- Variable selection and estimation in causal inference using Bayesian spike and slab priors

Plots of N { ( 0 , 0 ) T ,   I 2 } I ( Δ MSE j ≥ 0 ) (which appears in the prior for ( β j ,   γ j ) T under BSSCE) as a function of βj and ηj. The density of the prior is given by the color: white indicates a prior density of zero, and blue colors indicate a smaller prior density than red colors. The top left plot has σ Y | A , X − j 2 = 10 ,   σ X j | X − j , A 2 = 0.25 ,   σ A | X − j 2 = 10 , and σ X j | X − j 2 = 1 . The other three plots double one of these parameters while leaving the other parameters unchanged: the top right plot has σ Y | A , X − j 2 = 20 , the bottom left plot has σ A | X − j 2 = 20 , and the bottom right plot has σ X j | X − j , A 2 = 0.5 . For this figure, n = 250, σ 2 = 1 , and τ j 2 = 1 .