In recent years, a number of methods have been proposed to estimate the times at which a neuron spikes 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 used for testing. To overcome this problem, we propose a selective inference approach. 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间隔时间。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,它表明,在没有峰值的情况下,钙的衰变会成倍地成倍增加,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,古典假设试验导致I型型错误膨胀,因为峰值是在用于测试的同一数据上估计的。为了克服这一问题,我们提出了一个选择性的推论方法。我们描述一种有效的算法,用文献最近的一项提议来计算定型的I型误差,以及有准确选择性的间隔。我们在模拟中应用了我们的建议,并在尖峰峰挑战的钙成像数据上应用了我们的建议。