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Steven S. Shimozaki, Miguel P. Eckstein, Craig K. Abbey; Comparison of two weighted integration models for the cueing task: linear and likelihood. Journal of Vision 2003;3(3):3. doi: https://doi.org/10.1167/3.3.3.
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© ARVO (1962-2015); The Authors (2016-present)
In a task in which the observer must detect a signal at two locations, presenting a precue that predicts the location of a signal leads to improved performance with a valid cue (signal location matches the cue), compared to an invalid cue (signal location does not match the cue). The cue validity effect has often been explained with a limited capacity attentional mechanism improving the perceptual quality at the cued location. Alternatively, the cueing effect can also be explained by unlimited capacity models that assume a weighted combination of noisy responses across the two locations. We compare two weighted integration models, a linear model and a sum of weighted likelihoods model based on a Bayesian observer. While qualitatively these models are similar, quantitatively they predict different cue validity effects as the signal-to-noise ratios (SNR) increase. To test these models, 3 observers performed in a cued discrimination task of Gaussian targets with an 80% valid precue across a broad range of SNR’s. Analysis of a limited capacity attentional switching model was also included and rejected. The sum of weighted likelihoods model best described the psychophysical results, suggesting that human observers approximate a weighted combination of likelihoods, and not a weighted linear combination.
Human d’s were fit to the linear function d′ = b(Image SNR) + a. The criteria for the Sum of Weighted Likelihoods model are expressed as the log weighted likelihood ratio log(Ls/n). The criteria for the Linear model are expressed as the normalized distance from the mean of the hypothesized noise distribution for the weighted linear decision variable (yz).
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