Many recent advancements in single molecule localization microscopy exploit the stochastic photo-switching of fluorophores to reveal complex cellular structures beyond the classical diffraction limit. However, this same stochasticity makes counting the number of molecules to high precision extremely challenging. Modeling the photo-switching behavior of a fluorophore as a continuous time Markov process transitioning between a single fluorescent and multiple dark states, and fully mitigating for missed blinks and false positives, we present a method for computing the exact probability distribution for the number of observed localizations from a single photo-switching fluorophore. This is then extended to provide the probability distribution for the number of localizations in a dSTORM experiment involving an arbitrary number of molecules. We demonstrate that when training data is available to estimate photo-switching rates, the unknown number of molecules can be accurately recovered from the posterior mode of the number of molecules given the number of localizations.

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