  In this paper, we propose standard statistical tools as a solution to
commonly highlighted problems in the explainability literature. Indeed,
leveraging statistical estimators allows for a proper definition of
explanations, enabling theoretical guarantees and the formulation of evaluation
metrics to quantitatively assess the quality of explanations. This approach
circumvents, among other things, the subjective human assessment currently
prevalent in the literature. Moreover, we argue that uncertainty quantification
is essential for providing robust and trustworthy explanations, and it can be
achieved in this framework through classical statistical procedures such as the
bootstrap. However, it is crucial to note that while Statistics offers valuable
contributions, it is not a panacea for resolving all the challenges. Future
research avenues could focus on open problems, such as defining a purpose for
the explanations or establishing a statistical framework for counterfactual or
adversarial scenarios.
