Bayesian nonparametric methods have recently transformed emerging areas within data science. One such promising method, the infinite hidden Markov model (iHMM), generalizes the HMM that itself has become a workhorse in single molecule data analysis. The iHMM goes beyond the HMM by self-consistently learning all parameters learned by the HMM in addition to learning the number of states without recourse to any model selection steps. Despite its generality, simple features (such as drift), common to single molecule time traces, result in an overinterpretation of drift and the introduction of artifact states. Here we present an adaptation of the iHMM that can treat data with drift originating from one or many traces (e.g., Förster resonance energy transfer). Our fully Bayesian method couples the iHMM to a continuous control process (drift) self-consistently learned while learning all other quantities determined by the iHMM (including state numbers). A key advantage of this method is that all traces—regardless of drift or states visited across traces—may now be treated on an equal footing, thereby eliminating user-dependent trace selection (based on drift levels), preprocessing to remove drift, and postprocessing model selection based on state number.
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