Over the past decade, machine learning (ML) techniques have been widely applied to address various actuarial topics to the point of becoming the norm in some areas of the insurance value chain, such as pricing, reserving, or capital modeling. Regardless of successful implementations in terms of model performance, process automation, or ease of use, some issues remain, including: robustness, trust, continuity and optimality. 

Consequences are mainly the absence of confidence value to provide valuable and nuanced decisions, the impossibility to detect adversarial data, the lack of interpretability, missing robustness in predictions through time and the limitation in algorithmic learning guidance, etc. Bayesian Neural Network (BNN), a hybrid of deep neural networks and probabilistic models provides an interesting framework to address such issues.

In this presentation we propose to introduce BNN techniques by listing pros and cons compared to classical ML, presenting different approximation inference methods (SGLD, MCD, Deep ensemble) and introducing uncertainty measures. To illustrate these aspects, we use BNN for serious physical injury claims analysis related to a French motor insurance portfolio. We highlight in particular BNN benefits and evaluation (uncertainty, error and correlation) for regression tasks, the analysis of out of distribution data and model drift. Finally, we discuss further applications in insurance : underwriting, reserving and pricing.