  Recent advancements in miniaturized fluorescence microscopy have made it
possible to investigate neuronal responses to external stimuli in awake
behaving animals through the analysis of intra-cellular calcium signals. An
on-going challenge is deconvoluting the temporal signals to extract the spike
trains from the noisy calcium signals' time-series. In this manuscript, we
propose a nested Bayesian finite mixture specification that allows for the
estimation of spiking activity and, simultaneously, reconstructing the
distributions of the calcium transient spikes' amplitudes under different
experimental conditions. The proposed model leverages two nested layers of
random discrete mixture priors to borrow information between experiments and
discover similarities in the distributional patterns of neuronal responses to
different stimuli. Furthermore, the spikes' intensity values are also clustered
within and between experimental conditions to determine the existence of common
(recurring) response amplitudes. Simulation studies and the analysis of a data
set from the Allen Brain Observatory show the effectiveness of the method in
clustering and detecting neuronal activities.
