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Bayesian Inference in Processing Experimental Data
Principles and Basic Applications

G. D'Agostini
Università ``La Sapienza'' and INFN, Roma, Italia


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. 1

Note: This is an html version of the preprint of a review article published in Reports on Progress in Physics 66 (2003) 1383. See here for printable versions of the preprint as well as for related publications by the author.

Giulio D'Agostini 2003-05-13