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During the current Covid-19 pandemic in Italy, official data are collectedwith medical swabs following a pure convenience criterion which, at least in anearly 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; Mizumotoet al., 2020a, 2020b and Yelin et al., 2020). In this situation, in order toestimate the real number of infected (and to estimate the lethality rate), itshould be necessary to run a properly designed sample survey through which itwould be possible to calculate the probability of inclusion and hence drawsound probabilistic inference. Some researchers proposed estimates of the totalprevalence based on various approaches, including epidemiologic models, timeseries and the analysis of data collected in countries that faced the epidemicin earlier time (Brogi et al., 2020). In this paper, we propose to estimate theprevalence of Covid-19 in Italy by reweighting the available official datapublished by the Istituto Superiore di Sanit\`a so as to obtain a morerepresentative sample of the Italian population. Reweighting is a procedurecommonly used to artificially modify the sample composition so as to obtain adistribution which is more similar to the population (Valliant et al., 2018).In this paper, we will use post-stratification of the official data, in orderto derive the weights necessary for reweighting them using age and gender aspost-stratification variables thus obtaining more reliable estimation ofprevalence and lethality.

Observed and estimated prevalence of Covid-19 in Italy: Is it possible to estimate the total cases from medical swabs data?