Data Analysis: A Bayesian TutorialClarendon Press, 1996 - 189 pages Statistics lectures have often been viewed with trepidation by engineering and science students taking an ancillary course in this subject. Whereas there are many texts showing "how" statistical methods are applied, few provide a clear explanation for non-statisticians of how the principlesof data analysis can be based on probability theory. Data Analysis: A Bayesian Tutorial provides such a text, putting emphasis as much on understanding "why" and "when" certain statistical procedures should be used as "how". This difference in approach makes the text ideal as a tutorial guide forsenior 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. With its central emphasis on a fewfundamental rules, this book takes the mystery out of statistics by providing a clear rationale for some of the most widely-used procedures. |
Table des matières
The basics | 1 |
Parameter estimation I | 13 |
Parameter estimation II | 37 |
Model selection | 82 |
Assigning probabilities | 106 |
Nonparametric estimation | 132 |
Experimental design | 159 |
Gaussian integrals and related topics | 177 |
| 185 | |
Expressions et termes fréquents
0.5 Bias-weighting according to eqn algorithm Amax amplitude approximation assign background signal Bayes best estimate Bias-weighting for heads Bragg peak calculation Chapter coin consider corresponding covariance matrix D₁ data analysis datum distribution eigenvalues eigenvectors entropy equal error-bar evaluated example expected value experimental exponential flips form of eqn Gaussian pdf generalisation given H₁ heads H illustrated inference integral of eqn inverse Lagrange multiplier least-squares lighthouse likelihood function logarithm magnitude marginalisation MaxEnt maximum measurements model selection multivariate normalisation constant number of counts number of data obtain optimisation pdf of eqn pixels plotted Poisson position posterior pdf posterior probability prior of eqn prior pdf prob(a probability theory problem procedure product rule quadratic reliability resolution function result second derivative Section shown in Fig signal peak simple spectrum Taylor series theorem uniform prior variables width X₁ zero