Bayesian transfer in a complex spatial localization task

Abstract

Prior knowledge can help observers in various situations. Adults can simultaneously learn two location priors and integrate these with sensory information to locate hidden objects. Importantly, observers weight prior and sensory (likelihood) information differently depending on their respective reliabilities, in line with principles of Bayesian inference. Yet, there is limited evidence that observers actually perform Bayesian inference, rather than a heuristic, such as forming a look-up table. To distinguish these possibilities, we ask whether previously learned priors will be immediately integrated with a new, untrained likelihood. If observers use Bayesian principles, they should immediately put less weight on the new, less reliable, likelihood (“Bayesian transfer”). In an initial experiment, observers estimated the position of a hidden target, drawn from one of two distinct distributions, using sensory and prior information. The sensory cue consisted of dots drawn from a Gaussian distribution centered on the true location with either low, medium, or high variance; the latter introduced after block three of five to test for evidence of Bayesian transfer. Observers did not weight the cue (relative to the prior) significantly less in the high compared to medium variance condition, counter to Bayesian predictions. However, when explicitly informed of the different prior variabilities, observers placed less weight on the new high variance likelihood (“Bayesian transfer”), yet, substantially diverged from ideal. Much of this divergence can be captured by a model that weights sensory information, according only to internal noise in using the cue. These results emphasize the limits of Bayesian models in complex tasks.

Bayesian decision-making under stress-preserved weighting of prior and likelihood information

“…To ensure that the groups did not a priori differ in subjective mood, salivary cortisol, and systolic or diastolic blood pressure, we compared these values across groups before the beginning of the experiment. The data showed no significant differences between the two groups (d = 0.06 Cohen's d effect size, W (29,29) = 827, p = 0.67 for positive subjective mood; d = 0.14, W (31,29) = 859, p = 0.2 for negative mood; d = − 0.116, W (31,29) = 950, p = 0.95 for baseline cortisol differences, d = 0.17, t(58) = 0.66, p = 0.51 for baseline systolic blood pressure , d = 0.33, t(58) = 1.27, p = 0.21 for baseline diastolic blood pressure; see Fig. 1).…”

“…As a manipulation check, i.e., whether the stress induction was successful, increases in salivary cortisol after the stress induction were compared between the stressed group as opposed to the control group. The data showed a significantly higher cortisol increase in the stressed group (mean changes in cortisol: M = 3.13 nmol/L, SD = 5.35, n = 29) compared to the control group (M = − 0.28 nmol/L, SD = 1.98, n = 31; d = 0.86, W (31,29) = 748, p = 0.003; see Fig. 1a), leading both groups to differ significantly in their salivary cortisol levels after the stress induction (d = 0.82, W (31,29) = 771, p = 0.01).…”

“…The data showed a significantly higher cortisol increase in the stressed group (mean changes in cortisol: M = 3.13 nmol/L, SD = 5.35, n = 29) compared to the control group (M = − 0.28 nmol/L, SD = 1.98, n = 31; d = 0.86, W (31,29) = 748, p = 0.003; see Fig. 1a), leading both groups to differ significantly in their salivary cortisol levels after the stress induction (d = 0.82, W (31,29) = 771, p = 0.01). The stressed group also had larger average changes in the systolic (M = 19.2, SD = 12 vs. M = − 3.68, SD = 6.8 mmHg, d = 2.39, t(57) = 9.15, p < 10 -12 ) and diastolic blood pressure (M = 13.7, SD = 8.4 vs. M = − 1.35, SD = 3.7 mmHg, d = 2.37, t(57) = 9.08, p < 10 -11 ; see Fig.…”

“…1). Moreover, there were no group differences in state or trait anxiety (d = − 0.04, t(58) = 0.15, p = 0.88), depressive mood (d = − 0.18, W (31,29) = 863, p = 0.736), perceived chronic stress (d = 0.28, t(56) = 1.06, p = 0.29), or social anxiety (d = − 0.02, W (31,29) = 910, p = 0.60). As a manipulation check, i.e., whether the stress induction was successful, increases in salivary cortisol after the stress induction were compared between the stressed group as opposed to the control group.…”

“…1b). This resulted in a higher average systolic and diastolic blood pressure in the stressed group after the stress manipulation compared to the control group (137/94 mmHg vs. 112/76 mmHg, d = 2.06, t(57) = 7.9, p < 10 -10 for systolic; d = 2.23, W (31,29) = 547, p < 10 -10 for diastolic blood pressure; see Fig. 1b).…”