Effect of a Bayes factor of 13

To evaluate how a new piece of evidence modifies these levels of confidence, we need to quantify somehow the different priors. Since, as we have seen above, what really matters in these cases are the powers of ten of the odds, we could place Columbo's ones in the region $ 10^{2}$-$ 10^{3}$, the hypothetical jury ones around $ 10^{-2}$, perhaps up to $ 10^{-1}$. Multiplying these values by 13 we see that, while the lieutenant would be practically sure Galesco is guilty, the jury component could hardly reach the level of a sound suspicion.

Using the expressions of subsection 2.4, a Bayes factor of 13 corresponds to $ \Delta $JL$ =1.1$, that, added to initial leanings of $ \approx 2.5\pm 0.5$ (Colombo) and $ \approx -1.5 \pm 0.5$ (jury), could lead to combined JL's of $ 3.6\pm 0.5$ or $ -0.4 \pm 0.5$ in the two cases.

However, although such a small weight of evidence is not enough, by itself, to condemn a person, I do not agree that ``that kind of evidence would never stand up in court''[1] for the reasons expounded in section 3.4.

Nevertheless, my main point in this paper is not that even such a modest piece of evidence should stand up in court (provided it is not the only one), but rather that the weight of evidence provided by the rash Galesco's act is not 1.1, but much higher, infinitely higher.

Giulio D'Agostini 2010-09-30