Fitting Smooth Functions To Data

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Fitting Smooth Functions to Data

Charles Fefferman,Arie Israel
Fitting Smooth Functions to Data Book PDF

Author : Charles Fefferman,Arie Israel
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 46,7 Mb
Release : 2020-10-27
Category : Education
ISBN : 9781470461300

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Fitting Smooth Functions to Data by Charles Fefferman,Arie Israel Pdf

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 Cm. The target audience consists of graduate students and junior faculty in mathematics and computer science who are familiar with point set topology, as well as measure and integration theory. The book is based on lectures presented at the CBMS regional workshop held at the University of Texas at Austin in the summer of 2019.

Functional Data Analysis

James Ramsay,B. W. Silverman
Functional Data Analysis Book PDF

Author : James Ramsay,B. W. Silverman
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 50,8 Mb
Release : 2006-06-28
Category : Mathematics
ISBN : 9780387227511

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Functional Data Analysis by James Ramsay,B. W. Silverman Pdf

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.

Digital Functions and Data Reconstruction

Li Chen
Digital Functions and Data Reconstruction Book PDF

Author : Li Chen
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 44,7 Mb
Release : 2012-12-12
Category : Computers
ISBN : 9781461456384

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Digital Functions and Data Reconstruction by Li Chen Pdf

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.

Introduction to Data Science

Rafael A. Irizarry
Introduction to Data Science Book PDF

Author : Rafael A. Irizarry
Publisher : CRC Press
Page : 794 pages
File Size : 54,8 Mb
Release : 2019-11-20
Category : Mathematics
ISBN : 9781000708035

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Introduction to Data Science by Rafael A. Irizarry Pdf

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.

Integrating Omics Data

George Tseng,Debashis Ghosh,Xianghong Jasmine Zhou
Integrating Omics Data Book PDF

Author : George Tseng,Debashis Ghosh,Xianghong Jasmine Zhou
Publisher : Cambridge University Press
Page : 497 pages
File Size : 53,7 Mb
Release : 2015-09-23
Category : Mathematics
ISBN : 9781107069114

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Integrating Omics Data by George Tseng,Debashis Ghosh,Xianghong Jasmine Zhou Pdf

Tutorial chapters by leaders in the field introduce state-of-the-art methods to handle information integration problems of omics data.

A Practical Guide to Data Analysis Using R

John H. Maindonald,W. John Braun,Jeffrey L. Andrews
A Practical Guide to Data Analysis Using R Book PDF

Author : John H. Maindonald,W. John Braun,Jeffrey L. Andrews
Publisher : Cambridge University Press
Page : 551 pages
File Size : 46,6 Mb
Release : 2024-05-31
Category : Computers
ISBN : 9781009282277

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A Practical Guide to Data Analysis Using R by John H. Maindonald,W. John Braun,Jeffrey L. Andrews Pdf

Examples from diverse areas of statistical application demonstrate the use of R for data analysis and associated graphics.

Flexible Regression and Smoothing

Mikis D. Stasinopoulos,Robert A. Rigby,Gillian Z. Heller,Vlasios Voudouris,Fernanda De Bastiani
Flexible Regression and Smoothing Book PDF

Author : Mikis D. Stasinopoulos,Robert A. Rigby,Gillian Z. Heller,Vlasios Voudouris,Fernanda De Bastiani
Publisher : CRC Press
Page : 513 pages
File Size : 54,6 Mb
Release : 2017-04-21
Category : Mathematics
ISBN : 9781351980371

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Flexible Regression and Smoothing by Mikis D. Stasinopoulos,Robert A. Rigby,Gillian Z. Heller,Vlasios Voudouris,Fernanda De Bastiani Pdf

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.

Artificial Intelligence Frontiers in Statistics

David J. Hand
Artificial Intelligence Frontiers in Statistics Book PDF

Author : David J. Hand
Publisher : CRC Press
Page : 431 pages
File Size : 42,7 Mb
Release : 2020-11-26
Category : Business & Economics
ISBN : 9781000152913

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Artificial Intelligence Frontiers in Statistics by David J. Hand Pdf

This book presents a summary of recent work on the interface between artificial intelligence and statistics. It does this through a series of papers by different authors working in different areas of this interface. These papers are a selected and referenced subset of papers presented at the 3rd Interntional Workshop on Artificial Intelligence and Statistics, Florida, January 1991.

Modeling Psychophysical Data in R

Kenneth Knoblauch,Laurence T. Maloney
Modeling Psychophysical Data in R Book PDF

Author : Kenneth Knoblauch,Laurence T. Maloney
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 55,5 Mb
Release : 2012-09-02
Category : Computers
ISBN : 9781461444756

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Modeling Psychophysical Data in R by Kenneth Knoblauch,Laurence T. Maloney Pdf

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.

