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G. D'Agostini

Publications and source records attributed to G. D'Agostini.

65 records · Page 4Linked to original sources
arXiv2000

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'.

hep-ex↗
arXiv2000

Uncertainties due to imperfect knowledge of systematic effects: general considerations and approximate formulae

Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian approach), all sources of uncertainty can be included in a logically consistent way. Practical formulae for the first moments of the probability distribution are derived up to second-order approximations.

hep-ex↗
arXiv1999

Inferring the intensity of Poisson processes at the limit of the detector sensitivity (with a case study on gravitational wave burst search)

We consider the issue of reporting the result of search experiment in the most unbiased and efficient way, i.e. in a way which allows an easy interpretation and combination of results and which do not depend on whether the experimenters believe or not to having found the searched-for effect. Since this work uses the language of Bayesian theory, to which most physicists are not used, we find that it could be useful to practitioners to have in a single paper a simple presentation of Bayesian inference, together with an example of application of it in search of rare processes.

hep-ex↗
arXiv1999

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.

physics.data-an↗
arXiv1999

Overcoming priors anxiety

The choice of priors may become an insoluble problem if priors and Bayes' rule are not seen and accepted in the framework of subjectivism. Therefore, the meaning and the role of subjectivity in science is considered and defended from the pragmatic point of view of an ``experienced scientist''. The case for the use of subjective priors is then supported and some recommendations for routine and frontier measurement applications are given. The issue of reference priors is also considered from the practical point of view and in the general context of ``Bayesian dogmatism''.

physics.data-an↗
arXiv1999

Constraints on the Higgs Boson Mass from Direct Searches and Precision Measurements

We combine, within the framework of the Standard Model, the results of Higgs search experiments with the information coming from accurate theoretical calculation and precision measurements to provide a probability density function for the Higgs mass, from which all numbers of interest can be derived. The expected value is 170 GeV, with an expectation uncertainty, quantified by the standard deviation of the distribution, of about 80 GeV. The median of the distribution is 150 GeV, while 75 % of the probability is concentrated in the region $M_H \leq 200$ GeV. The 95 % probability upper limit comes out to be around 300 GeV.

hep-ph↗
arXiv1998

Bayesian reasoning versus conventional statistics in High Energy Physics

The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The combination of intuition and conventional statistics allows practitioners to get results which are very close, both in meaning and in numerical value, to those obtainable by Bayesian methods, at least in simple routine applications. There are, however, cases in which ``arbitrary'' probability inversions produce unacceptable or misleading results and in these cases the conscious application of Bayesian reasoning becomes crucial. Starting from these considerations, I will finally comment on the often debated question: ``is there any chance that all physicists will become Bayesian?''

physics.data-an↗
arXiv1998

Jeffreys priors versus experienced physicist priors - arguments against objective Bayesian theory

I review the problem of the choice of the priors from the point of view of a physicist interested in measuring a physical quantity, and I try to show that the reference priors often recommended for the purpose (Jeffreys priors) do not fit to the problem. Although it may seem surprising, it is easier for an ``experienced physicist'' to accept subjective priors, or even purely subjective elicitation of probabilities, without explicit use of the Bayes' theorem. The problem of the use of reference priors is set in the more general context of ``Bayesian dogmatism'', which could really harm Bayesianism.

physics.data-an↗
arXiv1996

A Theory of Measurement Uncertainty Based on Conditional Probability

A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International Organization for Standardization (ISO) recommendation on measurement uncertainty is reobtained as the limit case in which linearization is meaningful and one is interested only in the best estimates of the quantities and in their variances.

physics.data-an↗
arXiv1995

Probability and Measurement Uncertainty in Physics - a Bayesian Primer

Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental information. This was the original point of view of Bayes, Bernoulli, Gauss, Laplace, etc. and contrasts with later ``conventional'' (pseudo-)definitions of probabilities, which implicitly presuppose the concept of probability. These notes show that the Bayesian approach is the natural one for data analysis in the most general sense, and for assigning uncertainties to the results of physical measurements - while at the same time resolving philosophical aspects of the problems. The approach, although little known and usually misunderstood among the High Energy Physics community, has become the standard way of reasoning in several fields of research and has recently been adopted by the international metrology organizations in their recommendations for assessing measurement uncertainty. These notes describe a general model for treating uncertainties originating from random and systematic errors in a consistent way and include examples of applications of the model in High Energy Physics, e.g. ``confidence intervals'' in different contexts, upper/lower limits, treatment of ``systematic errors'', hypothesis tests and unfolding.

hep-ph↗