  The missing data problem pervasively exists in statistical applications. Even
as simple as the count data in mortality projections, it may not be available
for certain age-and-year groups due to the budget limitations or difficulties
in tracing research units, resulting in the follow-up estimation and prediction
inaccuracies. To circumvent this data-driven challenge, we extend the Poisson
log-normal Lee-Carter model to accommodate a more flexible time structure, and
develop the new sampling algorithm that improves the MCMC convergence when
dealing with incomplete mortality data. Via the overdispersion term and Gibbs
sampler, the extended model can be re-written as the dynamic linear model so
that both Kalman and sequential Kalman filters can be incorporated into the
sampling scheme. Additionally, our meticulous prior settings can avoid the
re-scaling step in each MCMC iteration, and allow model selection
simultaneously conducted with estimation and prediction. The proposed method is
applied to the mortality data of Chinese males during the period 1995-2016 to
yield mortality rate forecasts for 2017-2039. The results are comparable to
those based on the imputed data set, suggesting that our approach could handle
incomplete data well.
