The key to our approach is the use of sequential Monte Carlo methods to evaluate the likelihood of a generic epidemiological model. Once we have the likelihood, we specify priors and rely on a Markov chain Monte Carlo to sample from the posterior distribution. We show how to use the posterior simulation outputs as inputs for exercises in causality assessment. We apply our approach to Belgian data for the COVID-19 epidemic during 2020. Our estimated time-varying-parameters SIRD model captures the data dynamics very well, including the three waves of infections. We use the estimated (true) number of new cases and the time-varying effective reproduction number from the epidemiological model as information for structural vector autoregressions and local projections. We document how additional government-mandated mobility curtailments would have reduced deaths at zero cost or a very small cost in terms of output.