Presented by Prof Peter Smith as part of the ANU Demography Seminar Series
We propose a comprehensive mortality modelling framework, which overcomes several of the limitations associated with existing approaches. One such issue is that error models which do not adequately account for the variability in the data can lead to estimates and forecasts which over-fit and are insufficiently robust. Our approach accounts for this by specifying a negative binomial error structure. Another feature, lacking in many existing approaches, is the facility to impose smoothness in parameter series which vary over age, cohort and time. Such constraints are integrated into the modelling process, so that there is a natural feedback, whereby the smoothing of parameter series can appropriately impact other estimates, rather than being performed in a post hoc fashion. Generalised additive models (GAMs) are a flexible class of semiparametric statistical models which allow parametric functions and unstructured (but smooth) functions of explanatory variables to appear in the model simultaneously. We demonstrate the potential of GAMs for mortality modelling and forecasting. In particular, GAMs allow us to differentially smooth components, such as cohorts, more aggressively in areas of sparse data for the component concerned. While GAMs can provide a reasonable fit for the ages where there is adequate data, estimation and extrapolation of mortality rates using a GAM at higher ages is problematic due to high variation in crude rates. At these ages, parametric models can give a more robust fit, enabling a borrowing of strength across age groups. Our modelling methodology is based on a smooth transition between a GAM at lower ages and a fully parametric model at higher ages. Finally, our framework is fully probabilistic, and provides a coherent description of forecast uncertainty.
Professor Peter Smith is Professor of Social Statistics within Social Sciences: Social Statistics & Demography at the University of Southampton in the United Kingdom. Peter has worked at the University for over 25 years. He obtained a First Class BSc in Mathematics in 1986 from Lancaster University, and returned there to complete a PhD in Statistics in 1990, having obtained an MSc in Probability and Statistics with Distinction in 1987 from the University of Sheffield. Peter has research interests in developing new statistical methodology, including methods for handling non-response and for modelling longitudinal data, and applying sophisticated statistical methods to problems in demography, medicine and health sciences. His publications include articles in the Journal of the Royal Statistical Society, Series A, B and C, Biometrika and the Journal of the American Statistical Association. Peter was awarded the Royal Statistical Society Guy Medal in Bronze in 1999 and was Joint Editor of Series C of their Journal from 2013 to 2016.