Taking the cue from the incredibly precise value of the efficacy of
Moderna's COVID-19 vaccine candidate broadcasted by the media these days
(94.5%, without
any uncertainty attached to it, as instead it should always
be the case for a scientific result) we try to get the probability
distribution of such efficacy
with the limited information available.
The work has been done with the help of a simple Bayesian Network,
processed by a Markov Chain Monte Carlo. The inferred
efficacy results

(mean

standard uncertainty) and a
95% credible interval of
![$[86.6\%,97.6\%]$](img4.png)
. We have also processed through
the same model the new Pfizer results, claiming a 95% efficacy,
getting

with a
95% credible interval of
![$[90.0\%,97.5\%]$](img6.png)
. The efficacies reported
by the two companies correspond indeed
to the modal values of the distributions.
(R. Feynman)