Fitting Smooth Functions To Data

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Fitting Smooth Functions To Data

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Author : Charles Fefferman
language : en
Publisher:
Release Date : 2020

Fitting Smooth Functions To Data written by Charles Fefferman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Electronic books categories.

This book is an introductory text that charts the recent developments in the area of Whitney-type extension problems and the mathematical aspects of interpolation of data. It provides a detailed tour of a new and active area of mathematical research. In each section, the authors focus on a different key insight in the theory. The book motivates the more technical aspects of the theory through a set of illustrative examples. The results include the solution of Whitney's problem, an efficient algorithm for a finite version, and analogues for Hölder and Sobolev spaces in place of C^{m}.The target.

Least Squares Data Fitting With Applications

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Author : Per Christian Hansen
language : en
Publisher: JHU Press
Release Date : 2013-01-15

Least Squares Data Fitting With Applications written by Per Christian Hansen and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-15 with Mathematics categories.

Included are; an overview of computational methods together with their properties and advantages; topics from statistical regression analysis that help readers to understand and evaluate the computed solutions; many examples that illustrate the techniques and algorithmsLeast Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.

A Practical Guide To Data Analysis Using R

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Author : John H. Maindonald
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-31

A Practical Guide To Data Analysis Using R written by John H. Maindonald and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-31 with Computers categories.

Using diverse real-world examples, this text examines what models used for data analysis mean in a specific research context. What assumptions underlie analyses, and how can you check them? Building on the successful 'Data Analysis and Graphics Using R,' 3rd edition (Cambridge, 2010), it expands upon topics including cluster analysis, exponential time series, matching, seasonality, and resampling approaches. An extended look at p-values leads to an exploration of replicability issues and of contexts where numerous p-values exist, including gene expression. Developing practical intuition, this book assists scientists in the analysis of their own data, and familiarizes students in statistical theory with practical data analysis. The worked examples and accompanying commentary teach readers to recognize when a method works and, more importantly, when it doesn't. Each chapter contains copious exercises. Selected solutions, notes, slides, and R code are available online, with extensive references pointing to detailed guides to R.

Functional Data Analysis

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Author : James Ramsay
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-28

Functional Data Analysis written by James Ramsay and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-28 with Mathematics categories.

This is the second edition of a highly succesful book which has sold nearly 3000 copies world wide since its publication in 1997. Many chapters will be rewritten and expanded due to a lot of progress in these areas since the publication of the first edition. Bernard Silverman is the author of two other books, each of which has lifetime sales of more than 4000 copies. He has a great reputation both as a researcher and an author. This is likely to be the bestselling book in the Springer Series in Statistics for a couple of years.

Introduction To Data Science

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Author : Rafael A. Irizarry
language : en
Publisher: CRC Press
Release Date : 2019-11-12

Introduction To Data Science written by Rafael A. Irizarry and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-12 with Mathematics categories.

Introduction to Data Science: Data Analysis and Prediction Algorithms with R introduces concepts and skills that can help you tackle real-world data analysis challenges. It covers concepts from probability, statistical inference, linear regression, and machine learning. It also helps you develop skills such as R programming, data wrangling, data visualization, predictive algorithm building, file organization with UNIX/Linux shell, version control with Git and GitHub, and reproducible document preparation. This book is a textbook for a first course in data science. No previous knowledge of R is necessary, although some experience with programming may be helpful. The book is divided into six parts: R, data visualization, statistics with R, data wrangling, machine learning, and productivity tools. Each part has several chapters meant to be presented as one lecture. The author uses motivating case studies that realistically mimic a data scientist’s experience. He starts by asking specific questions and answers these through data analysis so concepts are learned as a means to answering the questions. Examples of the case studies included are: US murder rates by state, self-reported student heights, trends in world health and economics, the impact of vaccines on infectious disease rates, the financial crisis of 2007-2008, election forecasting, building a baseball team, image processing of hand-written digits, and movie recommendation systems. The statistical concepts used to answer the case study questions are only briefly introduced, so complementing with a probability and statistics textbook is highly recommended for in-depth understanding of these concepts. If you read and understand the chapters and complete the exercises, you will be prepared to learn the more advanced concepts and skills needed to become an expert. A complete solutions manual is available to registered instructors who require the text for a course.

Digital Functions And Data Reconstruction

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Author : Li Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-12

Digital Functions And Data Reconstruction written by Li Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-12 with Computers categories.

