Are we really Bayesian? Probabilistic inference shows sub-optimal knowledge transfer
Fig 2
visualisation of quantitative performance measures including slope (A), transfer score (B) and optimality index (C). A Slope in the coin task was calculated by linearly regressing participants’ estimated coin position over the centre of splashes. The values of slope vary between 0 and 1. A higher slope means a higher weighting on likelihood, with 1 meaning total reliance on likelihood and 0 meaning no reliance on likelihood. B A transfer score was calculated by normalising a measured slope change by a predicted slope change based on subject-specific prior and likelihood estimations. A transfer score of 1 means transferring following an optimal Bayesian observer model. A transfer score equals or smaller than 0 means no transfer. C optimality index. For each trial given the true posterior, we can compute the probability that a coin would be within the net from the chosen position (Xnet), i.e., the success probability. We defined the optimality index for a trial as the success probability normalised by the maximal success probability. In the figure, this equals to the blue area divided by the yellow area. Note that here for visualisation purpose only, there is no overlap between the two areas, which may not and does not have to be the case in real measurement.