With an estimated $10.4 billion in medical costs and 31.4 million outpatient visits each year, influenza poses a serious burden of disease in the United States. To provide insights and advance warning into the spread of influenza, the U.S. Centers for Disease Control and Prevention (CDC) runs a challenge for forecasting weighted influenza-like illness (wILI) at the national and regional level. Many models produce independent forecasts for each geographical unit, ignoring the constraint that the national wILI is a weighted sum of regional wILI, where the weights correspond to the population size of the region. We propose a novel algorithm that transforms a set of independent forecast distributions to obey this constraint, which we refer to as probabilistically coherent. Enforcing probabilistic coherence led to an increase in forecast skill for 79% of the models we tested over multiple flu seasons, highlighting the importance of respecting the forecasting system’s geographical hierarchy.

流感每年造成约104亿美元的医疗费用和3,140万例门诊，在美国构成严重的疾病负担。为了提供有关流感传播的见识和预警，美国疾病控制与预防中心（CDC）在国家和地区级别预测加权类流感样疾病（wILI）时面临挑战。许多模型忽略了国家wILI是地区wILI加权总和的约束，其中权重与该地区的人口规模相对应，从而对每个地理区域产生了独立的预测。我们提出了一种新颖的算法，该算法可以转换一组独立的预测分布以服从该约束，我们称其为概率相干。