Bibliographic note

The state of the art of Bayesian theory is summarized in Refs. [19] and [86], where many references can be found. A comprehensive and eloquent presentation of the Bayesian approach in scientific reasoning, covering philosophical, mathematical and statistical aspects is given in Ref. [87], a short account of which can be found in a ``Nature'' article [8]. Very interesting and insightful philosophical and historical aspects of subjective probability are provided in the introduction of Ref. [80]. To get an idea of what present philosophers think about Bayesian theory see also Refs. [88] and [89] and references therein. For a short introduction on subjective probability, as well as its importance in the physics curriculum, see Ref. [21].

As a classical book on subjective probability, de Finetti's ``Theory of probability''[11] is a must. I found Ref. [90] particularly stimulating and Ref. [32] very convincing (the latter represents, in my opinion, the only real introductory, calculus-based, textbook on subjective probability and Bayesian statistics available so far, with many examples and exercises). Unfortunately these two books are only available in Italian at the moment. For Italian readers, I also recommend Refs. [91] and [92].

I have consulted Refs. [30] and [31], which also contain many references. References [29], [93], [94], [95], [96] [97], [98], [99], [42] and [100] are well-known books among Bayesian. Some literature on Bayesian Networks can be found in Ref. [69], which also contains interesting URLs. Reference [101] is a recent Bayesian book close to the physicist's point of view. For developments on Bayesian theory and practical applications I recommend consulting the proceedings of ``Valencia Meetings'' [102] and ``Maxent Workshops'' [103]. An overview of maximum-entropy methods can also be found in Ref. [59]. This last reference and Ref. [36] show some applications of Bayesian reasoning in statistical mechanics. Other information on Bayesian literature methods can be found on web sites. As a starting point I would recommend Ref. [104], as well as other sites dedicated to Bayesian networks and artificial intelligence[69]. When integrals become complicated, the Markov Chain Monte Carlo (MCMC) technique becomes crucial: introductions and applications can be found, for example, in Refs. [95] and [105].

The applied part of these notes, as well as the critical part, is mostly original. References are given at the appropriate place in the text -- only those actually used have been indicated. Reference [106] contains applications of some of the methods described here in analyses of HEP data. A concise critical overview of Bayesian reasoning versus frequentistic methods in HEP can be found in Ref. [107], whilst Ref. [22] is recommended to those who are still anxious about priors.

As far as measurement uncertainty is concerned, consultation of the ISO Guide[3] is advised. At present the BIPM recommendations are also followed by the American National Institute of Standards and Technology (NIST), whose guidelines[5] are also on the web.