Figure 3.

(A) The joint distribution over “states of the world” θ and “experimental outcomes” r_n as a function of the prior distribution parameters α, β (rows) and the sample size n (columns). The first row depicts the joint distribution for the reference prior parameter settings, the second row for a prior distribution centered on 0.5 with higher implied certainty, and the last row for prior distribution parameters reflecting a biased assumption about the state of the world θ. (B) Dependence of the first two central moments of the beta distribution on its parameters. In general, if both α and β increase, the uncertainty implied by the beta distribution decreases.