extra variance of the data points and other complications

*Università ``La Sapienza'' and INFN, Rome, Italy*

(giulio.dagostini@roma1.infn.it,
`http://www.roma1.infn.it/~dagos`)

**Reference** to this paper: physics/0511182

**Printable versions and related topics** at this URL.

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.

- Preamble
- Introduction
- Probabilistic parametric inference from a set of data points with errors on both axes
- Linear fit with normal errors on both axes
- Approximated solution for non-linear fits with normal errors
- Extra variability of the data
- Computational issues: normalization, fit summaries, priors and approximations
- From power law to linear fit
- Systematic errors
- Conclusions
- Bibliography
- About this document ...