Neural substrates of cognitive biases during probabilistic inference

Decision making often requires simultaneously learning about and combining evidence from various sources of information. However, when making inferences from these sources, humans show systematic biases that are often attributed to heuristics or limitations in cognitive processes. Here we use a combination of experimental and modelling approaches to reveal neural substrates of probabilistic inference and corresponding biases. We find systematic deviations from normative accounts of inference when alternative options are not equally rewarding; subjects' choice behaviour is biased towards the more rewarding option, whereas their inferences about individual cues show the opposite bias. Moreover, inference bias about combinations of cues depends on the number of cues. Using a biophysically plausible model, we link these biases to synaptic plasticity mechanisms modulated by reward expectation and attention. We demonstrate that inference relies on direct estimation of posteriors, not on combination of likelihoods and prior. Our work reveals novel mechanisms underlying cognitive biases and contributions of interactions between reward-dependent learning, decision making and attention to high-level reasoning.

for 2-shape estimates (µ 2-shape ) versus the biases for 1-shape estimates (µ 1-shape ) for individual subjects. The histogram plots the frequency of subjects with a given bias for 1-shape estimates, and the solid line is the median for each set of subjects. (b) The same as in a, but for bias for 4shape estimates (µ 4-shape ) versus the bias for 2-shape estimates (µ 2-shape ). (c) The same as in a, but for the bias for 4-shape estimates (µ 4-shape ) versus the bias during the choice session (µ choice ) (d-f) Comparison of the stochasticity in choice and estimations, measured by σ from the ePF or PF for individual subjects. The lower and higher dashed lines show the lines with slope 1 and 2, respectively. The inset shows the histogram of σ values for 1-shape to 4-shape estimates, and the solid lines show the median for a given distribution.  data. Moreover, due to the averaging mechanism, this model predicts that as the number of shapes used for estimation increases, the stochasticity in estimation should significantly increase (by a factor of 2 from 1-shape to 2-shape estimates and from 2-shape to 4-shape estimates). Trial number median SWOE for blue S1 S2 S3 S4

Supplementary Note 1 Control experiment with equal prior
In order to show that observed biases were due to the unequal prior probability of reward for the two choice alternatives, we also ran a control experiment in which 12 subjects performed the task with equal prior (p(B) = 0.5).
Firstly, we did not observe any significant biases during the choice and estimation sessions. More specifically, there was no significant biases in choice toward either option (two-sided signtest P = 0.39, N = 12), resulting in an unbiased average PF across subjects ( Supplementary Fig. 2a). Similarly, there were no significant biases in estimation (two-sided signtest P = 1.0, 1.0, and 0.15 for 1-shape, 2-shape, and 4-shape estimates, respectively, N = 12). This is reflected in the distribution of µ values for individual subjects ( Supplementary Fig. 3a-c) and in the average ePF over all subjects (Supplementary Fig. 2c).
Secondly, despite lack of any biases in choice or estimations, we looked for progression of biases as observed in the main experiment. We found that the biases for 1shape estimates were not different from the biases for 2-shape estimates (two-sided signtest P = 1.0, N = 12). Moreover, the biases for 2-shape estimates were not different from the biases for 4-shape estimates (two-sided signtest P = 0.39, N = 12), and the biases in 4-shape estimates were similar to the biases in choice (two-sided signtest P = 1.0, N = 12).
Thirdly, we examined 1-shape estimates corresponding to the extent that individual shapes predicted the reward on a given option ( Supplementary Fig. 2d). We found that subjects accurately predicted the posteriors for each shape and, except for S4 where there was a small underestimation (median = -0.05, two-sided signtest P = 0.04, N = 12), there was no significant difference between the estimated and actual values across subjects (two-sided signtest P = 0.23, 1.0, and 0.77 for S1, S2, and S3, respectively, N = 12). Note that this small difference is equal to half of the precision of the estimation report (estimations were reported in 10% steps). Similarly, the SWOE extracted from choice behavior ( Supplementary Fig. 2b) were proportional to the actual log posterior odds, and except for S1, where there was a small overestimation (median = 0.1; two-