Past Event: Oden Institute Seminar

VoroSpokes: A nontraditional Bayesian Calibration method using implicit Voronoi Tessellation in Arbitrary dimensions

Mohamed Salah Ebeida, Sandia National Laboratory

Abstract

Bayesian inference provides a powerful framework for inductive reasoning which has proven applicable to an extensive range of disciplines and industrial applications. In this statistical theory, prior knowledge regarding quantities of interest are combined with observations to produce a full posterior distribution over the true values under consideration. MCMC methods have provided a practical framework for solving a very wide range of problems, yet there still remain a number of key difficulties and challenges for practitioners (e.g. issues with local trapping, inefficient mixing, correlated samples, and difficult convergence diagnostics). Our novel VoroSpokes framework for Bayesian inference resolves these issues by removing the underlying reliance on Markov Chains from the posterior sampling procedure. The posterior is instead adaptively approximated using an implicit domain partitioning in the form of Voronoi tessellations to construct a Voronoi Piecewise Surrogate (VPS) model. The surrogate model and domain partitioning are then used to prescribe a hierarchical sampling procedure designed to efficiently draw independent samples from the approximate posterior distribution. In this talk we will present the VoroSpokes framework, its theoretical properties and demonstrate its superior performance over MCMC in practice. ​​​ Bio Mohamed Ebeida is a research scientist at Sandia National Laboratories and an expert in computational geometry. He specializes in Voronoi diagrams, hyper-plane sampling and sphere packing. He developed a number of nontraditional Voronoi-based algorithms with application to meshing, uncertainty quantification, optimization, and machine learning. He graduated from University of California Davis in 2008 with a PhD in Mechanical and Aeronautical Engineering and a Masters in Applied Mathematics. He worked for two years as a Postdoc at Carnegie Mellon University. In 2010, he joined Sandia National Laboratories where he actively works in exploring the potential of implicit Voronoi tessellations for a wide range on applications in low and high-dimensions.