Minimally and vaguely informative priors to combat practical parameter non-identifiability of hidden Markov models exemplified by ion channel data
Hidden Markov Model (HMM) inference for time-series data from ion channels or other biomolecules is challenging. We argue that inference on partially observed chemical reaction networks (CRNs) suffers from practical parameter non-identifiability (non-PI) that often goes unnoticed in maximum likelihood (ML) inferences. Limitations in the signal bandwidth and a poor signal-to-noise ratio only add to the non-PI problem. We study the role of the prior distribution in the face of non-PI. In particular, we advocate using minimally informative (MI) priors and additional restrictions on the parameter space that can be derived from physical considerations. Using patch clamp (PC) ion-channel measurements as a prototypical time series, we demonstrate Bayesian strategies for alleviating non-PI problems with sharpened prior information. In Bayesian statistics, the prior can substantially modulate the posterior. We demonstrate that non-PI can be severely harmful when using uniform priors on the rate