8.1 · Book p. 215 · PDF p. 227
Introduction to the Proximal Sampler
Introduces the Gaussian augmentation and alternating conditional updates defining the proximal sampler.
Open this section in the canonical August 9 source ↗Section 8.1
A Gaussian augmentation creates alternating conditional distributions with the target as a marginal.
The proximal sampler augments the target with a Gaussian coupling between x and y, then alternates the two conditional laws. The x-marginal remains the original target, while the conditional structure exposes a restricted Gaussian oracle.
Why is this valid?
Before composing kernels, both conditional normalizers must be measurable, positive, and finite.
Source assumptions
- well-defined conditional samplers
Formal assumptions
- kernel measurability
- finite conditional normalizers
- joint-law marginal identity
View Lean formalization
ASTIS treats kernel measurability, normalization, Fubini/Tonelli, and marginal preservation as independent reusable roots.
No ASTIS-owned declaration is mapped yet.
Downstream consumers
- proximal sampler convergence
- structured sampling