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The problem of dealing with misreported data is very common in a wide rangeof contexts for different reasons. The current situation caused by the Covid-19worldwide pandemic is a clear example, where the data provided by officialsources were not always reliable due to data collection issues and to the highproportion of asymptomatic cases. In this work, we explore the performance ofBayesian Synthetic Likelihood to estimate the parameters of a model capable ofdealing with misreported information and to reconstruct the most likelyevolution of the phenomenon. The performance of the proposed methodology isevaluated through a comprehensive simulation study and illustrated byreconstructing the weekly Covid-19 incidence in each Spanish AutonomousCommunity in 2020.

Bayesian Synthetic Likelihood Estimation for Underreported Non-Stationary Time Series: Covid-19 Incidence in Spain