Nowcasting by Bayesian Smoothing: A flexible, generalizable model for real-time epidemic tracking

Sarah F. McGough; Michael A. Johansson; Marc Lipsitch; Nicolas A. Menzies

The logarithmic scoring rule was used to quantify the accuracy of the posterior predictive distribution of the nowcast. Predictive distributions were assigned to a series of bins categorized across possible values of true case counts. We used bin widths of 25 cases for dengue and 1000 cases for influenza, allowing for a larger number of bins for ILI cases based on case ranges of approx. 0-400 for dengue and 4,000-40,000 for ILI. For a predictive distribution with binned probability pi for a given nowcast target, the logarithmic score was calculated as ln(pi). For example, there were 115 cases eventually observed for the week of January 20, 1992. The NobBS nowcast for this week, which assigned a probability of 0.4 to the bin [100,125), thus received a log score of ln(0.4) = -0.92. As in (22, 23) , a very low log score of -10 was assigned for weeks in which the predictive distribution did not include the true case value, for weeks in which the bin probability ≤ e -10 . This rule provides a lower limit (-10) to the score of highly inaccurate predictions.