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

TL;DR

This paper introduces a Bayesian Synthetic Likelihood approach to estimate and reconstruct the true evolution of Covid-19 incidence in Spain, addressing issues of underreporting and data unreliability during the pandemic.

Contribution

It develops a novel Bayesian synthetic likelihood method tailored for non-stationary, underreported time series data, specifically applied to Covid-19 incidence in Spain.

Findings

Effective reconstruction of Covid-19 incidence in Spanish regions.

Robustness of the method against misreported data.

Improved parameter estimation in underreported scenarios.

Abstract

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.