I'm trying to calculate $$ \int \frac{\rho(x)}{\rho(f(x))} \nu(f(x)) dx, $$ where $\rho,\nu$ are regular probability densities (or corresponding marginal densities), $f$ is non-invertible, and cannot be extended as such (while matching the dimension of $x$). How can I proceed?
2026-04-18 13:24:18.1776518658
Integrating a transformed density without being able to do change-of-variable?
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