A defense of Columbo
(and of the use of Bayesian inference in forensics)
- A multilevel introduction to probabilistic reasoning -
Università ``La Sapienza'' and INFN, Roma, Italia
Note: the automatic translation LaTeX -> html (performed by latex2html)
is quite poor.
The original document (in several versions) can be found in
Triggered by a recent interesting New Scientist article
on the too frequent incorrect use of probabilistic
evidence in courts, I introduce the basic concepts of
probabilistic inference with a toy model, and
discuss several important issues that need to be
understood in order
to extend the basic reasoning to real life cases.
In particular, I emphasize
the often neglected point
that degrees of beliefs
are updated not by `bare facts' alone, but by all
available information pertaining to them,
including how they have been acquired.
In this light I show that,
contrary to what claimed in that article,
there was no ``probabilistic pitfall''
in the Columbo's episode pointed as example
of ``bad mathematics'' yielding ``rough justice''.
Instead, such a criticism could have a `negative
reaction' to the article itself and to the
use of Bayesian reasoning in courts,
as well as in all other places
in which probabilities need to be assessed and
decisions need to be made. Anyway, besides
introductory/recreational aspects, the paper touches important
questions, like: role and evaluation of priors;
subjective evaluation of Bayes factors;
role and limits of intuition;
`weights of evidence' and `intensities of beliefs'
(following Peirce) and `judgments leaning'
(here introduced), including their uncertainties
role of relative frequencies to assess and express
beliefs; pitfalls due to `standard' statistical education;
weight of evidences mediated by testimonies.
A small introduction to Bayesian networks, based
on the same toy model (complicated by the
possibility of incorrect testimonies) and implemented
using Hugin software, is also
provided, to stress the importance of formal, computer aided
``Use enough common sense to know
when ordinary common sense does not apply''
(I.J. Good's guiding principle of all science)