An Introduction to Bayesian Scientific Computing

Ten Lectures on Subjective Computing

Daniela Calvetti, E. Somersalo (Autoren)

Buch | Softcover

202 Seiten

2007 | 2007 ed.
Springer-Verlag New York Inc.
978-0-387-73393-7 (ISBN)

Infos

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.

Inhalt

Inverse problems and subjective computing.- Basic problem of statistical inference.- The praise of ignorance: randomness as lack of information.- Basic problem in numerical linear algebra.- Sampling: first encounter.- Statistically inspired preconditioners.- Conditional Gaussian densities and predictive envelopes.- More applications of the Gaussian conditioning.- Sampling: the real thing.- Wrapping up: hypermodels, dynamic priorconditioners and Bayesian learning.

Produkt-Details

• Reihe/Serie: Surveys and Tutorials in the Applied Mathematical Sciences ; 2
• Zusatzinfo: XIV, 202 p.
• Verlagsort: New York, NY
• Sprache: englisch
• Maße: 155 x 235 mm
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• ISBN-10: 0-387-73393-0 / 0387733930
• ISBN-13: 978-0-387-73393-7 / 9780387733937
• Zustand: Neuware