The starting point of our research is the inadequacy of assuming, in the construction of a model of mortality, that frailty is constant for the individuals comprising a demographic population. This assumption is implicitly made by standard life table techniques. The substantial differences in the individual susceptibility to specific causes of death lead to heterogeneity in frailty, and this can have a material effect on mortality models and projections—specifically a bias due to the underestimation of longevity improvements. Given these considerations, in order to overcome the misrepresentation of the future mortality evolution, we develop a stochastic model based on a stratification weighting mechanism, which takes into account heterogeneity in frailty. Furthermore, the stratified stochastic model has been adapted also to capture COVID-19 frailty heterogeneity, that is a frailty worsening due to the COVID-19 virus. Based on different frailty levels characterizing a population, which affect mortality differentials, the analysis allows for forecasting the temporary excess of deaths by the stratification schemes in a stochastic environment.

In the November 2016 U.S. presidential election, many state-level public opinion polls, particularly in the Upper Midwest, incorrectly predicted the winning candidate. One leading explanation for this polling miss is that the precipitous decline in traditional polling response rates led to greater reliance on statistical methods to adjust for the corresponding bias—and that these methods failed to adjust for important interactions between key variables like educational attainment, race, and geographic region. Finding calibration weights that account for important interactions remains challenging with traditional survey methods: raking typically balances the margins alone, while post-stratification, which exactly balances all interactions, is only feasible for a small number of variables. In this paper, we propose multilevel calibration weighting, which enforces tight balance constraints for marginal balance and looser constraints for higher-order interactions. This incorporates some of the benefits of post-stratification while retaining the guarantees of raking. We then correct for the bias due to the relaxed constraints via a flexible outcome model; we call this approach “double regression with post-stratification.” We use these tools to re-assess a large-scale survey of voter intention in the 2016 U.S. presidential election, finding meaningful gains from the proposed methods. The approach is available in the multical R package.

It is well known that Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model. A central limit theorem is established for the integration error if the number of control variates tends to infinity. The integration error is scaled by the standard deviation of the error term in the regression model. If the linear span of the control variates is dense in a function space that contains the integrand, the integration error tends to zero at a rate which is faster than the square root of the number of Monte Carlo replicates. Depending on the situation, increasing the number of control variates may or may not be computationally more efficient than increasing the Monte Carlo sample size.