Bayesian Poisson common factor model with overdispersion for mortality forecasting in multiple populations

References

• Antonio, K., A. Bardoutsos, and W. Ouburg. 2015. Bayesian poisson log-bilinear models for mortality projections with multiple populations. European Actuarial Journal 5 (2):245–81.
   Web of Science ®Google Scholar
• Betancourt, M. 2017. A conceptual introduction to Hamiltonian Monte Carlo. arXiv preprint arXiv:1701.02434.
   Google Scholar
• Bishop, C. M. 2006. Pattern recognition and machine learning. New York: Springer.
   Google Scholar
• Booth, H., and L. Tickle. 2008. Mortality modelling and forecasting: A review of methods. Annals of Actuarial Science 3 (1-2):3–43.
   Google Scholar
• Bozikas, A., and G. Pitselis. 2018. An empirical study on stochastic mortality modelling under the age-period-cohort framework: The case of Greece with applications to insurance pricing. Risks 6 (2):1–34.
   Google Scholar
• Brouhns, N., M. Denuit, and J. K. Vermunt. 2002. A poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics 31 (3):373–93.
   Web of Science ®Google Scholar
• Brown, J. R. 2003. Redistribution and insurance: Mandatory annuitization with mortality heterogeneity. Journal of Risk and Insurance 70 (1):17–41.
   Web of Science ®Google Scholar
• Butt, Z., S. Haberman, and H. L. Shang (2014). ilc: Lee-Carter Mortality Models using Iterative Fitting Algorithms. R package version 1.0.
   Google Scholar
• Cairns, A. J., D. Blake, and K. Dowd. 2006. A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance 73 (4):687–718.
   Web of Science ®Google Scholar
• Cairns, A. J., D. Blake, K. Dowd, G. D. Coughlan, D. Epstein, A. Ong, and I. Balevich. 2009. A quantitative comparison of stochastic mortality models using data from England and wales and the united states. North American Actuarial Journal 13 (1):1–35.
   Google Scholar
• Carpenter, B., A. Gelman, M. D. Hoffman, D. Lee, B. Goodrich, M. Betancourt, M. Brubaker, J. Guo, P. Li, and A. Riddell. 2017. Stan: A probabilistic programming language. Journal of Statistical Software 76 (1):1–32.
   PubMed Web of Science ®Google Scholar
• Celeux, G., F. Forbes, C. P. Robert, and D. M. Titterington. 2006. Deviance information criteria for missing data models. Bayesian Analysis 1 (4):651–73.
   Web of Science ®Google Scholar
• Chen, M.-H., Q.-M. Shao, and J. G. Ibrahim. 2000. Monte Carlo methods in Bayesian computation. In Springer series in statistics (1st ed.). New York: Springer-Verlag.
   Google Scholar
• Chen, R. Y., and P. Millossovich. 2018. Sex-specific mortality forecasting for UK countries: A coherent approach. European Actuarial Journal 8 (1):69–95.
   PubMed Web of Science ®Google Scholar
• Czado, C., A. Delwarde, and M. Denuit. 2005. Bayesian Poisson log-bilinear mortality projections. Insurance: Mathematics and Economics 36 (3):260–84.
   Web of Science ®Google Scholar
• Delwarde, A., M. Denuit, and C. Partrat. 2007. Negative binomial version of the lee–carter model for mortality forecasting. Applied Stochastic Models in Business and Industry 23 (5):385–401.
   Web of Science ®Google Scholar
• Enchev, V., T. Kleinow, and A. J. Cairns. 2017. Multi-population mortality models: Fitting, forecasting and comparisons. Scandinavian Actuarial Journal 2017 (4):319–42.
   Web of Science ®Google Scholar
• Fung, M. C., G. W. Peters, and P. V. Shevchenko. 2019. Cohort effects in mortality modelling: A bayesian state-space approach. Annals of Actuarial Science 13 (1):109–44.
   Google Scholar
• Gage, T. B., and K. O’Connor. 2009. Nutrition and the variation in level and age patterns of mortality. Human Biology 81 (5/6):551–74.
   PubMedGoogle Scholar
• Geisser, S., and W. F. Eddy. 1979. A predictive approach to model selection. Journal of the American Statistical Association 74 (365):153–60.
   Web of Science ®Google Scholar
• Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2014. Bayesian data analysis (3rd ed.), Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Gelman, A., and D. B. Rubin. 1992. Inference from iterative simulation using multiple sequences. Statistical Science 7 (4):457–72.
   Google Scholar
• Girosi, F., and G. King. 2008. Demographic forecasting. Princeton, New Jersey: Princeton University Press.
   Google Scholar
• Haberman, S., and A. Renshaw. 2011. A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics 48 (1):35–55.
   Web of Science ®Google Scholar
• Hilton, J., E. Dodd, J. J. Forster, and P. W. Smith. 2019. Projecting uk mortality by using Bayesian generalized additive models. Journal of the Royal Statistical Society: Series C (Applied Statistics) 68 (1):29–49.
   Google Scholar
• Hoffman, M. D., and A. Gelman. 2014. The no-u-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research 15 (1):1593–623.
   Google Scholar
• Hu, Y., and N. Goldman. 1990. Mortality differentials by marital status: An international comparison. Demography 27 (2):233–50.
   PubMed Web of Science ®Google Scholar
• Hummer, R. A., and E. M. Hernandez. 2013. The effect of educational attainment on adult mortality in the United States. Population Bulletin 68:1–16.
