Data Analysis A Bayesian Tutorial 2nd Edition by Devinderjit Sivia, John Skilling 0198568320 9780198568322

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ISBN 10: 0198568320
ISBN 13: 9780198568322
Author: Devinderjit Sivia, John Skilling

Statistics lectures have been a source of much bewilderment and frustration for generations of students. This book attempts to remedy the situation by expounding a logical and unified approach to the whole subject of data analysis. This text is intended as a tutorial guide for senior undergraduates and research students in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. Other topics covered include reliability analysis, multivariate optimization, least-squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy and experimental design. The Second Edition of this successful tutorial book contains a new chapter on extensions to the ubiquitous least-squares procedure, allowing for the straightforward handling of outliers and unknown correlated noise, and a cutting-edge contribution from John Skilling on a novel numerical technique for Bayesian computation called ‘nested sampling’.

Data Analysis A Bayesian Tutorial 2nd Table of contents:

PART I: THE ESSENTIALS
1. The basics
1.1 Introduction: deductive logic versus plausible reasoning
1.2 Probability: Cox and the rules for consistent reasoning
1.3 Corollaries: Bayes’ theorem and marginalization
1.4 Some history: Bayes, Laplace and orthodox statistics
1.5 Outline of book
2. Parameter estimation I
2.1 Example 1: is this a fair coin?
2.2 Reliabilities: best estimates, error-bars and confidence intervals
2.3 Example 2: Gaussian noise and averages
2.4 Example 3: the lighthouse problem
3. Parameter estimation II
3.1 Example 4: amplitude of a signal in the presence of background
3.2 Reliabilities: best estimates, correlations and error-bars
3.3 Example 5: Gaussian noise revisited
3.4 Algorithms: a numerical interlude
3.5 Approximations: maximum likelihood and least-squares
3.6 Error-propagation: changing variables
4. Model selection
4.1 Introduction: the story of Mr A and Mr B
4.2 Example 6: how many lines are there?
4.3 Other examples: means, variance, dating and so on
5. Assigning probabilities
5.1 Ignorance: indifference and transformation groups
5.2 Testable information: the principle of maximum entropy
5.3 MaxEnt examples: some common pdfs
5.4 Approximations: interconnections and simplifications
5.5 Hangups: priors versus likelihoods
PART II: ADVANCED TOPICS
6. Non-parametric estimation
6.1 Introduction: free-form solutions
6.2 MaxEnt: images, monkeys and a non-uniform prior
6.3 Smoothness: fuzzy pixels and spatial correlations
6.4 Generalizations: some extensions and comments
7. Experimental design
7.1 Introduction: general issues
7.2 Example 7: optimizing resolution functions
7.3 Calibration, model selection and binning
7.4 Information gain: quantifying the worth of an experiment
8. Least-squares extensions
8.1 Introduction: constraints and restraints
8.2 Noise scaling: a simple global adjustment
8.3 Outliers: dealing with erratic data
8.4 Background removal
8.5 Correlated noise: avoiding over-counting
8.6 Log-normal: least-squares for magnitude data
9. Nested sampling
9.1 Introduction: the computational problem
9.2 Nested sampling: the basic idea
9.3 Generating a new object by random sampling
9.4 Monte Carlo sampling of the posterior
9.5 How many objects are needed?
9.6 Simulated annealing
10. Quantification
10.1 Exploring an intrinsically non-uniform prior
10.2 Example: ON/OFF switching
10.3 Estimating quantities
10.4 Final remarks

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Tags: Data Analysis, Bayesian Tutorial, Devinderjit Sivia, John Skilling