Detailed balance of a random-scan Gibbs sampler
= Detailed balance of a random-scan Gibbs sampler
A single-coordinate <Gibbs sampler> update preserves the remaining coordinates and independently redraws the selected coordinate from its <full conditional distribution>. The joint measure of old and new states factors into a marginal and two identical conditional factors, making it symmetric. A fixed-probability mixture of such kernels therefore satisfies <detailed balance>.