   PubMedGoogle Scholar
• Hunt, A., and D. Blake. 2021. On the structure and classification of mortality models. North American Actuarial Journal 25 (Supp 1):S215–S234.
   Google Scholar
• Hyndman, R. J., H. Booth, and F. Yasmeen. 2013. Coherent mortality forecasting: The product-ratio method with functional time series models. Demography 50 (1):261–83.
   PubMed Web of Science ®Google Scholar
• Karlis, D., and E. Xekalaki. 2005. Mixed Poisson distributions. International Statistical Review 73 (1):35–58.
   Web of Science ®Google Scholar
• Kleinow, T. 2015. A common age effect model for the mortality of multiple populations. Insurance: Mathematics and Economics 63:147–52.
   Web of Science ®Google Scholar
• Lee, R. D., and L. R. Carter. 1992. Modeling and forecasting us mortality. Journal of the American Statistical Association 87 (419):659–71.
   Web of Science ®Google Scholar
• Lee, R. D., and R. Rofman. 1994. Modeling and projecting mortality in Chile. Notas de Poblacion 22 (59):183–213.
   PubMedGoogle Scholar
• Li, J. 2013. A Poisson common factor model for projecting mortality and life expectancy jointly for females and males. Population Studies 67 (1):111–26. doi:10.1080/00324728.2012.689316.
   PubMed Web of Science ®Google Scholar
• Li, J. 2014. An application of mcmc simulation in mortality projection for populations with limited data. Demographic Research 30:1–48.
   Google Scholar
• Li, J., L. Tickle, and N. Parr. 2016. A multi-population evaluation of the Poisson common factor model for projecting mortality jointly for both sexes. Journal of Population Research 33 (4):333–60.
   Web of Science ®Google Scholar
• Li, J. S.-H., M. R. Hardy, and K. S. Tan. 2009. Uncertainty in mortality forecasting: An extension to the classical lee-carter approach. ASTIN Bulletin: The Journal of the IAA 39 (1):137–64.
   Web of Science ®Google Scholar
• Li, N., and R. Lee. 2005. Coherent mortality forecasts for a group of populations: An extension of the lee-carter method. Demography 42 (3):575–94.
   PubMed Web of Science ®Google Scholar
• Neal, R. 1995. Bayesian learning for neural networks., PhD diss., University of Toronto.
   Google Scholar
• Neal, R. 2011. Chapter 5: MCMC using Hamiltonian dynamics. In Handbook of Markov chain Monte Carlo, eds. S. Brooks, A. Gelman, G. Jones, and X.-L. Meng, 113–62. New York: CRC press.
   Google Scholar
• Pedroza, C. 2006. A Bayesian forecasting model: Predicting us male mortality. Biostatistics (Oxford, England) 7 (4):530–50. doi:10.1093/biostatistics/kxj024.
   PubMed Web of Science ®Google Scholar
• Plat, R. 2009. On stochastic mortality modeling. Insurance: Mathematics and Economics 45 (3):393–404.
   Web of Science ®Google Scholar
• Renshaw, A. E., and S. Haberman. 2006. A cohort-based extension to the lee–carter model for mortality reduction factors. Insurance: Mathematics and Economics 38 (3):556–70.
   Web of Science ®Google Scholar
• Robards, J., M. Evandrou, J. Falkingham, and A. Vlachantoni. 2012. Marital status, health and mortality. Maturitas 73 (4):295–9.
   PubMed Web of Science ®Google Scholar
• Shair, S., S. Purcal, and N. Parr. 2017. Evaluating extensions to coherent mortality forecasting models. Risks 5 (1):16.
   Google Scholar
• Spiegelhalter, D. J., N. G. Best, B. P. Carlin, and A. Van Der Linde. 2002. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series b (Statistical Methodology) 64 (4):583–639.
   Web of Science ®Google Scholar
• Stan Development Team. 2018. RStan: The R interface to Stan. R package version 2.18.2.
   Google Scholar
• Thomas, S., and W. Tu. 2021. Learning Hamiltonian Monte Carlo in R. The American Statistician 75 (4):403–13.
   Web of Science ®Google Scholar
• Tuljapurkar, S., N. Li, and C. Boe. 2000. A universal pattern of mortality decline in the g7 countries. Nature 405 (6788):789–92.
   PubMed Web of Science ®Google Scholar
• Watanabe, S. 2010. Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research 11 (Dec):3571–94.
   Google Scholar
• Wedderburn, R. W. 1974. Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method. Biometrika 61 (3):439–47.
   Web of Science ®Google Scholar
• Wilmoth, J. R. 1996. Mortality projections for Japan: A comparison of four methods. New York: Oxford University Press.
   Google Scholar
• Wiśniowski, A., P. W. F. Smith, J. Bijak, J. Raymer, and J. J. Forster. 2015. Bayesian population forecasting: Extending the lee-carter method. Demography 52 (3):1035–59.
   PubMed Web of Science ®Google Scholar
• Wong, J. S., J. J. Forster, and P. W. Smith. 2018. Bayesian mortality forecasting with overdispersion. Insurance: Mathematics and Economics 83:206–21.
   Web of Science ®Google Scholar
• Wong, K., J. Li, and S. Tang. 2020. A modified common factor model for modelling mortality jointly for both sexes. Journal of Population Research 37 (2):1–32.
   Google Scholar
• Yang, B., J. Li, and U. Balasooriya. 2016. Cohort extensions of the poisson common factor model for modelling both genders jointly. Scandinavian Actuarial Journal 2016 (2):93–112.
   Web of Science ®Google Scholar