B1551
Title: Using optimal transport to assess the impact of prior choice on Bayesian parameter inference in dynamical systems
Authors: Mingo Ndiwago Damian - University of Luxembourg (Luxembourg) [presenting]
Christophe Ley - University of Luxembourg (Luxembourg)
Jack Hale - Department of Engineering - Faculty of Science - Technology and Medicine - University of Luxembourg - Esch--sur--Alzette - Luxembourg (Luxembourg)
Abstract: There exist many studies in the literature on the impact of prior choice in Bayesian inference. Some of these studies have proposed using probability distances that satisfy the properties of divergence instead of a metric. Regardless of the distance used, a lack of relative scaling typically complicates the interpretation of the computed distance in assessing prior impact, i.e. is this distance large or small? The use of the Wasserstein impact measure (WIM) proposed by a past study is extended to the problem of assessing prior impact in Bayesian models governed by systems of ordinary differential equations (ODEs). These ODE problems have moderate parametric dimensions ($\sim 10$). The results using the original WIM are consequently difficult to interpret due to this moderate dimensionality and a lack of relative scaling. The study consists of two main contributions; firstly, algorithms are utilised from computational optimal transport to extend the application of the WIM to problems of moderate parametric dimension. Secondly, a new standardized Wasserstein impact measure (sWIM) is proposed, which gives a relative sense of distance, easing with interpretation of the sWIM for the purposes of understanding the role of the prior. To illustrate the effectiveness of the approach, a Lotka-Voltera model predator-prey model is calibrated under a baseline and two alternative priors and assesses the impact of the prior using the proposed sWIM.
