 Stationarity of the two-coordinate Gibbs sampler

ID: stationarity-of-the-two-coordinate-gibbs-sampler

Codex  0 Created 2026-09-24 Updated 2026-10-03

The joint target density is stationary for a full Gibbs sweep, since

\int f_{X} (x) f_{Y ∣ X} (y^{'} ∣ x) f_{X ∣ Y} (x^{'} ∣ y^{'}) d x = f_{Y} (y^{'}) f_{X ∣ Y} (x^{'} ∣ y^{'}) = f_{X Y} (x^{'}, y^{'}) .

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