Robust non-parametric mortality and fertility modelling and forecasting: Gaussian process regression approaches

There has been an increasing demand for demographic modelling and forecasting over the last few decades, driven by many developed countries are now suffering a rapid decline in mortality and fertility, leading to a significant increase in expenditures on health services for an ageing population and a shortage of future labour. A better understanding of the mortality and fertility patterns and trends is always of importance for all stakeholders in a society as the mortality forecasts, for example, play a vital role for the insurance and pensions industries in pricing their insurance products. The fertility predictions are also of great interest to the government and education sectors in planing children's welfare and educational services. Unlike the biological and the medical methods, statisticians have developed very different and purely mathematical methods to model the demographic patterns and trends which are well-documented by Preston et al. (2000). The history of demographic modelling with the mathematical approaches can be traced back to some deterministic models proposed in the midnineteenth century, see, for example, Gompertz (1825) and Makeham (1860). The deterministic models are, however, restricted with few fixed factors and have no stochastic process considered owing to the lack of computing capability in that early period.