  Technological advancements have enabled the recording of spiking activities
from large neuron ensembles, presenting an exciting yet challenging opportunity
for statistical analysis. This project considers the challenges from a common
type of neuroscience experiments, where randomized interventions are applied
over the course of each trial. The objective is to identify groups of neurons
with unique stimulation responses and estimate these responses. The observed
data, however, comprise superpositions of neural responses to all stimuli,
which is further complicated by varying response latencies across neurons. We
introduce a novel additive shape invariant model that is capable of
simultaneously accommodating multiple clusters, additive components, and
unknown time-shifts. We establish conditions for the identifiability of model
parameters, offering guidance for the design of future experiments. We examine
the properties of the proposed algorithm through simulation studies, and apply
the proposed method on neural data collected in mice.
