A Vine-Copula--Based Adaptive MCMC Sampler for Efficient Inference of Dynamical Systems

• Activity Number: 278
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Claudia Czado*+
• Companies: Munich University of Technology
• Keywords: MCMC ; copulas ; differential equations ; dependence

Abstract

While Markov Chain Monte Carlo (MCMC) methods have become a common tool for Bayesian inference, high proposal rejection rates and strong autocorrelation within the Markov chains often result in bad mixing. In particular multivariate proposal distributions such as multivariate normals often do not capture adequately the dependence structure present, therefore we allow this dependence being modeled by a vine copula. Vine copulas are a very flexible class of copulas which allow for asymmetry and tail dependence. We will introduce this class and show how vine copulas can be used to design hybrid independence/random walk Metropolis Hastings (MH) samplers. The approach is illustrated for a differential equation model for the JAK2-STAT5 signaling pathway and compared to standard MH samplers demonstrating superior performance. Details can be found in Schmidl, Czado, Hug and Theis (2013, Bayesian Analysis, 8(1), 1-42).