Biological & Soft Matter Seminar: Correlation function for stochastic processes with biased observations. The case of photon detection in single-molecule FRET

Abstract:

An important tool to describe the dynamical properties of stochastic processes is the time-correlation function. Inferring it from experimental data is well established when observations are uniformly spaced in time. However, in a number of experimental settings, ranging from single-photon detection to observations in astrophysics, observations often only occur at random time points. In such instances, the estimate of the correlation function will be biased if the rate of detection is correlated with the signal itself. In this talk, I will show how different estimates of correlation functions are affected by this bias, which results in a seemingly paradoxical result. I will exemplify this analysis using single-molecule FRET as a doubly stochastic process and present a new estimate for the time correlation function of FRET efficiency that reduces bias and retrieves conformational dynamics of biomolecules from nano- to milliseconds.