The impact of specific prior specifications is reduced by calculation of combined estimates from multiple specifications.
These prior specifications are not fixed; they can be adjusted to specific forecast situations.
Bayesian approaches allow spatial dependence to be modeled in a hierarchical fashion, by introducing area or site-specific random effects with conditional autoregressive [18] or Gaussian random field prior specifications [19].
Despite these different prior specifications, the resulting marginal posterior densities are (very) similar Fig. 16 Prior sensitivity analysis: marginal posterior densities for σ in the validating forecasts for Danish women of our model using different prior specifications.
A simple prior sensitivity analysis suggests that our British and Danish mortality forecasts are relatively insensitive to the (rather weakly informative) prior specifications.
Despite these different prior specifications, the resulting marginal posterior densities are (very) similar Fig. 17 Prior sensitivity analysis: the validating forecasts (represented by the median and the 80% prediction intervals) of British (left) and Danish (right) life expectancy are (very) similar, although we use different prior specifications (differently colored circles) for our model.
Appendix Figures 15 and 16 show that these different prior specifications result in (very) similar marginal posterior densities and, beyond that, Appendix Figure 17 shows that these prior specifications also yield (very) similar forecasts for British (left) and Danish (right) female life expectancy at birth from 1991 to 2011.
To demonstrate this, we repeatedly generate validating forecasts with our model using different prior specifications, i.e., we use the Uniform, the Beta, and the Normal distribution with different parameter values to determine various levels for their location and spread.
We considered four prior specifications.
We evaluated these GEBV for single prior specifications and their averages across the four prior specifications considered.
Also for cross-validation, averaging GEBV across prior specifications improved accuracy, when compared to single prior specifications.
