= Solution
In a <normal linear model>, attach a <continuous spike-and-slab prior> to each <regression coefficient>. With suitably scaled predictors, introduce indicators $\gamma_j\sim\operatorname{Bernoulli}(\pi)$ and set
$$
\beta_j\mid\gamma_j=0\sim N(0,s_{0j}^2),\qquad
\beta_j\mid\gamma_j=1\sim N(0,s_{1j}^2),\quad s_{0j}\ll s_{1j}.
$$
The narrow component describes practically negligible effects; the wide component permits substantial ones. Fit the joint <Bayesian posterior> of coefficients, indicators and any unknown residual variance. <Bayesian model averaging> gives shrinkage toward zero for poorly supported effects, while $\mathbb P(\gamma_j=1\mid\mathcal D)$ quantifies wide-component support. A shared <Beta distribution> prior on $\pi$ can represent uncertainty about how many effects are substantial.
\b[Select on scientifically meaningful effect size], for example a high $\mathbb P(|\beta_j|>\delta_j\mid\mathcal D)$ for a prechosen threshold in meaningful predictor units. Membership in the wide component alone does not imply a large realized effect: its <normal distribution> still permits values near zero. Correlated predictors also require interpretation of the joint <Bayesian posterior>, rather than treating each coefficient as an isolated test.
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