Information Flow in Markov Chains

We consider the problem of characterizing the flow of information in stochastic systems. Recently, several measures of partial information decomposition (PID) have been proposed which, for a fixed target variable, can distinguish unique, redundant, and synergistic contributions from the predictor variables. We study how each of those partial informations travel in a Markov chain, entering at one variable, passing through several variables, and eventually exiting downstream. Our work is agnostic to specific partial information decomposition (PID) measures. We investigate partial information flow among variables relating to overflow events in a river system.