Inference of Median Subjective Threshold in Psychophysical Experiments

Abstract

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.

Extracting Human Reaction Time from Observations in the Method of Constant Stimuli

“…In the inference of c m , we fix the shape parameter at 2.5 k = and focus on estimating the scale parameter λ . As we discussed in our previous study [11], fixing k at a wrong value, especially at a smaller value (corresponding to a wider Weibull distribution), will not affect the inference accuracy of the median c m .…”

“…This subjective threshold is a random variable, reflecting the underlying biovariability. It fluctuates from one test subject to another, from one exposure test to another on the same subject [11].…”

“…First, we notice that the data set of binary outcomes is independent of the human reaction time; an adaptive Bayesian method has been proposed to design the MoCS tests and to infer the median subjective threshold from the observed binary outcomes [17]. This has been done in our previous study of millimeter wave exposure tests [11]. In the current study, we focus on extracting the human reaction time based on the data of observed flight action times collected in a sequence of MoCS tests designed by the adaptive Bayesian method [17].…”

“…lected in a sequence of exposure tests. As described in our previous study[11], the exposure tests are designed sequentially and adaptively in a Bayesian framework, based on the test results already collected. The inference of c m is based on the maximum likelihood estimation (MLE) formulation using a Weibull inference model.…”

“…The fraction of tests with occurrence of flight action ( = ) varies with the distribution of prescribed exposure duration { } j η . In a sequence of tests designed using the adaptive Bayesian method[11] [17], η is selected sequentially based on the current posterior to maximize the inference accuracy for c m given the total number of tests allocated. The sequence { } j η produced by the Bayesian method is a random walk of η toward and then around the true value of median subjective threshold c m .…”