Comparison between Distance Functions for Approximate Bayesian Computation to Perform Stochastic Model Updating and Model Validation under Limited Data

AbstractThe paper reviews the distance functions that have been or could be used to perform stochastic model updating via approximate Bayesian computation, namely: (1) Euclidean distance; (2) Bhattacharyya distance; (3) Bray–Curtis distance; and (4) 1-Wasserstein distance functions. For each of these distance functions, details on their mathematical formalism and implementation are provided along with an evaluation of their respective advantages and disadvantages illustrated though a numerical study. Subsequently, to provide a basis for comparison in the stochastic model updating performance by the respective distance functions, two case studies in the form of model validation problems are presented. The first problem is based on the 2014 NASA-LaRC Multidisciplinary Uncertainty Quantification Challenge. The second problem is based on the 2008 thermal problem presented by Sandia National Laboratories. Both problems provide a relatively complex and realistic setting to assess the strengths and robustness of each distance function in performing approximate Bayesian computation under polymorphic uncertainty and limited data for a one-dimensional output space. The comparison will be done based on the following: (1) the precision of the inference results on the inferred parameters; and (2) the precision of the corresponding stochastic model output against a set of validation data.