The multivariate adaptive design for efficient estimation of the time course of perceptual adaptation

  • Ping Chen
  • Steve Engel
  • Chun WangEmail author


In experiments on behavioral adaptation, hundreds or even thousands of trials per subject are often required in order to accurately recover the many psychometric functions that characterize adaptation’s time course. More efficient methods for measuring perceptual changes over time would be beneficial to such efforts. In this article, we propose two methods to adaptively select the optimal stimuli sequentially in an experiment on adaptation: These are the minimum entropy (ME) method and the match probability (MP) method. The ME method minimizes the uncertainty about the joint posterior distribution of the function parameters at each trial and is mathematically equivalent to Zhao, Lesmes, and Lu’s (2019) method, which efficiently measures time courses of perceptual change by maximizing information gain. The MP method selects the next stimulus that makes the value of the psychometric function closest to .5—that is, where the probability of choosing either one of the two options for each stimulus is closest to .5. We extended Zhao et al.’s (2019) work by evaluating the ME method in a new domain (contrast adaptation) with two simulation studies that compared it to MP and two other methods (i.e., traditional staircase and random methods), and also explored the optimal block length. ME outperformed the other three methods in general, and using fewer longer blocks generally produced better parameter recovery than using more shorter blocks.


Adaptive design Minimum entropy Perceptual adaptation Time course Tilt aftereffect 



This project was supported by grant numbers IES R305D160010, NSF SES-1659328, NIH R01HD079439, and NSFC 31300862.

Open Practice Statement

The simulated data and source code for all experiments are available at


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Copyright information

© The Psychonomic Society, Inc. 2019

Authors and Affiliations

  1. 1.Beijing Normal UniversityBeijingChina
  2. 2.University of MinnesotaMinneapolisUSA
  3. 3.University of WashingtonSeattleUSA

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