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An Introduction to Bayesian Scientific Computing

Ten Lectures on Subjective Computing

  • Textbook
  • © 2007

Overview

Authors:
  1. Daniela Calvetti

    1. Department of Mathematics, Case Western Reserve University, Cleveland

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    You can also search for this author in PubMed   Google Scholar

  2. Erkki Somersalo

    1. Institute of Mathematics Helsinki University of Technology, Finland

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    You can also search for this author in PubMed   Google Scholar

  • Expository accessible book, internationally known authors
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XIV
    Download chapter PDF

  2. Inverse problems and subjective computing

    • Daniela Calvetti, Erkki Somersalo
    Pages 1-20

  3. Basic problem of statistical inference

    • Daniela Calvetti, Erkki Somersalo
    Pages 21-38

  4. The praise of ignorance: randomness as lack of information

    • Daniela Calvetti, Erkki Somersalo
    Pages 39-59

  5. Basic problem in numerical linear algebra

    • Daniela Calvetti, Erkki Somersalo
    Pages 61-90

  6. Sampling: first encounter

    • Daniela Calvetti, Erkki Somersalo
    Pages 91-106

  7. Statistically inspired preconditioners

    • Daniela Calvetti, Erkki Somersalo
    Pages 107-126

  8. Conditional Gaussian densities and predictive envelopes

    • Daniela Calvetti, Erkki Somersalo
    Pages 127-146

  9. More applications of the Gaussian conditioning

    • Daniela Calvetti, Erkki Somersalo
    Pages 147-160

  10. Sampling: the real thing

    • Daniela Calvetti, Erkki Somersalo
    Pages 161-182

  11. Wrapping up: hypermodels, dynamic priorconditioners and Bayesian learning

    • Daniela Calvetti, Erkki Somersalo
    Pages 183-195

  12. Back Matter

    Pages 197-202
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Keywords

About this book

The book of nature, according to Galilei, is written in the language of mat- matics. The nature of mathematics is being exact, and its exactness is und- lined by the formalism used by mathematicians to write it. This formalism, characterized by theorems and proofs, and syncopated with occasional l- mas, remarks and corollaries, is so deeply ingrained that mathematicians feel uncomfortable when the pattern is broken, to the point of giving the - pression that the attitude of mathematicians towards the way mathematics should be written is almost moralistic. There is a de?nition often quoted, “A mathematician is a person who proves theorems”, and a similar, more alchemistic one, credited to Paul Erd? os, but more likely going back to Alfr´ ed R´ enyi,statingthat“Amathematicianisamachinethattransformsco?eeinto 1 theorems ”. Therefore it seems to be the form, not the content, that char- terizes mathematics, similarly to what happens in any formal moralistic code wherein form takes precedence over content. This book is deliberately written in a very di?erent manner, without a single theorem or proof. Since morality has its subjective component, to pa- phrase Manuel Vasquez Montalban, we could call it Ten Immoral Mathemat- 2 ical Recipes . Does the lack of theorems and proofs mean that the book is more inaccurate than traditional books of mathematics? Or is it possibly just a sign of lack of co?ee? This is our ?rst open question. Exactness is an interesting concept.

Reviews

From the reviews:

"This witty, erudite, and surprisingly practical book is made up of ten chapters. … A central topic of the book is the relationship between statistical inference and the inverse problems that define Bayesian (subjective) statistics. … This excellent book will be valuable to scientists of various stripes, statisticians, numerical analysts, those who work in image processing, and those who implement Bayesian belief nets." (George Hacken, ACM Computing Reviews, Vol. 49 (11), November, 2008)

"Introduction to Bayesian Scientific Computing is a 200-page, easily accessible, pleasant introduction fusing Bayesian approaches with numerical linear algebra methods for inverse problems … . What I like most about this book is the apparent enthusiasm of the authors and their genuine interest in explaining rather than showing off. This enthusiasm is contagious, and the result is very readable." (Uri Ascher, The Mathematical Intelligencer, Vol. 31 (1), 2009)

Authors and Affiliations

  • Department of Mathematics, Case Western Reserve University, Cleveland

    Daniela Calvetti

  • Institute of Mathematics Helsinki University of Technology, Finland

    Erkki Somersalo

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