mortality_weights {StanMoMo}

Model averaging/weighting via future-out stacking or pseudo-BMA weighting

Description

Mortality Model averaging via stacking of predictive distributions and Pseudo-BMA weighting. Based on Yao et al. (2018) but adapted by Barigou et al. (2021) for mortality forecasting.

Usage

mortality_weights(X)

Arguments

X

A list of stanfit objects.

Details

Mortality model averaging via stacking of predictive distributions or pseudo-BMA weighting. Both approaches were proposed in Yao et al. (2018) based leave-one-out cross-validation which is not suited for forecasting. Barigou et al. (2021) adapted both approaches based on leave-future-out validation which is more appropriate for mortality forecasting.

The stacking method combines all models by maximizing the leave-future-out predictive density of the combination distribution. That is, it finds the optimal linear combining weights for maximizing the leave-future-out log score.

The pseudo-BMA method finds the relative weights proportional to the expected log predictive density of each model.

Similar to Yao et al. (2018), we recommend stacking for averaging predictive distributions as pseudo-BMA tends to select only one model.

Value

A matrix containing one weight for each model and each approach.

References

Yao, Y., Vehtari, A., Simpson, D., & Gelman, A. (2018). Using stacking to average Bayesian predictive distributions (with discussion). Bayesian Analysis, 13(3), 917-1007.

Barigou K., Goffard P-O., Loisel S., Salhi Y. (2021). Bayesian model averaging for mortality forecasting using leave-future-out validation. arXiv preprint arXiv:2103.15434.

Examples

#10-year forecasts for French data for ages 50-90 and years 1970-2017 with a log-Poisson model
#where the 10 last years are held out for validation. We search for the model weights between
#the Lee-Carter model and the RH model (Lee-Carter with cohort effect).
ages.fit<-50:90
years.fit<-1970:2017
deathFR<-FRMaleData$Dxt[formatC(ages.fit),formatC(years.fit)]
exposureFR<-FRMaleData$Ext[formatC(ages.fit),formatC(years.fit)]
iterations<-1000 # Toy example, consider at least 2000 iterations
fitLC=lc_stan(death = deathFR,exposure=exposureFR, forecast = 10, validation=10,
family = "poisson",iter=iterations,chains=1)
fitRH=rh_stan(death = deathFR,exposure=exposureFR, forecast = 10, validation=10,
family = "poisson",iter=iterations,chains=1)
model_weights<-mortality_weights(list(fitLC,fitRH))