  Hospitals commonly project demand for their services by combining their
historical share of regional demand with forecasts of total regional demand.
Hospital-specific forecasts of demand that provide prediction intervals, rather
than point estimates, may facilitate better managerial decisions, especially
when demand overage and underage are associated with high, asymmetric costs.
Regional forecasts of patient demand are commonly available as a Poisson random
variable, e.g., for the number of people requiring hospitalization due to an
epidemic such as COVID-19. However, even in this common setting, no
probabilistic, consistent, computationally tractable forecast is available for
the fraction of patients in a region that a particular institution should
expect. We introduce such a forecast, DICE (Demand Intervals from Consistent
Estimators). We describe its development and deployment at an academic medical
center in California during the `second wave' of COVID-19 in the Unite States.
We show that DICE is consistent under mild assumptions and suitable for use
with perfect, biased, unbiased regional forecasts. We evaluate its performance
on empirical data from a large academic medical center as well as on synthetic
data.
