The effect of suboptimal inference can even be seen in a simple discrimination task. For instance, consider the problem of discriminating between two Gabor patches oriented at either +5° or –5°, and containing a small amount of additive noise, as shown in Figure 3A, first column. Here, the additive noise is meant to model internal noise, such as noise in the photoreceptors. Figure 3A shows two linear discriminators, whose responses are proportional to the dot product of each image with the linear filter (Figure 3A,

second column) associated with each discriminator. The linear filter for the top unit in the third column of this figure was optimized to maximize its ability to discriminate between the two orientations of the Gabor patches. The linear filter of the other unit (bottom one in the third column of Figure 3A) was optimized Selleckchem Vemurafenib for Gabor patches with the same Gaussian envelope but half the wavelength. The unit at the bottom thus performs suboptimal inference; it assumes the wrong statistical

structure of the task, just like the politician did with dˆav in the polling example. The graph in the right panel of Figure 3A shows the responses of the two units to a sequence of images with the same orientation but different Dorsomorphin mw noise. The responses have been normalized to ensure that the estimates are unbiased for both units. Given this normalization, greater response variability implies greater stimulus uncertainty and, therefore, greater behavioral variability. This simulation reveals two important facts. First, suboptimal inference has an amplifying effect on the tuclazepam internal noise. Indeed,

if we set the noise to zero, the variability in both units would be zero. Second, most of the behavioral variability can be due to suboptimal inference. This can be seen by comparing the variability of the two units. For the top unit, all the variability is due to internal noise. In the bottom unit, all the extra variability is due to suboptimal inference, which in this case is 54 times the variability from the noise alone; more than 98% of the total variability. The fraction of variability due to suboptimal inference depends, of course, on the severity of the approximation, i.e., on the discrepancy between the optimal frequency and the one assumed by the suboptimal filter. As shown in Figure 3B, the information loss grows quickly as the difference between the filter and image wavelengths grows. The point of this example is to show that in psychophysics experiments, much of the behavioral variability might be due to suboptimal inference and not noise.