Bayesian hypothesis testing and experimental design for two-photon imaging data

Variability, stochastic or otherwise, is a central feature of neural activity. Yet the means by which estimates of variation and uncertainty are derived from noisy observations of neural activity is often heuristic, with more weight given to numerical convenience than statistical rigour. For two-photon imaging data, composed of fundamentally probabilistic streams of photon detections, the problem is particularly acute. Here, we present a statistical pipeline for the inference and analysis of neural activity using Gaussian Process regression, applied to two-photon recordings of light-driven activity in ex vivo mouse retina. We demonstrate the flexibility and extensibility of these models, considering cases with non-stationary statistics, driven by complex parametric stimuli, in signal discrimination, hierarchical clustering and other inference tasks. Sparse approximation methods allow these models to be fitted rapidly, permitting them to actively guide the design of light stimulation in the midst of ongoing two-photon experiments.

无论是随机还是非随机的变异性，均为神经活动的核心特征。然而，从神经活动的带噪观测中推导变异性与不确定性估计的方法，往往采用启发式思路，更注重数值计算的便捷性而非统计严谨性。对于本质上由概率性光子探测流构成的双光子成像（two-photon imaging）数据而言，该问题尤为突出。本文提出一种基于高斯过程回归（Gaussian Process regression）的神经活动推断与分析统计流程，并将其应用于离体小鼠视网膜光驱动活动的双光子记录数据。文中展示了该类模型的灵活性与可扩展性，并针对由复杂参数化刺激驱动的非平稳统计特性场景，将其应用于信号判别、层次聚类及其他推断任务。稀疏近似方法可实现模型的快速拟合，使其能够在双光子实验进行过程中，主动指导光刺激的设计工作。