Digital Functions and Data Reconstruction: Digital-Discrete Methods provides a solid foundation to the theory of digital functions and its applications to image data analysis, digital object deformation, and data reconstruction. This new method has a unique feature in that it is mainly built on discrete mathematics with connections to classical methods in mathematics and computer sciences. Digitally continuous functions and gradually varied functions were developed in the late 1980s. A. Rosenfeld (1986) proposed digitally continuous functions for digital image analysis, especially to describe the “continuous” component in a digital image, which usually indicates an object. L. Chen (1989) invented gradually varied functions to interpolate a digital surface when the boundary appears to be continuous. In theory, digitally continuous functions are very similar to gradually varied functions. Gradually varied functions are more general in terms of being functions of real numbers; digitally continuous functions are easily extended to the mapping from one digital space to another. This will be the first book about digital functions, which is an important modern research area for digital images and digitalized data processing, and provides an introduction and comprehensive coverage of digital function methods. Digital Functions and Data Reconstruction: Digital-Discrete Methods offers scientists and engineers who deal with digital data a highly accessible, practical, and mathematically sound introduction to the powerful theories of digital topology and functional analysis, while avoiding the more abstruse aspects of these topics.

Handbook Of Regression Analysis With Applications In R

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Author : Samprit Chatterjee
language : en
Publisher: John Wiley & Sons
Release Date : 2020-07-30

Handbook Of Regression Analysis With Applications In R written by Samprit Chatterjee and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-30 with Mathematics categories.

Handbook and reference guide for students and practitioners of statistical regression-based analyses in R Handbook of Regression Analysis with Applications in R, Second Edition is a comprehensive and up-to-date guide to conducting complex regressions in the R statistical programming language. The authors' thorough treatment of "classical" regression analysis in the first edition is complemented here by their discussion of more advanced topics including time-to-event survival data and longitudinal and clustered data. The book further pays particular attention to methods that have become prominent in the last few decades as increasingly large data sets have made new techniques and applications possible. These include: Regularization methods Smoothing methods Tree-based methods In the new edition of the Handbook, the data analyst's toolkit is explored and expanded. Examples are drawn from a wide variety of real-life applications and data sets. All the utilized R code and data are available via an author-maintained website. Of interest to undergraduate and graduate students taking courses in statistics and regression, the Handbook of Regression Analysis will also be invaluable to practicing data scientists and statisticians.

Modeling Psychophysical Data In R

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Author : Kenneth Knoblauch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-02

Modeling Psychophysical Data In R written by Kenneth Knoblauch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-02 with Computers categories.

Many of the commonly used methods for modeling and fitting psychophysical data are special cases of statistical procedures of great power and generality, notably the Generalized Linear Model (GLM). This book illustrates how to fit data from a variety of psychophysical paradigms using modern statistical methods and the statistical language R. The paradigms include signal detection theory, psychometric function fitting, classification images and more. In two chapters, recently developed methods for scaling appearance, maximum likelihood difference scaling and maximum likelihood conjoint measurement are examined. The authors also consider the application of mixed-effects models to psychophysical data. R is an open-source programming language that is widely used by statisticians and is seeing enormous growth in its application to data in all fields. It is interactive, containing many powerful facilities for optimization, model evaluation, model selection, and graphical display of data. The reader who fits data in R can readily make use of these methods. The researcher who uses R to fit and model his data has access to most recently developed statistical methods. This book does not assume that the reader is familiar with R, and a little experience with any programming language is all that is needed to appreciate this book. There are large numbers of examples of R in the text and the source code for all examples is available in an R package MPDiR available through R. Kenneth Knoblauch is a researcher in the Department of Integrative Neurosciences in Inserm Unit 846, The Stem Cell and Brain Research Institute and associated with the University Claude Bernard, Lyon 1, in France. Laurence T. Maloney is Professor of Psychology and Neural Science at New York University. His research focusses on applications of mathematical models to perception, motor control and decision making.

Flexible Regression And Smoothing

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Author : Mikis D. Stasinopoulos
language : en
Publisher: CRC Press
Release Date : 2017-04-21

Flexible Regression And Smoothing written by Mikis D. Stasinopoulos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-21 with Mathematics categories.

This book is about learning from data using the Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS extends the Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) to accommodate large complex datasets, which are increasingly prevalent. In particular, the GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the response variable has any parametric (continuous, discrete or mixed) distribution which might be heavy- or light-tailed, and positively or negatively skewed. In addition, all the parameters of the distribution (location, scale, shape) can be modelled as linear or smooth functions of explanatory variables. Key Features: Provides a broad overview of flexible regression and smoothing techniques to learn from data whilst also focusing on the practical application of methodology using GAMLSS software in R. Includes a comprehensive collection of real data examples, which reflect the range of problems addressed by GAMLSS models and provide a practical illustration of the process of using flexible GAMLSS models for statistical learning. R code integrated into the text for ease of understanding and replication. Supplemented by a website with code, data and extra materials. This book aims to help readers understand how to learn from data encountered in many fields. It will be useful for practitioners and researchers who wish to understand and use the GAMLSS models to learn from data and also for students who wish to learn GAMLSS through practical examples.

Environmental Health Perspectives

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Author :
language : en
Publisher:
Release Date : 2004

Environmental Health Perspectives written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Environmental health categories.