Bias in the brain: a diffusion model analysis of prior probability and potential payoff

Abstract

In perceptual decision-making, advance knowledge biases people toward choice alternatives that are more likely to be correct and more likely to be profitable. Accumulation-to-bound models provide two possible explanations for these effects: prior knowledge about the relative attractiveness of the alternatives at hand changes either the starting point of the decision process, or the rate of evidence accumulation. Here, we used model-based functional MRI to investigate whether these effects are similar for different types of prior knowledge, and whether there is a common neural substrate underlying bias in simple perceptual choices. We used two versions of the random-dot motion paradigm in which we manipulated bias by: (1) changing the prior likelihood of occurrence for two alternatives ("prior probability") and (2) assigning a larger reward to one of two alternatives ("potential payoff"). Human subjects performed the task inside and outside a 3T MRI scanner. For each manipulation, bias was quantified by fitting the drift diffusion model to the behavioral data. Individual measurements of bias were then used in the imaging analyses to identify regions involved in biasing choice behavior. Behavioral results showed that subjects tended to make more and faster choices toward the alternative that was most probable or had the largest payoff. This effect was primarily due to a change in the starting point of the accumulation process. Imaging results showed that, at cue level, regions of the frontoparietal network are involved in changing the starting points in both manipulations, suggesting a common mechanism underlying the biasing effects of prior knowledge.

Figure 1.

Schematic representation of the drift-diffusion model. The model assumes that dichotomous decisions are based on the accumulation of noisy evidence over time that starts at the starting point and ends at a decision threshold. As the process is noisy, there is variability in the time to reach the threshold leading to variable RTs and possibly incorrect choices. Drift rate represents the average amount of evidence accumulated per time unit. Non-decision time is the time for processes other than the decision process, such as stimulus encoding and motor responses.

Figure 2.

Possible effects of bias on choice behavior. A, Effects of bias explained by the drift-diffusion model. When prior information is valid for the choice at hand, subjects will have faster and more correct choices, whereas invalid information results in slower and less correct choices compared with choices where no information is provided (neutral). These effects can be explained by changes in the starting point or the drift rate of the accumulation process. B, Expected effects of bias on RT and accuracy data for choices with valid, neutral and invalid cues. Note that bias effects for each of these parameters will result in a different pattern of RTs for incorrect choices. For example, when a valid cue shifts the starting point toward the correct bound, there is a greater distance for the accumulation process to hit the incorrect bound. In contrast, when the drift rate is biased by a valid cue, the rate toward the incorrect bound is increased, resulting in faster RTs for incorrect choices.

Figure 3.

Two versions of the random-dots motion task where choice bias was manipulated by providing information about the likelihood of the direction of the stimulus (prior probability) (A) or the value associated with the direction of the stimulus (potential payoff) (B).

Figure 4.

Effects of bias induced by prior probability and potential payoff in accuracy and RTs for correct and incorrect choices. Asterisks indicate a significant linear trend across trial-types. Error bars represent 1 SE from the mean.

Figure 5.

Effects of bias in DDM parameters. A, Bias is measured in starting point z, which is assumed to be half-way threshold when information is neutral (a/2), closer to the correct bound when valid (z + Δz), and further from the correct bound when invalid (z − Δz). Similarly, bias in the drift rate v is measured with Δv. The drift rate will increase for valid (v + Δv) but decrease for invalid (v − Δv) prior information. B, Average proportional bias effects across subjects for starting point (top) and the drift rate (bottom) for prior probability and potential payoff, in and outside the scanner environment. Results show significant effects for changes in the starting point, but not for changes in the drift rate. Error bars represent 1 SE from the mean.

Figure 6.

BOLD responses for starting point changes in the prior probability manipulation (cluster corrected, z > 2.6, p < 0.05).

Figure 7.

BOLD responses for starting point changes in the potential payoff manipulation (uncorrected, z > 2.6, with cluster extent > 20). Occ., Occipital lobe.

Figure 8.

BOLD responses for regions that were sensitive to starting point changes in both bias manipulations (conjunction, uncorrected, z > 2.3, with cluster extent >5 voxels). For visualization purposes we added a graphical representation of the relationship between changes in starting point and changes in BOLD signal for the prior probability and potential payoff manipulation. Data points are derived from individual subjects. These results suggest a common network involved in the underlying mechanism of bias in choice behavior. MTG, Middle temporal gyrus.