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A continuous spike-and-slab prior mixes a narrow continuous probability distribution around zero with a much wider component. It permits practical effect selection while retaining a continuous posterior density. Its narrow component is not the exact-zero mass of a point-null mixture prior. A latent component indicator aids computation; a wide-component draw can still have small magnitude, so posterior effect thresholds and component membership answer different questions.

In a normal linear model, attach a continuous spike-and-slab prior to each regression coefficient. With suitably scaled predictors, introduce indicators ${\gamma }_j\sim \mathrm{Bernoulli}(\pi )$ and setThe 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.

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.