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• W2402873482 abstract "Bayesian Adaptive Estimation of Psychometric Slope and Threshold with Differential Evolution Hairong Gu, Jay I. Myung, Mark A. Pitt, and Zhong-Lin Lu {Gu.124, Myung.1, Pitt.2, Lu.535}@Osu.Edu Department of Psychology, Ohio State University 1835 Neil Avenue, Columbus, OH 43210 USA The adaptive experimentation methodology has been adopted in visual psychophysical modeling in the pursuit of efficiency in experimental time and cost. The standard scheme only optimizes one design in each experimental stage, although simultaneous optimization of multiple designs per stage can be beneficial, but difficult to implement because of a surge in computation. In this study, we incorporated the adaptive experimentation methodology under a Bayesian framework with differential evolution (DE), an algorithm specialized in multi-dimensional optimization problems to explore the multiple-designs-per-stage approach. By taking advantage of parallel computing, DE is computationally fast. The results showed that the multiple-designs-per-stage scheme resulted in a more stable estimation in the early stages of the parameter estimation. Keywords: Visual psychophysics, Bayesian inference, adaptive estimation, evolutionary computing Not All Designs are Equally Informative Experimental design is a critical step in carrying out effective experiments. Traditionally, the practice of experimental design is guided by heuristic norms, using a one-shot design, chosen at the outset, throughout the course of the experiment. Although this approach may be adequate in some scientific quests, its shortcomings are obvious. First, not all experimental designs are equally informative. The traditional approach does not guarantee that the design, including the number of treatments, the values of treatments, and the number of participants in each treatment, is an optimal choice. A non-optimal design may contribute little to the goal of the experiment. Further, the most informative designs may change as the experiment progresses with more responses being observed. Thus, a one-shot design ignores utilizing what can be learned during the course of an experiment. Second, the traditional experimental design method typically relies on increasing the number of participants or the number of measurements to increase the power of statistical inference. Obviously, this increases the experimental cost, which would matter for experiments that use expensive technology such as fMRI, or research whose target population is difficult to recruit (children, senior citizens, mentally disordered). Third, the traditional methods of experimental design center on randomization, reduction of variation, blocking etc., with the purpose of revealing the group or treatment effects while ignoring the individual variation. However, more and more recognition has been given to the importance of individual differences. For example, in drug development, it is important to know how different people react differently to the same drug to guide the prescription. Thus, experimental designs should not be identical for every participant. To illustrate how experimental designs can be unequally informative, suppose that a researcher is interested in studying how the rate of detection changes with the brightness of a stimulus. A psychometric function is used to describe the probability p of detecting a stimulus of certain brightness x. A simplified example assumes a sigmoid function , where x is the design variable representing the brightness and t is the parameter, threshold, a characteristic associated with a particular individual, reflected in the shift of the model in the design dimension. Suppose that there are only 5 possible values of t. The corresponding predictions are depicted as the five lines in Figure 1. The red line represents a particular subject’s true t value and the other four blue lines are from the wrong t values. The researcher conducts an experiment to estimate the threshold value of that subject by presenting two designs with intensity D1 and D2. Visualization of the model suggests that D1 is a good design because the predictions from the five t values are very differentiable so that the observation can be informative of the true t value. On the other hand, D2 would be a bad design because the prediction differences are so small that little information about the exact shift of the true model is given. Detection probability Abstract misspecified correct D1 D2 X (design) Figure 1: A sample psychometric function with 5 possible parameter values (see text) with the true value indicated by the red line and the wrong values by the blue lines. A good design D1 offers the most discriminability, whereas D2 is a bad design for a lack of differentiability in prediction." @default.
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• W2402873482 date "2013-01-01" @default.
• W2402873482 modified "2023-10-17" @default.
• W2402873482 title "Adaptive Estimation of Psychometric Slope and Threshold with Differential Evolution" @default.
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