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Takeaways:

• State space models and traditional time series models are well-suited to forecast loss ratios in the insurance industry, although actuaries have been slow to adopt modern statistical methods.
• Working with limited data is a challenge, but informed priors and hierarchical models can help improve the modeling process.
• Bayesian model stacking allows for blending together different model predictions and taking the best of both (or all if more than 2 models) worlds.
• Model comparison is done using out-of-sample performance metrics, such as the expected log point-wise predictive density (ELPD). Brute leave-future-out cross-validation is often used due to the time-series nature of the data.
• Stacking or averaging models are trained on out-of-sample performance metrics to determine the weights for blending the predictions. Model stacking can be a powerful approach for combining predictions from candidate models. Hierarchical stacking in particular is useful when weights are assumed to vary according to covariates.
• BayesBlend is a Python package developed by Ledger Investing that simplifies the implementation of stacking models, including pseudo Bayesian model averaging, stacking, and hierarchical stacking.
• Evaluating the performance of patient time series models requires considering multiple metrics, including log likelihood-based metrics like ELPD, as well as more absolute metrics like RMSE and mean absolute error.
• Using robust variants of metrics like ELPD can help address issues with extreme outliers. For example, t-distribution estimators of ELPD as opposed to sample sum/mean estimators.
• It is important to evaluate model performance from different perspectives and consider the trade-offs between different metrics. Evaluating models based solely on traditional metrics can limit understanding and trust in the model. Consider additional factors such as interpretability, maintainability, and productionization.
• Simulation-based calibration (SBC) is a valuable tool for assessing parameter estimation and model correctness. It allows for the interpretation of model parameters and the identification of coding errors.
• In industries like insurance, where regulations may restrict model choices, classical statistical approaches still play a significant role. However, there is potential for Bayesian methods and generative AI in certain areas.