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

Abstract

Statistical inference in high dimensional dynamical systems is often hindered by the unknown dependency structure of model parameters. In particular, the inference of parameterized differential equations (DEs) via Markov chain Monte Carlo (MCMC) samplers often suffers from high proposal rejection rates and is exacerbated by strong autocorrelation structures within the Markov chains leading to poor mixing properties. In this paper, we develop a novel vine-copula based adaptive MCMC approach for efficient parameter inference in dynamical systems with strong parameter interdependence. We exploit the concept of a vine-copula decomposition of distribution densities in order to generate problem-specific proposals for a hybrid independence/random walk Metropolis-Hastings (MH) sampler. The key advantage of this approach is that the corresponding MH proposals generate independent samples from the posterior distribution more efficiently than common competitors. All copula densities can be updated during the sampling procedure for fine-tuning. The performance of our method is assessed on two small-scale examples and finally evaluated on a delay DE model for the JAK2-STAT5 signaling pathway fitted to time-resolved western blot data. We compare our copula-based approach to an independence sampler, a second-order moment-based random walk MH algorithm, and an adaptive MH sampler.