Risk-sensitivity in Bayesian sensorimotor integration

Abstract

Information processing in the nervous system during sensorimotor tasks with inherent uncertainty has been shown to be consistent with Bayesian integration. Bayes optimal decision-makers are, however, risk-neutral in the sense that they weigh all possibilities based on prior expectation and sensory evidence when they choose the action with highest expected value. In contrast, risk-sensitive decision-makers are sensitive to model uncertainty and bias their decision-making processes when they do inference over unobserved variables. In particular, they allow deviations from their probabilistic model in cases where this model makes imprecise predictions. Here we test for risk-sensitivity in a sensorimotor integration task where subjects exhibit Bayesian information integration when they infer the position of a target from noisy sensory feedback. When introducing a cost associated with subjects' response, we found that subjects exhibited a characteristic bias towards low cost responses when their uncertainty was high. This result is in accordance with risk-sensitive decision-making processes that allow for deviations from Bayes optimal decision-making in the face of uncertainty. Our results suggest that both Bayesian integration and risk-sensitivity are important factors to understand sensorimotor integration in a quantitative fashion.

Figure 1. Experimental setup.

Subjects move from a start bar to a goal bar and have to hit a target halfway in the reaching movement. In each trial the lateral position of the target was randomly drawn from a Gaussian distribution. The reliability of the visual feedback of the target position was manipulated, such that each trial belonged to one of three feedback conditions: , or . Furthermore, we imposed three different force functions (, and ) in the force area, where the force depended on the presumed target position as they indicated it by their forward movement. Screenshots of the actual display can be found in Text S1.

Figure 2. Lateral deviation from target as a function of target position in a risk-sensitive model (top row) and in a typical subject (bottom row).

The three columns correspond to the three levels of uncertainty of the target feedback (, and ). Each panel compares the three different force conditions (red), (green) and (blue). The model predicts that higher levels of uncertainty are associated with higher slopes and that higher forces are associated with shifts in the intercept that are proportional to the uncertainty.

Figure 3. Slopes (top row) and intercepts (bottom row) of linear regression for all subjects.

Linear regression was performed as in Figure 2. The three columns correspond to the three different force conditions , and . The three different feedback conditions , and are displayed within each panel. It can be seen that the slope increases with increasing uncertainty. The intercepts are modulated by both uncertainty and force condition.