Abstract
Numerous psychophysical studies have considered how subjects combine multiple sensory cues to make perceptual decisions, or how contextual information influences the perception of a target stimulus. In cases where cues interact in a linear manner, it is sufficient to characterize an observer’s sensitivity along each individual feature dimension to predict perceptual decisions when multiple cues are varied simultaneously. However, in many situations sensory cues interact non-linearly, and therefore quantitatively characterizing subject behavior requires estimating a complex non-linear psychometric model which may contain numerous parameters. In this computational methods study, we analyze three efficient implementations of the well-studied PSI procedure (Kontsevich & Tyler, 1999) for adaptive psychophysical data collection which generalize well to psychometric models defined in multi-dimensional stimulus spaces where the standard implementation is intractable. Using generic multivariate logistic regression models as a test bed for our algorithms, we present two novel implementations of the PSI procedure which offer substantial speed-up compared to previously proposed implementations: (1) A look-up table method where optimal stimulus placements are pre-computed for various values of the (unknown) true model parameters and (2) A Laplace approximation method using a continuous Gaussian approximation to the evolving posterior density. We demonstrate the utility of these novel methods for quickly and accurately estimating the parameters of hypothetical nonlinear cue combination models in 2- and 3-dimensional stimulus spaces. In addition to these generic examples, we further illustrate our methods using a biologically derived model of how stimulus contrast influences orientation discrimination thresholds. Finally, we consider strategies for further speeding up experiments and extensions to models defined in dozens of dimensions. This work is potentially of great significance to investigators who are interested in quantitatively modeling the perceptual representations of complex naturalistic stimuli like textures and occlusion contours which are defined by multiple feature dimensions.