Comments and conclusions

Well, this was meant to be a short note. Obviously it is not just a comment to the New Scientist article, that could have been contained in a couple of sentences. In fact, discussing with several people, I felt that yet another introduction to Bayesian reasoning, not focused on physics issues, might be useful. So, at the end of the work, Columbo's cameras were just an excuse.

Let us now summarize what we have learned and make further comments on some important issues.

First, we have to be aware that often we do not see `a fact' (e.g. Galesco killing his wife), but we infer it from other facts, assuming a causal connection among them.35But sometimes the observed effect can be attributed to several causes and, therefore, having observed an effect we cannot be sure about its cause. Fortunately, since our beliefs that each possible cause could produce that effect are not equal, the observation modifies our beliefs on the different causes. That is the essence of Bayesian reasoning. Since `Bayesian' has several flavors36 in the literature, I summarize the points of view expressed here:

And Galesco? Come on, there is little to argue.
$ [$Nevertheless, the reading of the instructive New Scientist article is warmly recommended!$ ]$

It is a pleasure to thank Pia and Maddalena, who introduced me Columbo, and Dino Esposito, Paolo Agnoli and Stefania Scaglia for having taken part to the post dinner jury that absolved him. The text has benefitted of the careful reading by Dino, Paolo and Enrico Franco (see in particular his interesting remark in footnote 44).

Giulio D'Agostini 2010-09-30