Bayesian Spike Train Inference via Non-Local Priors

Abstract: 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.