Bayesian methodsBayesian / computational
Gibbs Sampling
Gibbs sampling is a Markov chain Monte Carlo algorithm that approximates a high-dimensional posterior distribution by repeatedly drawing each parameter from its full conditional distribution given all other parameters and the data. Because each draw is exact from a conditional — not a proposal that may be rejected — the sampler is efficient when those conditionals are available in closed form.
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Sources
- Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721-741. DOI: 10.1109/TPAMI.1984.4767596 ↗
- Gelfand, A. E. & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(410), 398-409. DOI: 10.1080/01621459.1990.10476213 ↗
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Referenced by
Bayesian Inference with Missing DataDynamic Hamiltonian Monte CarloDynamic Metropolis-Hastings AlgorithmDynamic Monte Carlo SimulationDynamic Sequential Monte CarloGibbs Sampling for Model ComparisonGibbs Sampling with Measurement ErrorGibbs Sampling with Missing DataHierarchical Bayesian InferenceHierarchical Bootstrap SimulationHierarchical Markov Chain Monte CarloMCMC for Model ComparisonMCMC with Measurement ErrorMCMC with missing dataMetropolis-Hastings AlgorithmMultilevel Bayesian Model AveragingMultilevel Bootstrap SimulationMultilevel Gibbs SamplingMultilevel MCMCRobust Gibbs SamplingRobust Hamiltonian Monte CarloRobust Markov chain Monte CarloSequential Monte CarloSlice SamplingSpatial Gibbs SamplingSpatial MCMCSpatial Monte Carlo SimulationTime series MCMCTime series sequential Monte Carlo