# Bayesian CART models for insurance claims frequency

arXiv: https://arxiv.org/abs/2303.01923 · HTML: https://mlsanity.com/paper/2303.01923/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 77 references that are in the map.
- First posted on arXiv 3 Mar 2023.

## Builds on (most cited first, 11 of 11)

- [Understanding predictive information criteria for Bayesian models](https://mlsanity.com/paper/1307.5928/) (2013)
- [Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity](https://mlsanity.com/paper/1707.09461/) (2017)
- [bartMachine: Machine Learning with Bayesian Additive Regression Trees](https://mlsanity.com/paper/1312.2171/) (2013)
- [Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning](https://mlsanity.com/paper/2103.03635/) (2021)
- [Boosting insights in insurance tariff plans with tree-based machine learning methods](https://mlsanity.com/paper/1904.10890/) (2019)
- [Bayesian Additive Regression Trees with Model Trees](https://mlsanity.com/paper/2006.07493/) (2020)
- [Variable selection for BART: An application to gene regulation](https://mlsanity.com/paper/1310.4887/) (2013)
- [Semiparametric Mixed-Scale Models Using Shared Bayesian Forests](https://mlsanity.com/paper/1809.08521/) (2018)
- [Variable Selection with ABC Bayesian Forests](https://mlsanity.com/paper/1806.02304/) (2018)
- [Stability of decision trees and logistic regression](https://mlsanity.com/paper/1903.00816/) (2019)
- [Accounting for shared covariates in semi-parametric Bayesian additive regression trees](https://mlsanity.com/paper/2108.07636/) (2021)

## Built on by (most cited first, 2 of 2)

- [Automated Machine Learning in Insurance](https://mlsanity.com/paper/2408.14331/) (2024)
- [Bayesian CART models for aggregate claim modeling](https://mlsanity.com/paper/2409.01908/) (2024)

## Abstract (arXiv)

Accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, the classification and regression trees (CARTs) and their ensembles have gained popularity in the actuarial literature, since they offer good prediction performance and are relatively easily interpretable. In this paper, we introduce Bayesian CART models for insurance pricing, with a particular focus on claims frequency modelling. Additionally to the common Poisson and negative binomial (NB) distributions used for claims frequency, we implement Bayesian CART for the zero-inflated Poisson (ZIP) distribution to address the difficulty arising from the imbalanced insurance claims data. To this end, we introduce a general MCMC algorithm using data augmentation methods for posterior tree exploration. We also introduce the deviance information criterion (DIC) for the tree model selection. The proposed models are able to identify trees which can better classify the policy-holders into risk groups. Some simulations and real insurance data will be discussed to illustrate the applicability of these models.