September 2019
Volume 19, Issue 10
Open Access
Vision Sciences Society Annual Meeting Abstract  |   September 2019
Testing accuracy, additivity, and sufficiency of human use of probability density information in a visuo-cognitive task
Author Affiliations & Notes
  • Keiji Ota
    Dept of Psychology, New York University
    Dept of Engineering, Tokyo University of Agriculture and Technology
    Japan Society for the Promotion of Science Research Fellow
  • Jakob Phillips
    Dept of Psychology, New York University
  • Laurence T Maloney
    Dept of Psychology, New York University
    Center for Neuroscience, New York University
Journal of Vision September 2019, Vol.19, 276. doi:https://doi.org/10.1167/19.10.276
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      Keiji Ota, Jakob Phillips, Laurence T Maloney; Testing accuracy, additivity, and sufficiency of human use of probability density information in a visuo-cognitive task. Journal of Vision 2019;19(10):276. doi: https://doi.org/10.1167/19.10.276.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Eighteen observers viewed samples of dots from a 2D Gaussian pdf on a display. One more dots is about to be drawn and the rewards associated with possible outcomes are marked on the display. What is the probability the next dot will fall into any specified region? What is the expected value (EV) of the dot? We compared human performance in reasoning about pdfs and value to ideal in two experiments. An ideal observer accurately estimates the probability induced on any region and satisfies additivity when estimating the probability of an outcome falling in either two disjoint regions. It also satisfies an additional property: sufficiency. The estimated mean and covariance parameters are sufficient statistics and the ideal observer will correctly ignore everything else. Exp1: Observers saw Gaussian samples of size 5 or 30. They were shown regions R marked on the display and asked to estimate the probability that the next dot from the same pdf would fall in the region. We compared their estimates to the correct estimates (accuracy). There were three types of regions: symmetric S around the mean and the other two being the upper (SU) and lower (SL) halves of S. These triples allowed a test of additivity: P[S] = P[SU] + P[SL]. Exp2: Observers saw similar samples but with a penalty boundary (PB) marked on the display. Observers moved the visible samples (and underlying pdf) to any location on the display. Then a new dot from the translated Gaussian distribution determined a score in the trial. If the point was above the PB they suffered the penalty, if below, the reward decreased linearly with distance from the PB. Results: Observers’ estimates of probability were close to accurate but showed highly patterned super-additivity (roughly 7%). Observes violated sufficiency, assigning too much weight to extreme points.

Acknowledgement: KO: Japan Society for the Promotion of Science Research Fellowship, LTM: Guggenheim Fellowship 
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