Recurrence quantification for probabilistic recurrence matrices with timing uncertainties

Develop recurrence quantification analysis for recurrence plots in which the recurrence matrix entries are probabilities (rather than binary values), as produced by Bayesian formulations that explicitly encode timing uncertainties in the data, by defining appropriate measures and algorithms that operate on such non-binary recurrence matrices.

Background

Standard recurrence quantification analysis (RQA) operates on binary recurrence matrices derived from thresholded distances between state vectors or observations. When data contain substantial timing uncertainty (timing jitter), a Bayesian approach can yield recurrence plots whose matrix entries represent probabilities of recurrence rather than binary indicators.

The paper highlights that while such probabilistic recurrence matrices can be constructed to represent uncertainties, there is no established framework for performing RQA on them. This leaves open the task of defining meaningful extensions of RQA measures (e.g., recurrence rate, determinism) and computational procedures suited to probabilistic entries.