Weihs / Mersmann / Ligges Foundations of Statistical Algorithms

With References to R Packages
1. Auflage 2013
ISBN: 978-1-4398-7887-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 500 Seiten

Reihe: Chapman & Hall/CRC Computer Science & Data Analysis

A new and refreshingly different approach to presenting the foundations of statistical algorithms, Foundations of Statistical Algorithms: With References to R Packages reviews the historical development of basic algorithms to illuminate the evolution of today’s more powerful statistical algorithms. It emphasizes recurring themes in all statistical algorithms, including computation, assessment and verification, iteration, intuition, randomness, repetition and parallelization, and scalability. Unique in scope, the book reviews the upcoming challenge of scaling many of the established techniques to very large data sets and delves into systematic verification by demonstrating how to derive general classes of worst case inputs and emphasizing the importance of testing over a large number of different inputs.

Broadly accessible, the book offers examples, exercises, and selected solutions in each chapter as well as access to a supplementary website. After working through the material covered in the book, readers should not only understand current algorithms but also gain a deeper understanding of how algorithms are constructed, how to evaluate new algorithms, which recurring principles are used to tackle some of the tough problems statistical programmers face, and how to take an idea for a new method and turn it into something practically useful.

Zielgruppe

Statisticians Computer Science

Autoren/Hrsg.

Weihs, Claus

Mersmann, Olaf

Ligges, Uwe

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen

Inhaltsverzeichnis

Introduction

Computation
Motivation and History
Models for Computing: What Can a Computer Compute?
Floating-Point Computations: How Does a Computer Compute?
Precision of Computations: How Exact Does a Computer Compute?
Implementation in R

Verification
Motivation and History
Theory
Practice and Simulation
Implementation in R

Iteration
Motivation
Preliminaries
Univariate Optimization
Multivariate Optimization
Example: Neural Nets
Constrained Optimization
Evolutionary Computing
Implementation in R

Deduction of Theoretical Properties
PLS—from Algorithm to Optimality
EM Algorithm
Implementation in R

Randomization
Motivation and History
Theory: Univariate Randomization
Theory: Multivariate Randomization
Practice and Simulation: Stochastic Modeling
Implementation in R

Repetition
Motivation and Overview
Model Selection
Model Selection in Classification
Model Selection in Continuous Models
Implementation in R

Scalability and Parallelization
Introduction
Motivation and History
Optimization
Parallel Computing
Implementation in R

Bibliography

Index

Conclusion and Exercises appear at the end of each chapter.