Introduction to Bayesian Scientific Computing

Ten Lectures on Subjective Computing

  • Daniela Calvetti
  • Erkki Somersalo

Part of the Surveys and Tutorials in the Applied Mathematical Sciences book series (STAMS, volume 2)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Daniela Calvetti, Erkki Somersalo
    Pages 1-20
  3. Daniela Calvetti, Erkki Somersalo
    Pages 21-38
  4. Daniela Calvetti, Erkki Somersalo
    Pages 39-59
  5. Daniela Calvetti, Erkki Somersalo
    Pages 61-90
  6. Daniela Calvetti, Erkki Somersalo
    Pages 91-106
  7. Daniela Calvetti, Erkki Somersalo
    Pages 107-126
  8. Daniela Calvetti, Erkki Somersalo
    Pages 127-146
  9. Daniela Calvetti, Erkki Somersalo
    Pages 147-160
  10. Daniela Calvetti, Erkki Somersalo
    Pages 161-182
  11. Daniela Calvetti, Erkki Somersalo
    Pages 183-195
  12. Back Matter
    Pages 197-202

About this book

Introduction

A combination of the concepts subjective – or Bayesian – statistics and scientific computing, the book provides an integrated view across numerical linear algebra and computational statistics. Inverse problems act as the bridge between these two fields where the goal is to estimate an unknown parameter that is not directly observable by using measured data and a mathematical model linking the observed and the unknown.

Inverse problems are closely related to statistical inference problems, where the observations are used to infer on an underlying probability distribution. This connection between statistical inference and inverse problems is a central topic of the book. Inverse problems are typically ill-posed: small uncertainties in data may propagate in huge uncertainties in the estimates of the unknowns. To cope with such problems, efficient regularization techniques are developed in the framework of numerical analysis. The counterpart of regularization in the framework of statistical inference is the use prior information. This observation opens the door to a fruitful interplay between statistics and numerical analysis: the statistical framework provides a rich source of methods that can be used to improve the quality of solutions in numerical analysis, and vice versa, the efficient numerical methods bring computational efficiency to the statistical inference problems.

This book is intended as an easily accessible reader for those who need numerical and statistical methods in applied sciences.

 

Keywords

Bayesian Computing Lectures STATISTICA Scientific learning linear algebra modeling scientific computing

Authors and affiliations

  • Daniela Calvetti
    • 1
  • Erkki Somersalo
    • 2
  1. 1.Department of MathematicsCase Western Reserve UniversityCleveland
  2. 2.Institute of Mathematics Helsinki University of TechnologyFinland

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-73394-4
  • Copyright Information Springer Science+Business Media, LLC 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-73393-7
  • Online ISBN 978-0-387-73394-4
  • About this book