A Bayesian forecasting model: predicting U.S. male mortality.

This article presents a Bayesian approach to forecast mortality rates. This approach formalizes the Lee-Carter method as a statistical model accounting for all sources of variability. Markov chain Monte Carlo methods are used to fit the model and to sample from the posterior predictive distribution. This paper also shows how multiple imputations can be readily incorporated into the model to handle missing data and presents some possible extensions to the model. The methodology is applied to U.S. male mortality data. Mortality rate forecasts are formed for the period 1990-1999 based on data from 1959-1989. These forecasts are compared to the actual observed values. Results from the forecasts show the Bayesian prediction intervals to be appropriately wider than those obtained from the Lee-Carter method, correctly incorporating all known sources of variability. An extension to the model is also presented and the resulting forecast variability appears better suited to the observed data.

[1]  Nan Li,et al.  Using the Lee–Carter Method to Forecast Mortality for Populations with Limited Data * , 2004 .

[2]  Michel Denuit,et al.  Measuring the longevity risk in mortality projections , 2002 .

[3]  Joseph L Schafer,et al.  Analysis of Incomplete Multivariate Data , 1997 .

[4]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[5]  J. Barendregt,et al.  Global burden of disease , 1997, The Lancet.

[6]  Michael A. Salsburg,et al.  Modeling and Forecasting , 2007, Int. CMG Conference.

[7]  Xiao-Li Meng,et al.  Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage , 2000 .

[8]  J. Maindonald,et al.  Applying Lee-Carter under conditions of variable mortality decline , 2002, Population studies.

[9]  S. Frühwirth-Schnatter.  Data Augmentation and Dynamic Linear Models , 1994 .

[10]  J. Wilmoth,et al.  Are mortality projections always more pessimistic when disaggregated by cause of death? , 1995, Mathematical population studies.

[11]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[12]  R. Lee,et al.  Stochastic population forecasts for the United States: beyond high, medium, and low. , 1994, Journal of the American Statistical Association.

[13]  Melvin J. Hinich,et al.  Time Series Analysis by State Space Methods , 2001 .

[14]  B D Spencer,et al.  Error models for official mortality forecasts. , 1990, Journal of the American Statistical Association.

[15]  Roger A. Sugden,et al.  Multiple Imputation for Nonresponse in Surveys , 1988 .

[16]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[17]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[18]  W. Bell,et al.  Using principal components in time series modeling and forecasting of age-specific mortality rates. , 1991 .

[19]  N. Shephard,et al.  The simulation smoother for time series models , 1995 .

[20]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[21]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[22]  W. Bell,et al.  FORECASTING AGE SPECIFIC FERTILITY USING PRINCIPAL COMPONENTS , 1987 .

[23]  R. Lee,et al.  Modeling and forecasting U.S. sex differentials in mortality. , 1992, International journal of forecasting.

[24]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter. , 1991 .

[25]  Lawrence R. Carter.  FORECASTING U.S. MORTALITY:. A Comparison of Box-Jenkins ARIMA and Structural Time Series Models , 1995 .

[26]  Ingrid Van Keilegom,et al.  Bootstrapping the Poisson log-bilinear model for mortality forecasting , 2005 .

[27]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[28]  Ronald Lee.  The Lee-Carter Method for Forecasting Mortality, with Various Extensions and Applications , 2000 .

[29]  Ronald Lee,et al.  Modeling and forecasting U. S. mortality , 1992 .

[30]  Xiao-Li Meng,et al.  POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES , 1996 .

[31]  Claudia Czado,et al.  Bayesian Poisson log-bilinear mortality projections , 2005 .