Stochastic population forecasting based on a combination of experts evaluations and accounting for correlation of demographic components

Francesco C. Billari, Università Bocconi
Rebecca Graziani, Università Bocconi
Eugenio Melilli, Università Bocconi

We suggest a method for deriving expert based stochastic population forecasts, by combining evaluations of several experts and allowing for correlation among demographic components and among experts. Evaluations of experts are elicited resorting to the conditional method discussed in Billari et al. (2010) and are then combined resorting to the supra-Bayesian approach (Lindley, 1983) so to derive the joint forecast distribution of all summary indicators of the demographic change. In particular, the elicitation procedure makes it possible to elicit evaluations from experts not only on the future values of the indicators and on their expected variability, but also on the across time correlation of each indicator and on the correlation (at the same time and across time) between pairs of indicators. The central scenarios provided by the experts on future values of each summary indicator are treated as data and a likelihood function is specified by the analyst on the basis of all additional information provided by the experts, such likelihood been parametrized in terms of the unknown future values of the indicators. Therefore the posterior distribution, obtained on the basis of the Bayes theorem and updating the analyst prior opinions on the basis of the evaluations provided by the experts, can be used to describe the future probabilistic behavior of the vital indicators so to derive probabilistic population forecasts in the framework of the traditional cohort component model.