Stationarity of the two-coordinate Gibbs sampler

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^{'}) .

 Ancestors (8)