We study a finite-sample change-detection problem for one-dimensional noisy dynamical systems using partition-based empirical approximations of stationary behaviour. Given observations from an interval-valued process, we partition the state space into finitely many intervals and estimate a transition matrix from observed transitions between partition elements. After a small Doeblin-type regularisation, the resulting matrix has a unique stationary distribution. This stationary distribution is used as a finite-dimensional approximation of the invariant density, or stationary law, of the observed regime. Using an initial reference segment, we compute a baseline empirical stationary distribution bπ0,ρ. For each subsequent sliding window, we compute a window-based empirical stationary distribution bπt,ρ and define the score St = bπt,ρ bπ0,ρ 1. Large values of St indicate that the stationary behaviour of the observed regime has changed relative to the baseline. The statistic is therefore a detector of changes in stationary behaviour. It is not, by itself, a detector of all possible changes in transition dynamics that preserve the invariant density.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propose a tractable algorithm that estimates the probabilistic aggregation map from the system's trajectory. We adopt a soft-aggregation model, where each meta-state has a signature raw state, called an anchor state.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propose a tractable algorithm that estimates the probabilistic aggregation map from the system's trajectory. We adopt a soft-aggregation model, where each meta-state has a signature raw state, called an anchor state.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propose a tractable algorithm that estimates the probabilistic aggregation map from the system's trajectory. We adopt a soft-aggregation model, where each meta-state has a signature raw state, called an anchor state. This model includes several common state aggregation models as special cases.