We consider the psychophysical experiments in which a skin spot of a test subject is exposed to a high-energy millimeter wave beam. The absorbed electromagnetic energy increases the skin temperature and activates the thermal nociceptors when the activation temperature is reached. The activated nociceptors transduce an electrical signal (pain signal), which, when exceeding a subjective threshold, will trigger the brain to issue a flight signal. The observed flight action is delayed by the unknown human reaction time. Since the transduced signal increases monotonically with the exposed time, we measure the subjective threshold in terms of the critical exposure time, which fluctuates among subjects and among tests on the same subject. We consider a sequence of tests, each with a prescribed exposure duration. The measured data consist of the binary outcome regarding the occurrence of flight and the time of observed flight (if it occurs). We study the problem of extracting the median of the random subjective threshold when its distribution type is unknown. We examine four methods: 1) sample median, 2) maximum likelihood estimation (MLE) with two unknown variables, 3) MLE with one unknown variable, and 4) adaptive Bayesian method. The key findings of the study are: a) only the adaptive Bayesian method is practically applicable since no sample of critical exposure time is measurable in real tests due to the delay of human reaction; b) the adaptive Bayesian method converges to the correct value even when the assumed inference model is incorrect; it is as efficient as the sample median method; c) the robustness of the adaptive Bayesian method is lost when inferring the mean instead of the median; d) the predicted error obtained from the posterior standard deviation is unreliable. In a subsequent study, we will investigate the possibility of extracting the human reaction time.

Event Host: Maryam Adamzadeh, Ph.D. Student, Applied Mathematics

Advisor: Hongyun Wang

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