Biologically Realistic Bayesian Shape-Constrained MortalityForecasting with Wavelet Smoothing

Mortality forecasting plays an essential role in public health planning and pension systems. Traditional models without shape constraints may provide results that fail to respect biological realism. This study extends the classical Lee-Carter model within a Bayesian framework, combining wavelet smoothing and demographic constraints to enforce monotonic patterns in both the very young and the elderly. The Bayesian Lee-Carter approach includes domain knowledge priors, posterior distributions, and uncertainty quantification while enabling enforcement of shape constraints to maintain realistic age-specific mortality curves, building on an ensemble learning approach using ARIMA, Singular Spectrum Analysis (SSA), and Multi-Layer Perceptron (MLP). Using French mortality data from 1916-222, with 1916-22 for model training and 221-222 for out-of-sample testing, the constrained approach achieves improvements in accuracy measures (RMSE, MAE, MAPE). The model achieves convergence (R-hat) and 14−18% RMSE improvements with R-squared exceeding .94. Validation confirms improved predictive performance.