This supplementary appendix provides detailed information on the methodology and performance evaluation of the Bayesian model averaging (BMA) projections of future life expectancy in 35 industrialized countries. The appendix includes: 1. **Pre-processing Steps**: Details on adjusting for under-registration, imputing missing data, and smoothing death rates to reduce projection error. 2. **Model Ensemble**: descriptions of various models used in the ensemble, including age-time models, age-time-cohort models, piecewise-linear models, and weighted likelihood models. The Lee-Carter model is also discussed. 3. **Implementation**: Software used for model fitting, including R and R-INLA, and the methods for estimating model parameters and projecting death rates. 4. **Calculating Life Expectancy**: Methods for calculating life expectancy using age-specific death rates and life table methods. 5. **Measuring Performance**: Steps to evaluate the performance of BMA projections, including bias and deviation metrics, and the 90% coverage of projections. 6. **Metric for Projection Error**: Comparison of projection bias in life expectancy and age-specific death rates, and the relationship between these metrics. 7. **Figures and Tables**: Visual and tabular representations of projection bias, model weights, trends in life expectancy, and other key results. The appendix aims to provide a comprehensive understanding of the methodology and validation of the BMA projections, ensuring transparency and reproducibility.This supplementary appendix provides detailed information on the methodology and performance evaluation of the Bayesian model averaging (BMA) projections of future life expectancy in 35 industrialized countries. The appendix includes: 1. **Pre-processing Steps**: Details on adjusting for under-registration, imputing missing data, and smoothing death rates to reduce projection error. 2. **Model Ensemble**: descriptions of various models used in the ensemble, including age-time models, age-time-cohort models, piecewise-linear models, and weighted likelihood models. The Lee-Carter model is also discussed. 3. **Implementation**: Software used for model fitting, including R and R-INLA, and the methods for estimating model parameters and projecting death rates. 4. **Calculating Life Expectancy**: Methods for calculating life expectancy using age-specific death rates and life table methods. 5. **Measuring Performance**: Steps to evaluate the performance of BMA projections, including bias and deviation metrics, and the 90% coverage of projections. 6. **Metric for Projection Error**: Comparison of projection bias in life expectancy and age-specific death rates, and the relationship between these metrics. 7. **Figures and Tables**: Visual and tabular representations of projection bias, model weights, trends in life expectancy, and other key results. The appendix aims to provide a comprehensive understanding of the methodology and validation of the BMA projections, ensuring transparency and reproducibility.