Stochastic population modelling and forecasting

目前，除了进行人口估计和预测的中心目的外，地方当局和政府部门使用人口生育数据的原因有很多。其中包括规划生育服务，为政策和养老金模式提供信息，以及按地区确定学校名额的分配。因此，人们需要能够对生育率做出现实而精确预测的模型。尽管先前的研究本质上是确定性的，但目前的文献更倾向于采用随机方法来模拟生育率的随机性，因为这允许对预测的不确定性进行量化。为此目的，该项目的主要目标是开发一个针对特定年龄生育率的随机预测模型，该模型最好地利用各种数据来源、专家知识和最先进的统计方法。在这样做的过程中，我们的目标是获得有关未来生育率变化模式的信息，这些模式具有合理的和精心校准的不确定性水平。这项研究的一个特别创新是使用哈密顿蒙特卡罗拟合生育率预测模型，以汇总来自一系列国家的数据以及英国的调查数据。此外，我们正在使用评分规则来定量评估我们提出的模型与文献中的模型的预测性能。就数据来源而言，我们正在处理人口和个人层面的生育率数据。在前者的情况下，我们正在采用层次贝叶斯方法来开发一个队列生育率预测模型，该模型可以适用于世界各国的生育率。对于后者，我们拟合贝叶斯广义加性模型（GAMs）英国调查数据。通过这种方法，我们可以研究特定胎次生育率如何随年龄、队列和上次出生后的时间平稳变化，以及其他协变量（如资格水平和出生国家）的影响。当我们将生育率与死亡率和移民一起视为决定人口预测的人口变化的三个组成部分之一时，就可以看到这项研究的巨大潜力。因此，本项目开发的生育率预测模型可以与其他组成部分的随机模型相结合，以产生具有适当不确定性水平的人口预测。

Relevant EPSRC research area: Statistics and applied probabilityIn 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.