Inference of Median Subjective Threshold in Psychophysical Experiments

We consider the response of a test subject upon a skin area being heated with an electromagnetic wave or a contact surface. When the specifications of the electromagnetic beam are fixed, the stimulus is solely described by the heating duration. The binary response of a subject, escape or no escape, is determined by the stimulus and a subjective threshold that varies among test realizations. We study four methods for inferring the median subjective threshold in psychophysical experiments: 1) sample median, 2) maximum likelihood estimation (MLE) with 2 variables, 3) MLE with 1 variable, and 4) adaptive Bayesian method. While methods 1 - 3 require samples of time to escape measured in the method of limits, method 4 utilizes binary outcomes observed in the method of constant stimuli. We find that a) the adaptive Bayesian method converges and is as efficient as the sample median even when the assumed model distribution is incorrect; b) this robust convergence is lost if we infer the mean instead of the median; c) for the optimal performance in an uncertain situation, it is best to use a wide model distribution; d) the predicted error from the posterior standard deviation is unreliable, dominated by the assumed model distribution.