Assessing the intensity of a epidemic, such as the COVID-19 pandemic, during the epidemic outbreak, constitutes a significant technical challenge with high societal stakes. Elaborating on classical epidemiological models, this work aims to define a hierarchical Bayesian model that permits the robust estimation of the temporal evolution of the pandemic intensity despite highly corrupted daily new infection counts. It also outputs uncertainty assessment, in the form of credibility intervals robust to the priors choice, accounting for uncertainties on model parameters. The estimation is performed by carefully designed Monte Carlo samplers. The relevance of the proposed estimation procedure is illustrated on real COVID-19 pandemic data for several countries and periods, made available from the Johns Hopkins University repository.