Bayesian modeling and inference for one-shot experiments

In one-shot experiments, units are subjected to varying levels of stimulus and their binary response (go/no-go) is recorded. Experimental data is used to estimate the ‘sensitivity function’, which characterizes the probability of a ‘go’ for a given level of stimulus. We review the current GLM approaches to modeling and inference, and identify some deficiences. To address these, we propose a novel Bayesian approach using an adjustable number of cubic splines, with physically-plausible smoothness, monotonicity, and tail constraints introduced through the prior distribution on the coefficients. Our approach runs ‘out of the box’, and in roughly the same time as the GLM approaches. We illustrated with two contrasting datasets, and show that our more flexible Bayesian approach gives different inferences to the GLM approaches for both the sensitivity function and its inverse. The code and datasets are available online in the Supplementary Material.

在单试次实验中，实验单元接受不同强度的刺激，并记录其二分类响应（触发/不触发）。实验数据被用于估计灵敏度函数（sensitivity function），该函数可表征给定刺激强度下触发响应的概率。我们综述了当前用于建模与推断的广义线性模型（Generalized Linear Model，简称GLM）方法，并指出了其中存在的若干缺陷。为解决上述缺陷，我们提出了一种新颖的贝叶斯方法：该方法采用可调数量的三次样条基函数，并通过系数的先验分布引入符合物理实际的平滑性、单调性与尾部约束。我们的方法可直接开箱即用，且运行耗时与广义线性模型方法大致相当。我们通过两组对比鲜明的数据集开展了演示，结果表明：相较于广义线性模型方法，我们的灵活贝叶斯方法在灵敏度函数及其逆函数的推断中得到了差异化的结论。代码与数据集已在补充材料中在线发布。