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Bayesian inference in processing experimental data: principles and basic applications

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G D'Agostini

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This paper 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 the following: 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; and Monte Carlo (MC) estimates of expectation, including a short introduction to Markov Chain MC methods.


PACS

02.50.Ga Markov processes

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

02.50.Cw Probability theory

02.50.Ng Distribution theory and Monte Carlo studies

Subjects

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 9 (September 2003)

Received 26 February 2003, in final form 7 July 2003

Published 11 August 2003



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