A Bayesian Approach for Extracting Fluorescence Lifetimes from Sparse Data Sets and Its Significance for Imaging Experiments. (21st December 2018) - Santra, Kalyan; Smith, Emily A.; Song, Xueyu; Petrich, Jacob W.
Abstract: The measurement of fluorescence lifetimes, especially in small sample volumes, presents the dual challenge of probing a small number of fluorophores and fitting the concomitant sparse data set to the appropriate excited‐state decay function. A common method of analysis, such as the maximum likelihood (ML) technique, assumes a uniform probability distribution of the parameters describing the fluorescence decay function. An improvement is thus suggested by implementing a suitable nonuniform distribution, as is provided by a Bayesian framework, where the distribution of parameters is obtained from both their prior knowledge and the evidence‐based likelihood of an event for a given set of parameters. We have also considered the Dirichlet prior distribution, whose mathematical form enables analytical solutions of the fitting parameters to be rapidly obtained. If Gaussian and exponential prior distributions are judiciously chosen, they reproduce the experimental target lifetime to within 20% with as few as 20 total photon counts for the data set, as does the Dirichlet prior distribution. But because of the analytical solutions afforded by the Dirichlet prior distribution, it is proposed to employ a Dirichlet prior to search parameter space rapidly to provide, if necessary, appropriate parameters for subsequent employment of a Gaussian or exponential prior distribution. Abstract : The fluorescence lifetime of a fluorophore can be estimated from the experimental data using the Bayesian framework, in which the prior distribution ( i.e . Gaussian, exponential or Dirichlet) of the lifetime is incorporated along with the likelihood ( i.e . the experimental data) to obtain the posterior distributions, which are presented as histograms of the frequency of the retrieved lifetime. Three examples are shown for data sets comprised of a total of 20, 200 and 20 000 total photon counts, respectively. An experimentally obtained target lifetime can be reproduced to within 20% with as few as 20 total counts for the data set.