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

Fits, and especially linear fits, with errors on both axes, extra variance of the data points and other complications

The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the construction of model that describes the `network of dependences' (a Bayesian network) that connects experimental observations to model parameters and upon which the probabilistic inference relies. The particular case of linear fit with errors on both axes and extra variance of the data points around the straight line (i.e. not accounted by the experimental errors) is shown in detail. Some questions related to the use of linear fit formulas to log-linearized exponential and power laws are also sketched, as well as the issue of systematic errors.Comment: 20 pages, 4 figures, hyperlinked bibliography in pdf versio

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

From Observations to Hypotheses: Probabilistic Reasoning Versus Falsificationism and its Statistical Variations

Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of causes and effects. Formulated with Poincare's words, the "essential problem of the experimental method" becomes then solving a "problem in the probability of causes", i.e. ranking the several hypotheses, that might be responsible for the observations, in credibility. This probabilistic approach to the problem (nowadays known as the Bayesian approach) differs from the standard (i.e. frequentistic) statistical methods of hypothesis tests. The latter methods might be seen as practical attempts of implementing the ideal of falsificationism, that can itself be viewed as an extension of the proof by contradiction of the classical logic to the experimental method. Some criticisms concerning conceptual as well as practical aspects of na\"\i ve falsificationism and conventional, frequentistic hypothesis tests are presented, and the alternative, probabilistic approach is outlined.Comment: 17 pages, 4 figures (V2 fixes some typos and adds a reference). Invited talk at the 2004 Vulcano Workshop on Frontier Objects in Astrophysics and Particle Physics, Vulcano (Italy) May 24-29, 2004. This paper and related work are also available at http://www.roma1.infn.it/~dagos/prob+stat.htm

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