  The problem of dealing with misreported data is very common in a wide range
of contexts for different reasons. The current situation caused by the Covid-19
worldwide pandemic is a clear example, where the data provided by official
sources were not always reliable due to data collection issues and to the high
proportion of asymptomatic cases. In this work, we explore the performance of
Bayesian Synthetic Likelihood to estimate the parameters of a model capable of
dealing with misreported information and to reconstruct the most likely
evolution of the phenomenon. The performance of the proposed methodology is
evaluated through a comprehensive simulation study and illustrated by
reconstructing the weekly Covid-19 incidence in each Spanish Autonomous
Community in 2020.
