March 3, 2026Open Access

Actuarial Bayesian nonparametric regression modelling for survival data

Key Points

Complex features of individual mortality are captured effectively by the dependent dirichlet process model, showcasing its flexibility.
The model outperforms standard parametric alternatives, indicating its superiority in capturing varying mortality patterns.
Assessment of a mid-sized UK pension scheme dataset illustrates the practical effectiveness of the model in real-world scenarios.
Incorporating individual-specific random effects, the model provides a robust framework for analyzing nonmonotonic mortality relationships.

Abstract

This paper introduces a flexible regression model for the statistical analysis of the individual mortality profile of pension scheme members. The model incorporates individual-specific random effects, which follow a discrete distribution drawn from a Dirichlet Process, enhancing its adaptability to complex data structures. This results in a Dependent Dirichlet Process mixture model in the spirit of De Iorio et al. (Biometrics 65(3):762–771. https://doi.org/10.1111/j.1541-0420.2008.01166.x , 2009), which accommodates nonmonotonic relationships between covariates and the regression function. The application of the model is illustrated through the analysis of a mid-sized UK pension scheme dataset. The model shows the ability to capture complex features of the data, such as the late life mortality deceleration at no cost in terms of model parsimony, and an improved out-of-sample performance compared with standard parametric alternatives, making it particularly suitable for actuarial modelling applications.

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