Linganisha mbinu

	Sampo ya Gibbs kwa Ulinganishaji wa Modeli	Metropolis-Hastings kwa ajili ya Kulinganisha Mifumo
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1995	1970 (extended 1995)
Mwanzilishi	Carlin and Chib	W. K. Hastings (1970); extended for model comparison by P. J. Green (1995)
Aina	Bayesian model selection via MCMC	MCMC-based model comparison
Chanzo asilia	Carlin, B. P. & Chib, S. (1995). Bayesian model choice via Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Series B, 57(3), 473-484.	Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97-109.
Majina mbadala	Gibbs-based model selection, MCMC model comparison via Gibbs, Bayesian model comparison with Gibbs sampling, Gibbs sampler model selection	MH model comparison, Metropolis-Hastings Bayes factor estimation, reversible-jump Metropolis-Hastings, MH model selection
Zinazohusiana	3	4
Muhtasari	Gibbs sampling for model comparison is a Bayesian MCMC approach that simultaneously samples from the space of competing models and their parameters. By augmenting the Gibbs sampler with a discrete model-index variable, posterior model probabilities and Bayes factors are estimated from the resulting Markov chain without requiring separate runs per model.	Metropolis-Hastings for model comparison uses the Metropolis-Hastings MCMC algorithm to explore both parameter and model space simultaneously, producing posterior probabilities for competing models and enabling Bayes factor estimation without requiring closed-form marginal likelihoods. The canonical extension — reversible-jump MCMC by Green (1995) — handles models of different dimensionalities within a single sampler.