EJECUCIÓN FORZOSA.

human task, it is interesting to explore whether the human reward Bayesian model performs well on the archival rat data used in the previous chapter (see Section 2.1). The evaluation of the human behavioural reward Bayesian model requires that we know what response patterns have been actually used by rats. However, we can never know for certain the rats’ internal decision-making processes in any given learning stage. Even so, we may assume a rat used the perseveration response pattern when the rat directly chose bowls on the same side (either left side or right side) over six or more trials in a row, without going to check the other bowl. Note that in this case, the rat cannot make six correct choices in a row because the configurations of bowls were designed such that the reward-relevant stimulus would not appear on the same side for more than three trials in a row. Similarly, the rat probably won’t make choice based on other perceptual response patterns. In this case, we may evaluate whether a Bayesian model can correctly estimate that the rat is actually using the perseveration response pattern to choose bowls. From all the 47 control rats, I observed that there are 28 stages where the rats chose bowls on the same side over six or more consecutive trials. For these 28 stages, the rat behavioural Bayesian model developed for the rat task (aka ‘rat model’) correctly estimated that the rat used the perseveration response pattern in all the 28 stages, while the human behavioural reward Bayesian model (aka ‘human model’) found the perseveration response pattern was used in only 11 stages (Table 7.2). Each Bayesian model estimated that a rat used the perseveration response pattern when the posterior probability of the corresponding hypothesis is larger than 0.6. A Chi-square test shows that the rat model performs significantly better than the human model in correctly estimating the perseveration hypothesis, Chi-square(1) = 24.4, p<0.001. Figure 7.12 shows an example where the rat model found that the rat used the perseveration response pattern (red dotted curve) while the human model did not, based on the criterion that the Bayesian estimate of the hypothesis is larger than 0.6. A similar result was obtained when the parameter in the human model was changed, precisely by varying the parameter in the feedback effect function (Equations 6.4 – 6.7). The results suggest that although the human model can accurately estimate the response patterns used by human participants in the human task it does not work well on the rat task. This is because the human model estimated that the rat would be more likely to use certain other response pattern(s) than the perseveration response pattern once the rat made a wrong choice, whereas the rat made choices on the same side even after making multiple wrong choices.

Table 7.2: estimate of perseveration response pattern (based on the threshold 0.6; see main text) with two Bayesian models from those stages where rats chose bowls from the same side on at least six consecutive trials.

Correct estimate Incorrect estimate Rat behavioural Bayesian model

(rat model) (expected: 19.5) 28 (100%) (expected: 8.5) 0 (0%) Human behavioural reward

Bayesian model (human model) (expected: 19.5) 11 (39.3%) (expected: 8.5) 17 (60.7%)

(a) from rat Bayesian model (b) from human Bayesian model Figure 7.12: a representative example of the Bayesian estimate of the ‘perseveration hypothesis’ (red dotted curve) with the rat model (left) and the human model (right) when the rat (‘09/143’) probably used the spatial perseveration response pattern to make its choice over eight consecutive trials in the REV3 stage. The rat model correctly estimated the hypothesis, but the human model did not. A red dashed bar above each figure indicates trials in which rats used perseveration for bowl choice.

To further compare the rat model and the human model on rat data, I also evaluated their performance in predicting whether a rat’s next trial choice is correct or not based on the current trial’s b-value, where the b-value is either from the rat model or from the human model. Specifically, an individual logistic regression was fitted to predict the next trial’s choice correctness, based on the current trial’s b-value over all seven stages’ learning trials for each individual rat, resulting in 93 individual logistic regressions for each b-value predictor. The residual of prediction for each trial was computed as the difference between predicted value (within the range 0 to 1) and the actual correctness (with ‘1’ for correct choice and ‘0’ for incorrect choice).

If the b-value from the rat model and the b-value from the human reward Bayesian model have similar prediction performance, the mean absolute residuals over all trials per participant from both predictors should be similar when predicting the actual value. A paired t-test showed that the absolute residual from the human model (m=0.350, sd=0.061) is significantly lower than that from the rat model (m=0.357, sd=0.060), t(92)=−4.58, p<0.001,

d=0.48. However, considering the very large absolute residual (0.350 vs. 0.357; the expected absolute residual from random guess is 0.500) and the very small difference (−0.007) in average absolute residual between the two models, it suggests that the rat model and the human model have similar performance in predicting the next trial’s outcome. A similar finding was obtained when the b-value is from the human latent probabilistic model, replacing the b-value from the human behavioural reward Bayesian model.