Figure 5. Experiment 2. (a) The reaching task. Left: The task. Same as Experiment 1 except that a horizontal line was used as the target. Right: The endpoints for one subject. (b) The choice task. Similar to Experiment 1 but each pair of targets consisted of a rectangle on the line and a rectangle off the line. (c) Non-parametric visualization of the internal pdf for one subject. Shaded regions denote±SEM. is in the unit of the subject’s vertical standard deviation estimated from the reaching task. (d–h) Internal pdfs estimated from different models for the same subject. (i) AICc difference between the Gaussian model and the other four models summed over the 10 subjects. The unimodal models (including vG-mix) and mixture models are respectively coded in light gray and dark gray. Positive difference indicates better fit. (j) Number of subjects best fit by each U-mix model.  

In many laboratory visuo-motor decision tasks subjects compensate for their own visuo-motor error, earning close to the maximum reward possible. To do so they must combine information about the distribution of possible error with values associated with different movement outcomes. The optimal solution is a potentially difficult computation that presupposes knowledge of the probability density function (pdf) of visuo-motor error associated with each possible planned movement. It is unclear how the brain represents such pdfs or computes with them. In three experiments, we used a forced-choice method to reveal subjects’ internal representations of their spatial visuo-motor error in a speeded reaching movement. While subjects’ objective distributions were unimodal, close to Gaussian, their estimated internal pdfs were typically multimodal, better described as mixtures of a small number of distributions differing only in location and scale. Mixtures of a small number of uniform distributions outperformed other mixture distributions including mixtures of Gaussians.

Zhang H*, Daw ND, Maloney LT. (2015). Human representation of visuo-motor uncertainty as mixtures of orthogonal basis distributions. Nature Neuroscience. DOI: 10.1038/nn.4055