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 optimisation, 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'.
1. The Basics; 2. Parameter Estimation I; 3. Parameter Estimation II; 4. Model Selection; 5. Assigning Probabilities; 6. Non-parametric Estimation; 7. Experimental Design; 8. Least-Squares Extensions; 9. Nested Sampling; 10. Quantification; Appendices; Bibliography
One of the strengths of this book is the author's ability to motivate the use of Bayesian methods through simple yet effective examples. Katie St. Clair MAA Reviews