Browsing by Subject "Bayesian nonparametrics"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Direct Photon-by-Photon Analysis of Time-Resolved Pulsed Excitation Data using Bayesian Nonparametrics
    (Cell Press, 2020-11-18) Tavakoli, Meysam; Jazani, Sina; Sgouralis, Ioannis; Heo, Wooseok; Ishii, Kunihiko; Tahara, Tahei; Pressé, Steve; Physics, School of Science
    Lifetimes of chemical species are typically estimated by either fitting time-correlated single-photon counting (TCSPC) histograms or phasor analysis from time-resolved photon arrivals. While both methods yield lifetimes in a computationally efficient manner, their performance is limited by choices made on the number of distinct chemical species contributing photons. However, the number of species is encoded in the photon arrival times collected for each illuminated spot and need not be set by hand a priori. Here, we propose a direct photon-by-photon analysis of data drawn from pulsed excitation experiments to infer, simultaneously and self-consistently, the number of species and their associated lifetimes from a few thousand photons. We do so by leveraging new mathematical tools within the Bayesian nonparametric. We benchmark our method for both simulated and experimental data for 1-4 species.
  • Thumbnail Image
    Item
    Pitching single-focus confocal data analysis one photon at a time with Bayesian nonparametrics
    (American Physical Society, 2020) Tavakoli, Meysam; Jazani, Sina; Sgouralis, Ioannis; Shafraz, Omer M.; Sivasankar, Sanjeevi; Donaphon, Bryan; Levitus, Marcia; Pressé, Steve; Physics, School of Science
    Fluorescence time traces are used to report on dynamical properties of molecules. The basic unit of information in these traces is the arrival time of individual photons, which carry instantaneous information from the molecule, from which they are emitted, to the detector on timescales as fast as microseconds. Thus, it is theoretically possible to monitor molecular dynamics at such timescales from traces containing only a sufficient number of photon arrivals. In practice, however, traces are stochastic and in order to deduce dynamical information through traditional means-such as fluorescence correlation spectroscopy (FCS) and related techniques-they are collected and temporally autocorrelated over several minutes. So far, it has been impossible to analyze dynamical properties of molecules on timescales approaching data acquisition without collecting long traces under the strong assumption of stationarity of the process under observation or assumptions required for the analytic derivation of a correlation function. To avoid these assumptions, we would otherwise need to estimate the instantaneous number of molecules emitting photons and their positions within the confocal volume. As the number of molecules in a typical experiment is unknown, this problem demands that we abandon the conventional analysis paradigm. Here, we exploit Bayesian nonparametrics that allow us to obtain, in a principled fashion, estimates of the same quantities as FCS but from the direct analysis of traces of photon arrivals that are significantly smaller in size, or total duration, than those required by FCS.