  A key challenge in estimating the infection fatality rate (IFR) -- and its
relation with various factors of interest -- is determining the total number of
cases. The total number of cases is not known because not everyone is tested,
but also, more importantly, because tested individuals are not representative
of the population at large. We refer to the phenomenon whereby infected
individuals are more likely to be tested than non-infected individuals, as
"preferential testing." An open question is whether or not it is possible to
reliably estimate the IFR without any specific knowledge about the degree to
which the data are biased by preferential testing. In this paper we take a
partial identifiability approach, formulating clearly where deliberate prior
assumptions can be made and presenting a Bayesian model which pools information
from different samples. When the model is fit to European data obtained from
seroprevalence studies and national official COVID-19 statistics, we estimate
the overall COVID-19 IFR for Europe to be 0.53%, 95% C.I. = [0.39%, 0.69%].
