the use of wavelet decompositions and the relation to Bayesian inference. The remaining papers in this volume are divided into six parts: independent prior modeling; decision theoretic aspects; dependent prior modeling; spatial models using bivariate wavelet bases; empirical Bayes approaches; and case studies. Chapters are written by experts who published the original research papers establishing the use of wavelet-based models in Bayesian inference. Peter Muller is Associate Professor and Brani Vidakovic is Assistant Professor of Statistics at Duke University.

A comprehensive, step-by-step introduction to wavelets in statistics. What are wavelets? What makes them increasingly indispensable in statistical nonparametrics? Why are they suitable for "time-scale" applications? How are they used to solve such problems as denoising, regression, or density estimation? Where can one find up-to-date information on these newly "discovered" mathematical objects? These are some of the questions Brani Vidakovic answers in Statistical Modeling by Wavelets. Providing a much-needed introduction to the latest tools afforded statisticians by wavelet theory, Vidakovic compiles, organizes, and explains in depth research data previously available only in disparate journal articles. He carefully balances both statistical and mathematical techniques, supplementing the material with a wealth of examples, more than 100 illustrations, and extensive references-with data sets and S-Plus wavelet overviews made available for downloading over the Internet. Both introductory and data-oriented modeling topics are featured, including:* Continuous and discrete wavelet transformations.* Statistical optimality properties of wavelet shrinkage.* Theoretical aspects of wavelet density estimation.* Bayesian modeling in the wavelet domain.* Properties of wavelet-based random functions and densities.* Several novel and important wavelet applications in statistics.* Wavelet methods in time series. Accessible to anyone with a background in advanced calculus and algebra, Statistical Modeling by Wavelets promises to become the standard reference for statisticians and engineers seeking a comprehensive introduction to an emerging field.

This book examines multiple classes of random processes from the standpoints of statistical analysis, inference, and modeling. It describes several traditional models (fGn, fBm, mBm, ARFIMA, multiplicative cascades) and their appropriateness for modeling measured processes; offers brief discussions on ways to stimulate traditional processes and fit them to the data; and uses case studies to emphasize the real-life applicability of the subject matter. Accessible to anyone with a background in advanced calculus and algebra, this book is perfect for statisticians and engineers seeking a comprehensive introduction to an emerging field

Provides a one-stop resource for engineers learning biostatistics using MATLAB® and WinBUGSThrough its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing bio-oriented engineering fields while implementing software packages that are familiar to engineers. The book is heavily oriented to computation and hands-on approaches so readers understand each step of the programming. Another dimension of this book is in parallel coverage of both Bayesian and frequentist approaches to statistical inference. It avoids taking sides on the classical vs. Bayesian paradigms, and many examples in this book are solved using both methods. The results are then compared and commented upon. Readers have the choice of MATLAB® for classical data analysis and WinBUGS/OpenBUGS for Bayesian data analysis. Every chapter starts with a box highlighting what is covered in that chapter and ends with exercises, a list of software scripts, datasets, and references.Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS also includes: parallel coverage of classical and Bayesian approaches, where appropriatesubstantial coverage of Bayesian approaches to statistical inferencematerial that has been classroom-tested in an introductory statistics course in bioengineering over several yearsexercises at the end of each chapter and an accompanying website with full solutions and hints to some exercises, as well as additional materials and examplesEngineering Biostatistics: An Introduction using MATLAB® and WinBUGS can serve as a textbook for introductory-to-intermediate applied statistics courses, as well as a useful reference for engineers interested in biostatistical approaches.

NONPARAMETRIC STATISTICS WITH APPLICATIONS TO SCIENCE AND ENGINEERING WITH R Introduction to the methods and techniques of traditional and modern nonparametric statistics, incorporating R code Nonparametric Statistics with Applications to Science and Engineering with R presents modern nonparametric statistics from a practical point of view, with the newly revised edition including custom R functions implementing nonparametric methods to explain how to compute them and make them more comprehensible. Relevant built-in functions and packages on CRAN are also provided with a sample code. R codes in the new edition not only enable readers to perform nonparametric analysis easily, but also to visualize and explore data using R’s powerful graphic systems, such as ggplot2 package and R base graphic system. The new edition includes useful tables at the end of each chapter that help the reader find data sets, files, functions, and packages that are used and relevant to the respective chapter. New examples and exercises that enable readers to gain a deeper insight into nonparametric statistics and increase their comprehension are also included. Some of the sample topics discussed in Nonparametric Statistics with Applications to Science and Engineering with R include: Basics of probability, statistics, Bayesian statistics, order statistics, Kolmogorov–Smirnov test statistics, rank tests, and designed experimentsCategorical data, estimating distribution functions, density estimation, least squares regression, curve fitting techniques, wavelets, and bootstrap samplingEM algorithms, statistical learning, nonparametric Bayes, WinBUGS, properties of ranks, and Spearman coefficient of rank correlationChi-square and goodness-of-fit, contingency tables, Fisher exact test, MC Nemar test, Cochran’s test, Mantel–Haenszel test, and Empirical Likelihood Nonparametric Statistics with Applications to Science and Engineering with R is a highly valuable resource for graduate students in engineering and the physical and mathematical sciences, as well as researchers who need a more comprehensive, but succinct understanding of modern nonparametric statistical methods.

Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing engineering fields, bioengineering and biomedical engineering, while implementing software familiar to engineers.

Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing engineering fields, bioengineering and biomedical engineering, while implementing software that engineers are familiar with.The author integrates introductory statistics for engineers and  introductory biostatistics as a single textbook heavily oriented to computation and hands on approaches. For example, topics ranging from the aspects of disease and device testing, Sensitivity, Specificity and ROC curves, Epidemiological Risk Theory, Survival Analysis, or Logistic and Poisson Regressions are covered.In addition to the synergy of engineering and biostatistical approaches, the novelty of this book is in the substantial coverage of Bayesian approaches to statistical inference. Many examples in this text are solved using both the traditional and Bayesian methods, and the results are compared and commented.