Bayesian detection of event spreading pattern from multivariate binary time series

Abstract

This paper concerns the inference of the event spreading path from noisy event occurrence time series. We propose a probabilistic tree model for the event spreading path, and provide a full Bayesian approach with a Metropolis-Hastings (MH) algorithm to detect the tree path from multivariate binary time series. Our approach allows a node to spread the event in a probabilistic way to an arbitrary number of downstream nodes, the input data to contain an unknown number of nodes which are not inside the event spreading path, and the algorithm to sample only tree spreading structures. Efficient MH moves and iterative procedures guarantee the detection even if none or multiple event spreading paths are presented in the data. Simulations on synthesized data sets showed that our method can accurately detect the event spreading topologies, has good one-step-ahead prediction accuracy and outperforms existing approaches. We also analyzed the influence of model parameters on estimation accuracy in depth and obtained some interesting conclusions. Furthermore, we applied our method to the PM2.5 data in provincial capitals of north and east China. The inferred path is largely consistent with the known pollutant spreading trend.