Bayesian Modeling and Inference for One-Shot Experiments

Abstract

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 deficiencies. 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 illustrate 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.

Keywords:

• go/no-go
• No-Fire Threshold (NFT)
• Quantal function
• Sensitivity testing

Supplementary Materials

The MCMC sampler is described in the Supplementary Material, along with diagnostics for ESD dataset. The code and datasets are also available, including the oneshot package for R.

Acknowledgments

We would like to thank the following for their very helpful comments on previous versions of this article: Rod Drake, David Steinberg, Simon Wood, Andrew Zammit Mangion, and Matt Stapleton. The comments of the Editor, an Associate Editor, and three reviewers substantially improved the paper’s focus and clarity.

Disclosure Statement

The authors report there are no competing interests to declare.