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.

翻译：技术进步使得记录大规模神经元集群的锋电活动成为可能，这为统计分析带来了激动人心的挑战性机遇。本研究关注一类常见神经科学实验中的挑战——此类实验会在每个试验过程中施加随机干预。研究目标是识别具有独特刺激响应模式的神经元群组并估计其响应特征。然而观测数据包含所有刺激诱发的神经响应叠加信号，不同神经元的响应潜伏期差异进一步加剧了分析复杂性。我们提出一种新型加性形态不变模型，该模型能同时处理多聚类、加性分量和未知时间偏移。我们建立了模型参数可识别性条件，为未来实验设计提供理论指导。通过模拟研究考察了所提算法的特性，并将该方法应用于小鼠神经数据的分析中。