Stochastic population modelling and forecasting

Relevant EPSRC research area: Statistics and applied probability
In the present day, aside from the central purpose of producing population estimates and forecasts, local authorities and governmental departments use fertility data from populations for many reasons. These include planning maternity services, informing policies and pensions models, and determining the allocation of school places by region. As a result, models that can produce realistic and precise forecasts of fertility rates are in demand. Although previously deterministic in nature, the current literature is favouring stochastic approaches that model the randomness of fertility, as this allows the quantification of forecast uncertainty. To this end, the key objective of this project is to develop a stochastic predictive model for age-specific fertility rates that best utilises a variety of data sources, expert knowledge and state-of-the-art statistical methodology. In doing this, we aim to obtain information about future patterns of variability of fertility rates with plausible and well-calibrated levels of uncertainty. One particular innovation in this research is the use of Hamiltonian Monte Carlo to fit fertility forecasting models to aggregate data from a range of countries as well as UK survey data. In addition, we are using scoring rules to quantitatively assess the predictive performance of our proposed models with those in the literature. In terms of data sources, we are working with both population- and individual-level fertility data. In the case of the former, we are taking a hierarchical Bayesian approach to develop a cohort fertility forecasting model that can be fitted to fertility rates from countries around the world. For the latter, we are fitting Bayesian Generalised Additive Models (GAMs) to UK survey data. Through this, we can investigate how parity-specific fertility rates vary smoothly with age, cohort and time since last birth, and also the effects of additional covariates such as qualification level and country of birth. The great potential of the research can be seen when we view fertility as one of the three components of population change - along with mortality and migration - that determine population projections. Therefore the predictive model for the fertility component developed during this project could be combined with stochastic models for the other components in order to generate population projections with appropriate levels of uncertainty.