  Optimal designs minimize the number of experimental runs (samples) needed to
accurately estimate model parameters, resulting in algorithms that, for
instance, efficiently minimize parameter estimate variance. Governed by
knowledge of past observations, adaptive approaches adjust sampling constraints
online as model parameter estimates are refined, continually maximizing
expected information gained or variance reduced. We apply adaptive Bayesian
inference to estimate transition rates of Markov chains, a common class of
models for stochastic processes in nature. Unlike most previous studies, our
sequential Bayesian optimal design is updated with each observation, and can be
simply extended beyond two-state models to birth-death processes and multistate
models. By iteratively finding the best time to obtain each sample, our
adaptive algorithm maximally reduces variance, resulting in lower overall error
in ground truth parameter estimates across a wide range of Markov chain
parameterizations and conformations.
