question: A key challenge in estimating the infection fatality rate (IFR) of COVID-19 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. Results suggest that when limited knowledge is available about the magnitude of preferential testing, reliable estimation of the IFR is still possible so long as there is sufficient"heterogeneity of bias"across samples.