  Advances in neuroscience have enabled researchers to measure the activities
of large numbers of neurons simultaneously in behaving animals. We have access
to the fluorescence of each of the neurons which provides a first-order
approximation of the neural activity over time. Determining the exact spike of
a neuron from this fluorescence trace constitutes an active area of research
within the field of computational neuroscience. We propose a novel Bayesian
approach based on a mixture of half-non-local prior densities and point masses
for this task. Instead of a computationally expensive MCMC algorithm, we adopt
a stochastic search-based approach that is capable of taking advantage of
modern computing environments often equipped with multiple processors, to
explore all possible arrangements of spikes and lack thereof in an observed
spike train. It then reports the highest posterior probability arrangement of
spikes and posterior probability for a spike at each location of the spike
train. Our proposals lead to substantial improvements over existing proposals
based on L1 regularization, and enjoy comparable estimation accuracy to the
state-of-the-art L0 proposal, in simulations, and on recent calcium imaging
data sets. Notably, contrary to optimization-based frequentist approaches, our
methodology yields automatic uncertainty quantification associated with the
spike-train inference.
