1,178 research outputs found
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
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