Bayesian analysis can estimate individual set formation

The human Gabor patch 7-stage task also provides evidence to support the view that Bayesian analysis can check whether each individual participant has formed an attentional set. Using the human behavioural reward Bayesian model, I found that, for 17 out of 19 participants’ data, the posterior probability of responding to stimuli from the previously reward relevant, but currently irrelevant, dimension becomes relatively high (i.e., >0.6) at the first several trials in the ED (Figure 9.4, left). Based on the participants’ oral responses, these 17 participants did use stimuli from the previously relevant dimension to make their choices at the beginning of the ED stage, indicating that these participants had formed an attentional set before starting the ED stage. Furthermore, for the remaining two participants’ data where the posterior probability of each stimulus from the previously relevant dimension is relatively low (all less than 0.4) at the first several trials in the ED, these participants’ oral responses are not consistent with making choices based on the previously relevant dimension at the beginning of the ED stage. The perfect match between the Bayesian estimate and the participant’s oral response, again, suggests that the human behavioural reward Bayesian model can be used to analyse whether each individual participant has formed an attentional set or not from the first several trials in the ED stage.

In comparison, for those 17 participants who made choices based on the irrelevant dimension stimuli at the beginning of the ED stage, the human behavioural simple Bayesian model (incorrectly) estimated that 13 out of 17 participants did not use the stimuli in the irrelevant dimension to make their choices (Figure 9.4, right). For those two participants who did not make their choices based on irrelevant dimension stimuli at the beginning of the ED stage, the human behavioural simple Bayesian model correctly estimated that the two participants used the stimuli in the irrelevant dimension to make their choices. As explained in Section 7.3, if a participant has formed an attentional set, the participant should use stimuli from the previously relevant but currently irrelevant dimension to make their choices at the first several trials in the ED stage., This result suggests, therefore, that the human behavioural

simple Bayesian model, which did not consider the effect of choice result, cannot reliably estimate whether or not each participant has formed an attentional set.

Figure 9.4: posterior probability of each hypothesis over ED trials by the two Bayesian models for one representative participant who made choices based on the previously relevant dimension’s stimuli at the beginning (first three trials) of the ED stage, with correct estimate (arrow in the left figure) of set-formation from the human behavioural reward Bayesian model, and the incorrect estimate (arrow in the right figure) from the human behavioural simple Bayesian model. Solid and dotted black curves are for the two stimuli from the previously relevant but currently irrelevant dimension; Solid blue curve: rewarded stimulus; Dotted blue curve: non-rewarded stimulus from currently relevant dimension; Solid and dotted red curves: frequency alternation and orientation alternation hypotheses; Solid and dotted magenta and green curves: four orientation-frequency combinations.

9.4 Bayesian learning criterion based on the latent probabilistic model performs better

Since we may assume that we know which response patterns (or rules) participants used for each learning trial, based on their oral report for each trial, we can evaluate how good the Bayesian learning criterion is, based on both the human behavioural simple Bayesian model and the human latent probabilistic model, and also how good the 6-in-a-row criterion is, just as in the human blob-stick 7-stage task.

From participants’ oral reporting, I found that 18 out of 19 participants started to use the correct rules from one of the last six trials in each learning stage. This suggests that the 6-in- a-row criterion is well aligned with the point at which participants learned the correct rules. The remaining participant made the last six correct choices in the REV1 and REV2 stages by remembering specific exemplars.

Based on the human behavioural simple Bayesian model, I found that the Bayesian learning criterion was not satisfied by the last trial of the three reversal stages for most participants

and by the last trial of the ED stage for about half of the participants (Figure 9.5). This suggests that the human behavioural simple Bayesian model is not good enough from the perspective of learning criterion.

In comparison, with the human latent probabilistic model, the Bayesian learning criterion is satisfied by the last trial of all stages for all participants (Figure 9.6). Detailed analysis also shows that the criterion is satisfied within the last 3 trials for ID, ED, and reversal stages. This suggests that the Bayesian learning criterion based on the human latent probabilistic model is consistent with the 6-in-a-row criterion and consistent with participants’ oral reporting of the point at which they learn the correct rules for all learning stages except the 2 false positive learning stages.

Figure 9.5: histogram of probability of ‘correct’-associated hypotheses at the last trial for each learning stage over 19 participants with the human behavioural simple Bayesian model. The Bayesian learning criterion based on the simple Bayesian model is not working well, at least in the three reversal stages and the ED stage.

Figure 9.6: histogram of probability of ‘correct’-associated hypotheses at the last trial for each learning stage over 19 participants with the human latent probabilistic model. The Bayesian learning criterion based on the human latent probabilistic model is consistent with the 6-in-a-row criterion.