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A common approach to analysis of single particle trajectories (SPTs) is to compute the mean-square displacement (MSD) of the particle(s) as a function of lag-time. Analytical solutions to the dependence of MSD on temporal lag are known for many common models of motion, rendering the use of MSD analysis practical for inference of both the mode of motion as well as relevant parameter values (Qian et al. '91; Saxton and Jacobson '97). In most biological applications, however, the underlying mode of motion is unknown a priori, and both experimental limitations (sampling rate, trajectory length, trajectory number) and heterogeneity between different particles in a biological dataset can confound the objective analysis of SPTs. Strong correlations intrinsic to MSD curves (Qian et al. '91; Michalet '10) further complicate the analysis and can lead to overly complex interpretations.

For these reasons, we developed an objective framework to automatically analyze SPTs and evaluate competing motion models objectively and systematically, handling the aforementioned limitations in data acquisition and sample heterogeneity (Monnier et al. '12). Our approach is based on Bayesian inference for multiple hypothesis testing (Raftery '95; Posada and Buckley '04; Sivia and Skilling '06; Bronson et al. '09; Voisinne et al. '10). This approach is applicable to non-nested competing models that standard statistical tests cannot handle (Posada and Buckley '04) and makes no assumptions about trajectory length, sampling rate, or heterogeneity, automatically identifying the simplest model that fits the observed MSDs according to the Principle of Parsimony or Okham's razor (Raftery '95; Posada and Buckley '04; Sivia and Skilling '06). This approach follows closely on recent work applying Bayesian inference to fluorescence correlation spectroscopy (FCS) data (He et al. '12; Guo et al. '12).


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