Precise motor insurance claim forecasting is critical to the insurance industry as claims impact the industry’s profitability. In the literature, there has been a rise in the exploration of machine learning techniques to model motor insurance claims. This chapter presents a Bayesian approach to detecting insurance claims in motor insurance policies, which is a first in the literature. Our framework entails training Bayesian Neural Networks with Automatic Relevance Determination (BNN-ARD) prior distributions. The posterior of this model is not available in closed form, and numerical approaches such as Markov Chain Monte Carlo and variational inference techniques must be utilized. This chapter employs the Laplace approximation for the posterior, allowing us to scale to wide and deep neural network architectures. This modeling setup also allows us to select between different neural network architectures through the Bayesian evidence metric. Using the ARD prior, we automatically rank the input variables that are the most relevant for the motor insurance claim prediction task. Our results show that the Bayesian evidence metric can select models or the neural network architecture on training data that performs well on unseen data. We find that deeper architectures perform better than wider architectures, highlighting the benefit of adding more layers of non-linearization. We further find that the claims history, type of fuel of vehicle, power of the vehicle, lapse, and number of policies are the most important features for the claim prediction task. These results could prove useful for stakeholders as this framework makes the usually black-box neural network models more interpretable to non-expert audiences.