In recent years, a number of methods have been proposed to estimate the times at which neurons spike on the basis of calcium imaging data. However, quantifying the uncertainty associated with these estimated spikes remains an open problem. We consider a simple and well-studied model for calcium imaging data, which states that calcium decays exponentially in the absence of a spike, and instantaneously increases when a spike occurs. We wish to test the null hypothesis that the neuron did not spike -- i.e., that there was no increase in calcium -- at a particular timepoint at which a spike was estimated. In this setting, classical hypothesis tests lead to inflated Type I error, because the spike was estimated on the same data. To address this problem, we propose a selective inference approach to test the null hypothesis. We describe an efficient algorithm to compute finite-sample p-values that control selective Type I error, and confidence intervals with correct selective coverage, for spikes estimated using a recent proposal from the literature. We apply our proposal in simulation and on calcium imaging data from the spikefinder challenge.

翻译：近年来,根据钙成像数据,提出了若干方法来估计神经元峰值的上升时间。然而,量化与这些估计的峰值有关的不确定性仍然是一个尚未解决的问题。我们认为一个简单的、经过充分研究的钙成像数据模型,该模型指出,在没有峰值的情况下,钙分解会指数化,在峰值发生时会瞬间增加。我们希望测试神经元没有上升的无效假设 -- -- 即钙没有增加 -- -- 在估计峰值的特定时间点。在这个设置中,古典假设测试导致I型错误膨胀,因为峰值是在同一数据上估计的。为解决这一问题,我们建议采用选择性推论方法测试无效假设。我们描述一种有效的算法,对控制I型选择性误差的定值进行计算,并用准确的选择性覆盖度进行信任间隔,以利用文献最近的建议估算的峰值。我们的建议用于模拟和对钉壁成物挑战的钙成像数据。