  During the current Covid-19 pandemic in Italy, official data are collected
with medical swabs following a pure convenience criterion which, at least in an
early phase, has privileged the exam of patients showing evident symptoms.
However, there are evidences of a very high proportion of asymptomatic patients
(e. g. Aguilar et al., 2020; Chugthai et al, 2020; Li, et al., 2020; Mizumoto
et al., 2020a, 2020b and Yelin et al., 2020). In this situation, in order to
estimate the real number of infected (and to estimate the lethality rate), it
should be necessary to run a properly designed sample survey through which it
would be possible to calculate the probability of inclusion and hence draw
sound probabilistic inference. Some researchers proposed estimates of the total
prevalence based on various approaches, including epidemiologic models, time
series and the analysis of data collected in countries that faced the epidemic
in earlier time (Brogi et al., 2020). In this paper, we propose to estimate the
prevalence of Covid-19 in Italy by reweighting the available official data
published by the Istituto Superiore di Sanit\`a so as to obtain a more
representative sample of the Italian population. Reweighting is a procedure
commonly used to artificially modify the sample composition so as to obtain a
distribution which is more similar to the population (Valliant et al., 2018).
In this paper, we will use post-stratification of the official data, in order
to derive the weights necessary for reweighting them using age and gender as
post-stratification variables thus obtaining more reliable estimation of
prevalence and lethality.
