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Fits, and especially linear fits, with errors on both axes,
extra variance of the data points and other complications
Reference to this paper: physics/0511182
Printable versions and related topics at this URL.
Abstract:
The aim of this paper, triggered by some discussions in the astrophysics
community raised by
http://arxiv.org/abs/astro-ph/0508529astro-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.
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Giulio D'Agostini
2005-11-21