  Based on the information communicated in press releases, and finally
published towards the end of 2020 by Pfizer, Moderna and AstraZeneca, we have
built up a simple Bayesian model, in which the main quantity of interest plays
the role of {\em vaccine efficacy} (`$\epsilon$'). The resulting Bayesian
Network is processed by a Markov Chain Monte Carlo (MCMC), implemented in JAGS
interfaced to R via rjags. As outcome, we get several probability density
functions (pdf's) of $\epsilon$, each conditioned on the data provided by the
three pharma companies. The result is rather stable against large variations of
the number of people participating in the trials and it is `somehow' in good
agreement with the results provided by the companies, in the sense that their
values correspond to the most probable value (`mode') of the pdf's resulting
from MCMC, thus reassuring us about the validity of our simple model. However
we maintain that the number to be reported as `vaccine efficacy' should be the
mean of the distribution, rather than the mode, as it was already very clear to
Laplace about 250 years ago (its `rule of succession' follows from the simplest
problem of the kind). This is particularly important in the case in which the
number of successes equals the numbers of trials, as it happens with the
efficacy against `severe forms' of infection, claimed by Moderna to be 100%.
The implication of the various uncertainties on the predicted number of
vaccinated infectees is also shown, using both MCMC and approximated formulae.
