C13. Full conditionals and Gibbs

Topic: Markov chains, Gibbs sampling, and Metropolis–Hastings · more questions on this topic
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What is a full conditional distribution, and how does a Gibbs sampler use full conditionals?

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Definitions/notation. For a target \pi(\theta_1,\ldots,\theta_p), a full conditional \pi(\theta_j\mid\theta_{-j}) conditions on all other coordinates, denoted \theta_{-j}. A systematic Gibbs sweep draws each coordinate from its exact full conditional using the latest available values of the others; each such coordinate update is accepted automatically.