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Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing 2007 ed. [Pehme köide]

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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,statingthatAmathematicianisamachinethattransformsco 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.

Arvustused

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)

Inverse problems and subjective computing
1(20)
What do we talk about when we talk about random variables?
2(3)
Through the formal theory, lightly
5(11)
How normal is it to be normal?
16(5)
Basic problem of statistical inference
21(18)
On averaging
22(9)
Maximum Likelihood, as frequentists like it
31(8)
The praise of ignorance: randomness as lack of information
39(22)
Construction of Likelihood
41(7)
Enter, Subject: Construction of Priors
48(7)
Posterior Densities as Solutions of Statistical Inverse Problems
55(6)
Basic problem in numerical linear algebra
61(30)
What is a solution?
61(2)
Direct linear system solvers
63(4)
Iterative linear system solvers
67(10)
Ill-conditioning and errors in the data
77(14)
Sampling: first encounter
91(16)
Sampling from Gaussian distributions
92(7)
Random draws from non-Gaussian densities
99(3)
Rejection sampling: prelude to Metropolis-Hastings
102(5)
Statistically inspired preconditioners
107(20)
Priorconditioners: specially chosen preconditioners
108(10)
Sample-based preconditioners and PCA model reduction
118(9)
Conditional Gaussian densities and predictive envelopes
127(20)
Gaussian conditional densities
128(6)
Interpolation, splines and conditional densities
134(10)
Envelopes, white swans and dark matter
144(3)
More applications of the Gaussian conditioning
147(14)
Linear inverse problems
147(4)
Aristotelian boundary conditions
151(10)
Sampling: the real thing
161(22)
Metropolis-Hastings algorithm
168(15)
Wrapping up: hypermodels, dynamic priorconditioners and Bayesian learning
183(14)
Map estimation or marginalization?
189(4)
Bayesian hypermodels and priorconditioners
193(4)
References 197(2)
Index 199