Data Analysis: A Bayesian Tutorial
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'.
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algorithm amplitude approximation assign background Bayes Bayesian best estimate calculation Chapter coin components constant correlation corresponding covariance covariance matrix data analysis datum defined derivatives distribution double eigenvalues eigenvectors entropy error-bar evaluated example experimental exponential flips form of eqn free-form Gaussian pdf given inference integral inverse iterates least-squares lighthouse likelihood constraint likelihood function linear logarithm loge marginal marginal likelihood matrix MaxEnt maximum measurements model selection Mplus nested sampling noise normalization normalization constant object obtain optimal parameters pdf of eqn Poisson position posterior pdf posterior probability principle of indifference prior pdf prob prob(Dk prob(X prob(X|I probability theory problem procedure product rule quadratic quantity random resolution function result Section shown in Fig signal peak solution switches Taylor series theorem transition uncertainty uniform prior variables width yields zero