Inferring COVID-19 spreading rates and potential change points for case number forecasts

Jonas Dehning; Johannes Zierenberg; Frank Paul Spitzner; Michael Wibral; Joao Pinheiro Neto; Michael Wilczek; Viola Priesemann

For each MCMC step, the new parameters are drawn so that a set of parameters that minimizes the previous deviation is more likely to be chosen. In our case, this is done with an advanced gradient-based method (NUTS [43] ). To reiterate, every time integration that is performed has its own set of parameters and yields one complete model time series. If the time integration describes the data well the parameter set is accepted, and this yields one Monte Carlo sample of the model parameters for the posterior distribution; the MCMC step is then repeated to create more samples from the posterior. Eventually, the majority of accepted parameter samples will describe the real-world data well, so that consistent forecasts are possible in the forecast phase.