Bayesian Inference of Two-Dimensional Contrast Sensitivity Function from Data Obtained with Classical One-Dimensional Algorithms Is Efficient

Xiaoxiao Wang, Huan Wang, Jinfeng Huang, Yifeng Zhou, Tzvetomir Tzvetanov

The contrast sensitivity function that spans the two dimensions of contrast and spatial frequency is crucial in predicting functional vision both in research and clinical applications. In this study, the use of Bayesian inference was proposed to determine the parameters of the two-dimensional contrast sensitivity function. Two-dimensional Bayesian inference was extensively simulated in comparison to classical one-dimensional measures. Its performance on two-dimensional data gathered with different sampling algorithms was also investigated. The results showed that the two-dimensional Bayesian inference method significantly improved the accuracy and precision of the contrast sensitivity function, as compared to the more common one-dimensional estimates. In addition, applying two-dimensional Bayesian estimation to the final data set showed similar levels of reliability and efficiency across widely disparate and established sampling methods (from classical one-dimensional sampling, such as Ψ or staircase, to more novel multi-dimensional sampling methods, such as quick contrast sensitivity function and Fisher information gain). Furthermore, the improvements observed following the application of Bayesian inference were maintained even when the prior poorly matched the subject's contrast sensitivity function. Simulation results were confirmed in a psychophysical experiment. The results indicated that two-dimensional Bayesian inference of contrast sensitivity function data provides similar estimates across a wide range of sampling methods. The present study likely has implications for the measurement of contrast sensitivity function in various settings (including research and clinical settings) and would facilitate the comparison of existing data from previous studies.