Using Bayesian priors to overcome non-identifiablility issues in Hidden Markov models

Hidden Markov models (HMMs) for biomolecules suffer from various forms of parameter non-identifiability. This poses severe challenges to both maximum likelihood and Bayesian inference. However, Bayesian inference offers effective means of overcoming these pathologies. We study the role of prior distributions in the face of practical parameter non-identifiability in Bayesian inference applied to prototypical patch clamp data of ligand-gated ion channels. We advocate the use of minimally informative priors, as they increase the accuracy and decrease the uncertainty of the inference. For complex HMMs, stronger prior assumptions are needed to render the posterior sufficiently proper. This can be achieved by confining the parameter space to physically motivated limits. Another beneficial assumption is finite cooperativity of ligand-binding and unbinding events, which introduces a bias towards non-cooperativity but still allows for a non-vanishing degree of cooperativity that is inferred from the data. Despite its vagueness, our prior renders the posterior sufficiently proper for all datasets that we considered without imposing the assumption of non-cooperativity. Combining all prior factors allows for meaningful inferences with a dataset of a thousand times lower quality.