Physics – Data Analysis – Statistics and Probability
Scientific paper
2003-04-28
Rept.Prog.Phys. 66 (2003) 1383-1420
Physics
Data Analysis, Statistics and Probability
40 pages, 2 figures, invited paper for Reports on Progress in Physics
Scientific paper
10.1088/0034-4885/66/9/201
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as: model comparison (including the automatic Ockham's Razor filter provided by the Bayesian approach); parametric inference; quantification of the uncertainty about the value of physical quantities, also taking into account systematic effects; role of marginalization; posterior characterization; predictive distributions; hierarchical modelling and hyperparameters; Gaussian approximation of the posterior and recovery of conventional methods, especially maximum likelihood and chi-square fits under well defined conditions; conjugate priors, transformation invariance and maximum entropy motivated priors; Monte Carlo estimates of expectation, including a short introduction to Markov Chain Monte Carlo methods.
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