PROBABILISTIC PSYCHOPHYSICS WITH NOISY STIMULI

Mental representations of physical objects may vary from moment to moment. This occurs because of stimulus variation prior to the initiation of a neural signal and also because of neural variation in the neural mechanism. A psychophysical transformation function formalizes the connection between stimulus measures and mental representations, and this function will be assumed to be a one-to-one function (monotonic in one dimension). A very general equation is derived for the probability density function (pdf) of the momentary psychological magnitudes given any particular positive stimulus pdf, any one-to-one psychophysical transformation function and any neural pdf. Special cases of this general model are applied to the method of paired comparisons. These models for paired comparisons are derived on the basis of assumed lognormally distributed stimulus values on a stimulus continuum, a log or power psychophysical transformation and added neural normally distributed noise. The parameters of sample problems are estimated using maximum likelihood, nonlinear least squares and minimum chi-square criteria. These methods are compared with respect to bias in and the variance of the estimators.