Nonparametric analysis of noisy, multivariable time series using high-order correlation functions: Single-molecule FRET as an example

High-order correlation functions offer a model-free (nonparametric) method of analyzing single-molecule data with high resolution in both time and state space. However, they have only been demonstrated for single-channel experiments, whereas many single-molecule experiments measure multiple data channels. This paper identifies the central problem with multichannel datasets and presents a roadmap for its general solution. The process is demonstrated using the specific example of fluorescence resonance energy transfer (FRET), one of the most common single-molecule experiments. The method's practicality is demonstrated on FRET data published as a data-analysis benchmark. The paper emphasizes the need to work at high noise levels to optimize single-molecule experiments and the importance of effective noise removal in their analysis. Overall, an additional step is taken toward making correlation analysis a general, model-free method of treating experimental time series with optimum performance.