Projections for first-wave COVID-19 deaths across the US using social-distancing measures derived from mobile phones

Spencer Woody; Mauricio Garcia Tec; Maytal Dahan; Kelly Gaither; Spencer Fox; Lauren Ancel Meyers; James G Scott

In the IHME model, the choice of using penalized-least-squares fit on the logcumulative-deaths scale has major consequences for statistical inference. In particular, the authors use the inverse-Hessian matrix at the MAP estimate in order to produce uncertainty estimates. This uncertainty quantification procedure, however, implicitly assumes that successive observations are independent. Indeed, without this assumption, it is not generally true that the inverse-Hessian at the MAP provides a valid large-sample estimate for the covariance matrix of an estimator, Bayesian or otherwise. This important technical condition simply cannot be true on the scale used for fitting the IHME model, for the simple reason that the data used for fitting are cumulative: if today's prediction for cumulative death rate is too high, then tomorrow's prediction is more likely to be too high as well. This is easily verified by a simple calculation. The covariance of two successive cumulative death rates r it is: cov(r i,t , r i,t+1 ) = cov(r i,t , r i,t + y i,t+1 ) = var(r it ) + cov(r i,t , y i,t+1 ) = N −2 var ∑ s