Bayesian Poisson Log-Bilinear Models for Mortality Projections with Multiple Populations

European Actuarial Journal, 2015, 5(2), 245-281

37 Pages Posted: 7 May 2015 Last revised: 17 May 2017

See all articles by Katrien Antonio

Katrien Antonio

KU Leuven; University of Amsterdam

Anastasios Bardoutsos

University of Groningen - Faculty of Spatial Sciences; KU Leuven - Faculty of Business and Economics (FEB)

Wilbert Ouburg

Delta Lloyd

Date Written: August 20, 2015


Life insurers, pension funds, health care providers and social security institutions face increasing expenses due to continuing improvements of mortality rates. The actuarial and demographic literature has introduced a myriad of (deterministic and stochastic) models to forecast mortality rates of single populations. This paper presents a Bayesian analysis of two related multi-population mortality models of log-bilinear type, designed for two or more populations. Using a larger set of data, multi-population mortality models allow joint modelling and projection of mortality rates by identifying characteristics shared by all sub-populations as well as sub-population specific effects on mortality. This is important when modeling and forecasting mortality of males and females, regions within a country and when dealing with index-based longevity hedges. Our first model is inspired by the two factor Lee & Carter model of Renshaw and Haberman (2003) and the common factor model of Carter and Lee (1992). The second model is the augmented common factor model of Li and Lee (2005). This paper approaches both models in a statistical way, using a Poisson distribution for the number of deaths at a certain age and in a certain time period. Moreover, we use Bayesian statistics to calibrate the models and to produce mortality forecasts. We develop the technicalities necessary for Markov Chain Monte Carlo ([MCMC]) simulations and provide software implementation (in R) for the models discussed in the paper. Key benefits of this approach are multiple. We jointly calibrate the Poisson likelihood for the number of deaths and the times series models imposed on the time dependent parameters, we enable full allowance for parameter uncertainty and we are able to handle missing data as well as small sample populations. We compare and contrast results from both models to the results obtained with a frequentist single population approach and a least squares estimation of the augmented common factor model.

The appendices for this paper are available at the following URL:

Keywords: projected life tables, multi-population stochastic mortality models, Bayesian statistics, Poisson regression, one factor Lee & Carter model, two factor Lee & Carter model,Li & Lee model, augmented common factor model

Suggested Citation

Antonio, Katrien and Bardoutsos, Anastasios and Ouburg, Wilbert, Bayesian Poisson Log-Bilinear Models for Mortality Projections with Multiple Populations (August 20, 2015). European Actuarial Journal, 2015, 5(2), 245-281. Available at SSRN: or

Katrien Antonio

KU Leuven ( email )

Leuven, Vlaams-Brabant


University of Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB

Anastasios Bardoutsos (Contact Author)

University of Groningen - Faculty of Spatial Sciences ( email )

P.O. Box 800
9700 AV
Groningen, 9747

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000

Wilbert Ouburg

Delta Lloyd ( email )

Spaklerweg 4
Amsterdam, Noord-Holland 1096BA

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