Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing

Daniela Calvetti, Erkki Somersalo978-0-387-73393-7

This book has been written for undergraduate and graduate students in various areas of mathematics and its applications. It is for students who are willing to get acquainted with Bayesian approach to computational science but not necessarily to go through the full immersion into the statistical analysis. It has also been written for researchers working in areas where mathematical and statistical modeling are of central importance, such as biology and engineering.

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Table of contents :
Cover Page……Page 1
Title Page……Page 4
ISBN 0387733930……Page 5
Preface……Page 7
Contents (with page links)……Page 12
1 Inverse problems and subjective computing……Page 14
What do we talk about when we talk about random variables?……Page 15
Through the formal theory, lightly……Page 18
How normal is it to be normal?……Page 29
2 Basic problem of statistical inference……Page 34
On averaging……Page 35
Maximum Likelihood, as frequentists like it……Page 44
3 The praise of ignorance: randomness as lack of information……Page 52
Construction of Likelihood……Page 54
Enter, Subject: Construction of Priors……Page 61
Posterior Densities as Solutions of Statistical Inverse Problems……Page 68
What is a solution?……Page 74
Direct linear system solvers……Page 76
Iterative linear system solvers……Page 80
Ill-conditioning and errors in the data……Page 90
5 Sampling: first encounter……Page 104
Sampling from Gaussian distributions……Page 105
Random draws from non-Gaussian densities……Page 112
Rejection sampling: prelude to Metropolis-Hastings……Page 115
6 Statistically inspired preconditioners……Page 120
Priorconditioners: specially chosen preconditioners……Page 121
Sample-based preconditioners and PCA model reduction……Page 131
7 Conditional Gaussian densities and predictive envelopes……Page 140
Gaussian conditional densities……Page 141
Interpolation, splines and conditional densities……Page 147
Envelopes, white swans and dark matter……Page 157
Linear inverse problems……Page 160
Aristotelian boundary conditions……Page 164
9 Sampling: the real thing……Page 174
Metropolis–Hastings algorithm……Page 181
10 Wrapping up: hypermodels, dynamic priorconditioners and Bayesian learning……Page 196
MAP estimation or marginalization?……Page 202
Bayesian hypermodels and priorconditioners……Page 206
References……Page 210
Index (with page links)……Page 212