In brief, let b denote the vector of true effects for a single unit across R conditions. We capture correlations and sharing of effects among conditions using a mixture model, (1)p(b;π, U)= ∑k=1K∑l=1Lπk,lNR(b;0, ωlUk), where NR(∙ ;μ, Σ) denotes the multivariate normal density in R dimensions with mean μ and variance-covariance matrix Σ; each Uk is a covariance matrix that captures a pattern of effects; each ωl is a scaling coefficient that corresponds to a different effect size; and the mixture proportions πk,l etermine the relative frequency of each covariance-scale combination. The scaling coefficients ωl take values on a fixed dense grid that spans from “very small” to “very large”, capturing the full range of possible effects.
