  This paper proposes a data-driven approximate Bayesian computation framework
for parameter estimation and uncertainty quantification of epidemic models,
which incorporates two novelties: (i) the identification of the initial
conditions by using plausible dynamic states that are compatible with
observational data; (ii) learning of an informative prior distribution for the
model parameters via the cross-entropy method. The new methodology's
effectiveness is illustrated with the aid of actual data from the COVID-19
epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential
equation-based model with a generalized SEIR mechanistic structure that
includes time-dependent transmission rate, asymptomatics, and hospitalizations.
A minimization problem with two cost terms (number of hospitalizations and
deaths) is formulated, and twelve parameters are identified. The calibrated
model provides a consistent description of the available data, able to
extrapolate forecasts over a few weeks, making the proposed methodology very
appealing for real-time epidemic modeling.
