  The Morris-Lecar (ML) model has applications to neuroscience and cognition. A
simple network consisting of a pair of synaptically coupled ML neurons can
exhibit a wide variety of deterministic behaviors including asymmetric
amplitude state (AAS), equal amplitude state (EAS), and steady state (SS). In
addition, in the presence of noise this network can exhibit mixed-mode
oscillations (MMO), which represent the system being stochastically driven
between these behaviors. In this paper, we develop a method to specifically
estimate the parameters representing the coupling strength (gsyn) and the
applied current (Iapp) of two reciprocally coupled and biologically similar
neurons. This method employs conditioning the likelihood on cumulative power
and mean voltage. Conditioning has the potential to improve the identifiability
of the estimation problem. Conditioning likelihoods are typically much simpler
to model than the explicit joint distribution, which several studies have shown
to be difficult or impossible to determine analytically. We adopt a rejection
sampling procedure over a closed defined region determined by bifurcation
continuation analyses. This rejection sampling procedure is easily embedded
within the proposal distribution of a Bayesian Markov chain Monte Carlo (MCMC)
scheme and we evaluate its performance. This is the first report of a Bayesian
parameter estimation for two reciprocally coupled Morris-Lecar neurons, and we
find a proposal utilizing rejection sampling reduces parameter estimate bias
relative to naive sampling. Application to stochastically coupled ML neurons is
a future goal.
