Statistical inference for continuous‐time Markov processes with block structure based on discrete‐time network data

Abstract

A widely used approach to modeling discrete‐time network data assumes that discrete‐time network data are generated by an unobserved continuous‐time Markov process. While such models can capture a wide range of network phenomena and are popular in social network analysis, the models are based on the homogeneity assumption that all nodes share the same parameters. We remove the homogeneity assumption by allowing nodes to belong to unobserved subsets of nodes, called blocks, and assuming that nodes in the same block have the same parameters, whereas nodes in distinct blocks have distinct parameters. The resulting models capture unobserved heterogeneity across nodes and admit model‐based clustering of nodes based on network properties chosen by researchers. We develop Bayesian data‐augmentation methods and apply them to discrete‐time observations of an ownership network of non‐financial companies in Slovenia in its critical transition from a socialist economy to a market economy. We detect a small subset of shadow‐financial companies that outpaces others in terms of the rate of change and the desire to accumulate stocks of other companies.