Least Squares Data Fitting with Applications

Per Christian Hansen,Víctor Pereyra,Godela Scherer
Least Squares Data Fitting with Applications Book PDF

Author : Per Christian Hansen,Víctor Pereyra,Godela Scherer
Publisher : JHU Press
Page : 325 pages
File Size : 55,8 Mb
Release : 2013-01-15
Category : Mathematics
ISBN : 9781421407869

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Least Squares Data Fitting with Applications by Per Christian Hansen,Víctor Pereyra,Godela Scherer Pdf

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.

Handbook of Regression Analysis With Applications in R

Samprit Chatterjee,Jeffrey S. Simonoff
Handbook of Regression Analysis With Applications in R Book PDF

Author : Samprit Chatterjee,Jeffrey S. Simonoff
Publisher : John Wiley & Sons
Page : 384 pages
File Size : 42,9 Mb
Release : 2020-08-18
Category : Mathematics
ISBN : 9781119392378

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Handbook of Regression Analysis With Applications in R by Samprit Chatterjee,Jeffrey S. Simonoff Pdf

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.

Recent Advances and Trends in Nonparametric Statistics

M.G. Akritas,D.N. Politis
Recent Advances and Trends in Nonparametric Statistics Book PDF

Author : M.G. Akritas,D.N. Politis
Publisher : Elsevier
Page : 524 pages
File Size : 50,9 Mb
Release : 2003-10-31
Category : Computers
ISBN : 9780444513786

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Recent Advances and Trends in Nonparametric Statistics by M.G. Akritas,D.N. Politis Pdf

The advent of high-speed, affordable computers in the last two decades has given a new boost to the nonparametric way of thinking. Classical nonparametric procedures, such as function smoothing, suddenly lost their abstract flavour as they became practically implementable. In addition, many previously unthinkable possibilities became mainstream; prime examples include the bootstrap and resampling methods, wavelets and nonlinear smoothers, graphical methods, data mining, bioinformatics, as well as the more recent algorithmic approaches such as bagging and boosting. This volume is a collection of short articles - most of which having a review component - describing the state-of-the art of Nonparametric Statistics at the beginning of a new millennium. Key features: . algorithic approaches . wavelets and nonlinear smoothers . graphical methods and data mining . biostatistics and bioinformatics . bagging and boosting . support vector machines . resampling methods

Dynamic Data Analysis

James Ramsay,Giles Hooker
Dynamic Data Analysis Book PDF

Author : James Ramsay,Giles Hooker
Publisher : Springer
Page : 230 pages
File Size : 48,7 Mb
Release : 2017-06-27
Category : Mathematics
ISBN : 9781493971909

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Dynamic Data Analysis by James Ramsay,Giles Hooker Pdf

This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in the properties of differential equations estimated from data will find rather less to work with. This book fills that gap.

Proceedings of the Ninth International Colloquium on Differential Equations

D. Bainov
Proceedings of the Ninth International Colloquium on Differential Equations Book PDF

Author : D. Bainov
Publisher : VSP
Page : 484 pages
File Size : 49,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9067642967

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Proceedings of the Ninth International Colloquium on Differential Equations by D. Bainov Pdf

The Ninth International Colloquium on Differential Equations was organized by the Institute for Basic Science of Inha University, the International Federation of Nonlinear Analysts, the Mathematical Society of Japan, Pharmaceutical Faculty of the Medical University of Sofia, the University of Catania and UNESCO, with the cooperation of a number of international mathematical organizations, and was held at the Technical University of Plovdiv, Bulgaria, August 18-23, 1998. This proceedings volume contains selected talks which deal with various aspects of differential equations and applications

Multilevel Statistical Models

Harvey Goldstein
Multilevel Statistical Models Book PDF

Author : Harvey Goldstein
Publisher : John Wiley & Sons
Page : 306 pages
File Size : 46,9 Mb
Release : 2011-07-08
Category : Mathematics
ISBN : 9781119956822

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Multilevel Statistical Models by Harvey Goldstein Pdf

Throughout the social, medical and other sciences the importance of understanding complex hierarchical data structures is well understood. Multilevel modelling is now the accepted statistical technique for handling such data and is widely available in computer software packages. A thorough understanding of these techniques is therefore important for all those working in these areas. This new edition of Multilevel Statistical Models brings these techniques together, starting from basic ideas and illustrating how more complex models are derived. Bayesian methodology using MCMC has been extended along with new material on smoothing models, multivariate responses, missing data, latent normal transformations for discrete responses, structural equation modeling and survival models. Key Features: Provides a clear introduction and a comprehensive account of multilevel models. New methodological developments and applications are explored. Written by a leading expert in the field of multilevel methodology. Illustrated throughout with real-life examples, explaining theoretical concepts. This book is suitable as a comprehensive text for postgraduate courses, as well as a general reference guide. Applied statisticians in the social sciences, economics, biological and medical disciplines will find this book beneficial.