  Time series data provided by single-molecule Forster resonance energy
transfer (sm-FRET) experiments offer the opportunity to infer not only model
parameters describing molecular complexes, e.g. rate constants, but also
information about the model itself, e.g. the number of conformational states.
Resolving whether or how many of such states exist requires a careful approach
to the problem of model selection, here meaning discriminating among models
with differing numbers of states. The most straightforward approach to model
selection generalizes the common idea of maximum likelihood-selecting the most
likely 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 termed
variational Bayes. We demonstrate how this technique can be applied to temporal
data such as smFRET time series; show superior statistical consistency relative
to the maximum likelihood approach; and illustrate how model selection in such
probabilistic or generative modeling can facilitate analysis of closely related
temporal data currently prevalent in biophysics. Source code used in this
analysis, including a graphical user interface, is available open source via
http://vbFRET.sourceforge.net
