An Evaluation of Validation Metrics for Probabilistic Model Outputs

Probabilistic modelling methods are increasingly being employed in engineering applications. These approaches make inferences about the distribution, or summary statistical moments, for output quantities. A challenge in applying probabilistic models is validating output distributions. An ideal validation metric is one that intuitively provides information on key divergences between the output and validation distributions. Furthermore, it should be interpretable across different problems in order to informatively select the appropriate statistical method. In this paper, two families of measures for quantifying differences between distributions are compared: f-divergence and integral probability metrics (IPMs). Discussions and evaluation of these measures as validation metrics are performed with comments on ease of computation, interpretability and quantity of information provided.