Methods used to explore Efficiency Results of SARS-CoV-2 Policies
Method 1: Bayesian Convolutional Neural Networks
Convolutional neural networks (CNNs) are deep learning approaches, which are typically used to solve image classification tasks (Krizhevsky et al., 2012; Szegedy et al., 2014). In our investigation, however, we use CNNs in a novel context. CNNs require usually huge amounts of data to prevent overfitting. CNNs might also not be fit to incorporate the factor uncertainty, which is crucial when dealing with relatively small or uncertain data areas. In contrast to CNNs, the Bayesian neural networks (BNNs) approach, which is developed in the 1990s and studied extensively since then (MacKay, 1992; Neal, 1995), delivers a robust method in terms of offering uncertainty estimates. BNNs can easily learn from small and uncertain datasets. Integration of BNNs and CNNs means a probabilistic interpretation of the deep learning CNN model by inferring distributions over the models’ weights and offering distributions over the models’ outputs, i.e. BCNN. The aim of the BCNN in our study is to predict the reproduction of the virus one month ahead of the time from each day.
Method 2: Bayesian statistical correlation inference
To analyze the role of each influencing input factor (selected from the set of 66 government measures, virus variant distributions of 31 virus types, the vaccinated population percentages by the first five doses as well as the reported daily infections in each country) on the pandemic growth, the distribution of pandemic growth rates, in the days where the selected explanatory factor has been active, is compared with the distribution of the pandemic growth rates in the days where the selected explanatory variable has not been active. To obtain the posterior probabilities with regard to presence and not-presence of a selected factor, we analyze the data based on a hierarchical Bayesian model (Congdon, 2019; Johnson et. al., 2022). A hierarchical Bayesian model considers a hyper parameter at the top level of its analysis, as well as specific parameters in its lower level. The top hierarchical level takes the overall distribution of growth rates in a country into account regardless of the condition whether a certain factor E has been active or not. The lower level takes the situation-specific developments into account i.e. whether the selected influential factor is implemented or not. The sampling procedure of the posterior distributions are accomplished via using No-U-turn sampler (NUTS) implemented in the probabilistic programming package for python PyMC3.