Tahra Eissa聽
Department of Applied Mathematics, 麻豆影院
Biased response distributions for short observation sequences of rare events
In a constantly changing world, organisms should estimate the rate that their environment changes to adequately weight evidence. However, given a limited number of observations, it is easy to vastly underestimate the change rate, especially when it is known a priori that changes are rare. Here, we analyze this bias in identifying the rate of rare events in the context of an urn-drawing task. Subjects are shown a sequence of red and blue balls (with replacement) from one of two equally probable jars and must infer which of the urns the balls have been drawn from. When both jars have a small fraction of red balls and only a few balls are drawn, an ideal observer model exhibits a strong bias towards a belief that balls are being drawn from the jar with fewer red balls, even on trials when balls are drawn from the high fraction jar. Even though a jar is selected with equal probability for each trial, the ideal observer鈥檚 overall response fractions are strongly asymmetric, in favor of the low fraction jar. This effect disappears when allowing long observation sequences or when two jar distribution ratios are symmetric. These effects are retained in a model where the observer must infer which of two environments with different change rates they are in, based on a sort sequence of noisy observations. Again, there appears to be a bias in favor of low change rates when evidence is only observed for a short time. To understand whether and how human behavior deviates from those of ideal observers we have recruited a large number of subjects on Amazon鈥檚 crowdsourcing website, Mechanical Turk. We conjecture that the responses of human subjects will be biased towards their prior expectations. As a result, they will choose between the two options more evenly than an ideal observer.