MALA: Removing Discretization Bias with Accept-Reject

Unadjusted Langevin algorithm discretizes continuous physics into finite steps. This approximation introduces a systematic bias, causing the sampled cloud to drift away from the true distribution.

Look at the orange particles moving with unadjusted Langevin. When step size eta is large, the particles scatter too broadly, wider than the true distribution, drawn in blue on the walls.

The rest of the narration is in the book's Companion.