Dissecting Bayes: Using influence measures to test normative use of probability density information derived from a sample
Fig 3
A. A hypothetical experiment. A sample is drawn from a bivariate Gaussian pdf marked by a heat map and contours of equal probability density. The blue bar represents the decision maker’s estimate of the probability that an additional point drawn from the same underlying pdf will be in the region above the green line T. The precise task is not important. B. Measuring influence. The (vertical) influence of one point in the sample can in principle be measured by perturbing it slightly in the vertical direction and measuring the effect of the perturbation on the decision maker’s estimate P[T]. The ratio of the change in estimate to the magnitude of perturbation is the influence of the point on the setting. We do not use this method (single point perturbation) but instead use a method based on linear regression. See Methods. The influence measures allow us to characterize how each point in the sample affects decision-making.