Abstract
Prior expectation affects posterior perceptual experience. This psychological effect is called expectation effect. In this paper, we proposed mathematical model of the expectation effect. The model consists of three statistic distributions, prior, likelihood, and posterior. We assumed that a combination of prior and likelihood estimates the posterior that represents posterior perceptual experience using Bayes' inference and efficient coding hypothesis. Based on the proposed model, we formalized the expectation effect as a function of three parameters: expectation error (difference between expectation values of prior and likelihood), uncertainty (variance of prior), and external noise (variance of noise distributions for sensory input). We conducted both computer simulation and experiment using size-weight illusion (SWI) to examine the characteristics of expectation effect. We investigated the effects of the three parameters on intensity of expectation effect and the conditions of two types of expectation effect, i.e. contrast and assimilation. From the result of both simulations and experiments, we found following characteristics of the expectation effect. 1) Assimilation shifts to contrast as expectation error increased. 2) Uncertainty decreased intensity of both assimilation and contrast effect. 3) External noise increase assimilation and decrease contrast.
