Paper:
The Brain Uses Reliability of Stimulus Information when Making Perceptual Decisions
In simple perceptual decisions the brain has to identify a stimulus based on noisy sensory samples from the stimulus. Basic statistical considerations state that the reliability of the stimulus information, i.e., the amount of noise in the samples, should be taken into account when the decision is made. However, for perceptual decision making experiments it has been questioned whether the brain indeed uses the reliability for making decisions when confronted with unpredictable changes in stimulus reliability. We here show that even the basic drift diffusion model, which has frequently been used to explain experimental findings in perceptual decision making, implicitly relies on estimates of stimulus reliability. We then show that only those variants of the drift diffusion model which allow stimulusspecific reliabilities are consistent with neurophysiological findings. Our analysis suggests that the brain estimates the reliability of the stimulus on a short time scale of at most a few hundred milliseconds.

Review:
The authors show the drift diffusion model (DDM) of perceptual decision making implicitly assumes that the brain makes online estimates of stimulus reliability. By formulating a probabilistic equivalent, the authors compare versions of the DDM with and without trial-dependent reliability estimates, and show that behavioral and neurophysiological data are consistent with DDMs that do estimate reliability.In the introduction, it seems to me that the authors conflate two points: first, that the brain uses estimates of stimulus reliability when making decision; and second, that stimulus reliability affects tuning curves multiplicatively. Although the two are related in the PPC framework cited by the authors, in general the former relates to decoding, the latter to encoding. Also in the introduction, the authors propose that "the multiplicative effect on tuning curves results from adaptation of internal estimates of measurement reliability". However, throughout the paper there is no further explanation of what they mean by adaptation, and the above idea is not further elaborated, except perhaps in the last paragraph of discussion. Section 2, first paragraph: since the authors highlighted multiplicative effects of tuning curves, it is worth pointing out that the exact definition of coherence actually matters and could determine how reliability (or coherence) changes tuning curves. For instance, in the experiments cited, coherent dots move in a fixed direction and the other dots directions are sampled from the uniform distribution; an alternative choice could be to draw all dots from eg a circular Gaussian peaked at the chosen direction, and vary reliability by changing the width of the distribution. Importantly, this is in fact the generative model of the stimulus considered in eq. 3. This latter choice would lead to changes in tuning width, not just multiplicative scaling, when reliability changes. Fig 1, the use of rose histograms is misleading: the area of the circular sector is quadratic (not linear) in the radius (i.e the count). Eq 2 requires some more detail about \rho, the "population" firing rate. To be optimal, the "population rate" should be obtained by weighting each neuron's response by a weight that depends on its tuning curve derivative and on the covariance matrix of the population (see eg Ma et al 2006).Eq 4 is not precise; It should be x_t conditioned on the true stimulus being left (or right). Similarly, in eq. 5, the l.h.s. should be similarly conditioned. Eq 6: the term \delta y defined in this equation is Gaussian distributed only if conditioned on a particular (left or right) true value of the stimulus. Otherwise, across different true stimuli, it is a mixture of gaussians.