Identification and Forecasting in Mortality Models

Mortality models often have inbuilt identification issues challenging the statistician. The statistician can choose to work with well-defined freely varying parameters, derived as maximal invariants in this paper, or with ad hoc identified parameters which at first glance seem more intuitive, but which can introduce a number of unnecessary challenges. In this paper we describe the methodological advantages from using the maximal invariant parameterisation and we go through the extra methodological challenges a statistician has to deal with when insisting on working with ad hoc identifications. These challenges are broadly similar in frequentist and in Bayesian setups. We also go through a number of examples from the literature where ad hoc identifications have been preferred in the statistical analyses.