Signal Detection Theory (SDT) is a widely-used framework for analyzing data from yes/no tasks, disentangling response bias from sensitivity. Traditional SDT assumes Gaussian distributions with equal variance for signal and noise. However, Gaussian SDT is incapable of modeling asymmetries often observed in receiver operating characteristic (ROC) curves stemming from experimental data. Poisson distributions are well-suited for modeling rare events like neuronal firing close to threshold. Poisson-based ROC curves naturally exhibit asymmetries akin to those observed in experimental findings. Despite its potential, Poisson SDT has been seldom proposed (e.g., Egan, 1975; Kaernbach, 1991) and, to the best of our knowledge, never been applied to experimental datasets. This may be attributed to the lack of tools for analyzing experimental data within the Poisson SDT framework. To address this, we offer a new method employing a maximum-likelihood approach to estimate the optimal parameters of a Poisson SDT model from experimental data. We discuss the challenges encountered in optimizing such models and the strategies employed to overcome them. The software package incorporates likelihood-ratio tests to assist users in determining the most appropriate model for their data. Through simulations, we evaluate various experimental designs to assess their capacity to distinguish between Gaussian and Poisson SDT. Our findings offer guidance for experimentalists aiming to investigate decision-making processes close to threshold.

Egan, J. P. (1975). Signal detection theory and ROC analysis. New York: Academic Press.

Kaernbach, C. (1991). Poisson signal detection theory: Link between threshold models and the Gaussian assumption. Perception & Psychophysics 50(5), 498-506.