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Time series data provided by single-molecule Forster resonance energytransfer (sm-FRET) experiments offer the opportunity to infer not only modelparameters describing molecular complexes, e.g. rate constants, but alsoinformation about the model itself, e.g. the number of conformational states.Resolving whether or how many of such states exist requires a careful approachto the problem of model selection, here meaning discriminating among modelswith differing numbers of states. The most straightforward approach to modelselection generalizes the common idea of maximum likelihood-selecting the mostlikely parameter values-to maximum evidence: selecting the most likely model.In either case, such inference presents a tremendous computational challenge,which we here address by exploiting an approximation technique termedvariational Bayes. We demonstrate how this technique can be applied to temporaldata such as smFRET time series; show superior statistical consistency relativeto the maximum likelihood approach; and illustrate how model selection in suchprobabilistic or generative modeling can facilitate analysis of closely relatedtemporal data currently prevalent in biophysics. Source code used in thisanalysis, including a graphical user interface, is available open source viahttp://vbFRET.sourceforge.net

Learning Rates and States from Biophysical Time Series: A Bayesian Approach to Model Selection and Single-Molecule FRET Data