Minimum Bias Legacy of Search Results

The end of LEP and SLC is a good moment to review the way to summarize search results in order to exploit at best, in future analyses and speculations, the pieces of information coming from all experiments. Some known problems with the usual way of reporting results in terms ``CL limits'' are shortly recalled, and a plea is formulated to publish just parametrized likelihoods, possibly rescaled to the asymptotic insensitivity limit level.Comment: Talk given at the Seventh Topical Seminar on ``The legacy of LEP and SLC '', Siena, Italy, 8-11 October 2001. This paper and related work are also available at http://www-zeus.roma1.infn.it/~agostini/prob+stat.htm

Probability, propensity and probabilities of propensities (and of probabilities)

The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real life applications, arise quite naturally and the resulting discussion among non-ideologized, free-minded people offers an opportunity for clarifications.Comment: Invited contribution to the proceedings MaxEnt 2016 based on the talk given at the workshop (Ghent, Belgium, 10-15 July 2016), supplemented by work done within the program Probability and Statistics in Forensic Science at the Isaac Newton Institute for Mathematical Sciences, Cambridg

Confidence limits: what is the problem? Is there the solution?

This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in general, not possible, still a search result can be reported in a mostly unbiased and efficient way, which satisfies some desiderata which I believe are shared by the people interested in the subject. The simpler case of `closed likelihood' will also be treated, and I will discuss why a uniform prior on a sensible quantity is a very reasonable choice for most applications. In both cases, I think that much clarity will be achieved if we remove from scientific parlance the misleading expressions `confidence intervals' and `confidence levels'.Comment: 20 pages, 6 figures, using cernrepp.cls (included). Contribution to the Workshop on Confidence Limits, CERN, Geneva, 17-18 January 2000. This paper and related work are also available at http://www-zeus.roma1.infn.it/~agostini/prob+stat.htm

Asymmetric Uncertainties: Sources, Treatment and Potential Dangers

The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the physical quantity of interest is biased with respect to what would be obtained using at best all experimental and theoretical information that contribute to evaluate the combined uncertainty. The probabilistic solution to the problem is provided both in exact and in approximated forms.Comment: 21 pages, 5 figures. improved version with some corrections, additional remarks and references (download of new version is recommended). This paper and related work are also available at http://www.roma1.infn.it/~dagos/prob+stat.htm

Teaching statistics in the physics curriculum: Unifying and clarifying role of subjective probability

Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief introduction to subjective probability and Bayesian inference is given, with comments on typical misconceptions which tend to discredit it and comparisons to other approaches.Comment: 15 pages, LateX, 1 eps figure, corrected some typos. Invited paper for the American Journal of Physics. This paper and related work are also available at http://www-zeus.roma1.infn.it/~agostini

The Fermi's Bayes Theorem

It is curious to learn that Enrico Fermi knew how to base probabilistic inference on Bayes theorem, and that some influential notes on statistics for physicists stem from what the author calls elsewhere, but never in these notes, {\it the Bayes Theorem of Fermi}. The fact is curious because the large majority of living physicists, educated in the second half of last century -- a kind of middle age in the statistical reasoning -- never heard of Bayes theorem during their studies, though they have been constantly using an intuitive reasoning quite Bayesian in spirit. This paper is based on recollections and notes by Jay Orear and on Gauss' ``Theoria motus corporum coelestium'', being the {\it Princeps mathematicorum} remembered by Orear as source of Fermi's Bayesian reasoning.Comment: 4 pages, to appear in the Bulletin of the International Society of Bayesian Analysis (ISBA). Related links and documents are available in http://www.roma1.infn.it/~dagos/history