Mardin Ghobadi Soltanpanah: Classifying medical datasets: Frequentist versus Bayesian approaches

Abstract.

This thesis is based on Andrea Gabrielli’s paper, ’An Individual Claims Reserving Model for Reported Claims’, in which Gabrielli introduces a neural network-based method for reserve prediction using individual claims data instead of aggregated data. Inspired by this, we introduce a Gradient Boosting Machine (GBM) model. The model introduced is simpler than Gabrielli’s neural network model, since it directly predicts expected claim payments. In contrast, Gabrielli’s neural network model first determines if there is a payment during a certain development year for a claim and then predicts the expected size of the payment. The GBM model will be compared not only to Gabrielli’s neural network model but also to the Chain-Ladder method to assess how well these methods perform in terms of estimating reserves for reported but not settled (RBNS) claims.

The results, for a simulated dataset, demonstrate that the method with the lowest estimation error is Gabrielli’s neural network, with an error rate of 0.8%. GBM closely follows with an error rate of 1.04%. The results from the Chain-Ladder are not far off from the neural network and GBM, with an error rate of 1.20%. However, it has a Root Mean Square Error (RMSE) that is more than 60% larger than that of the GBM. The reason Chain-Ladder can be compared to the RBNS reserve is that Chain-Ladder is only used starting from the second development year, where only 0.32% of the total number of claims are still IBNR (Incurred But Not Reported). Therefore, the total reserve from Chain-Ladder can be assumed to be equivalent to the RBNS reserve.