Erland Ekheden: Modeling mortality

We analyse the stochasticity in mortality data from the USA, the UK and Sweden and decompose the variance of the observations into three parts: binomial risk - the variance due to random mortality variation in a finite population, systematic - explained by the covariates and unexplained systematic risk - variance that comes from real changes in mortality rates, not captured by the covariates. The fraction of unexplained variance caused by binomial risk provides a limit in terms of the resolution that can be achieved by a model. This can be used as a model selection tool for selecting the number of covariates and regression parameters of the deterministic part of the regression function, and for testing whether unexplained systematic variation should be explicitly modelled or not. We perform the variance decomposition for a simple two-factor model with age and calendar year as covariates and then extend the model with a multivariate Gaussian time series part not explained by the covariates with the aim to provide prediction and confidence intervals for future mortality, as well as smoothing historical data, using the best linear unbiased predictor (BLUP).