A novel measure-theoretic framework

$$\pi^{\dagger}_\Lambda(\lambda) := \pi_\Lambda(\lambda)\frac{\pi_{\mathcal{D}}(Q(\lambda))}{\pi^{Q}_{\mathcal{D}}(Q(\lambda))} $$


We use Bayes’ Rule along contours.

The prior \(\pi_\Lambda(\lambda)\) plays a role only in these directions.

It differentiates among sets that belong to the same contour $\sigma$-algebra.