We assume b^j is normally distributed about bj, with variance-covariance matrix Vj (defined below), and that bj follows eq. 1: (2)p(b^j | bj, Vj)=NR(b^j;bj, Vj) (3)p(bj | π, U)=∑k=1K∑l=1Lπk,lNR(bj;0, ωlUk), where NR( ⋅ ;μ, Σ) denotes the multivariate normal (MVN) density in R dimensions with mean μ and variance-covariance matrix Σ. Here, 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 determine the relative frequency of each covariance-scale combination. The scaling coefficients ωl take values on a fixed dense grid that spans “very small” to “very large” so as to capture the full range of effects that could occur.
