Linganisha mbinu

	Metropolis-Hastings kwa ajili ya Kulinganisha Mifumo	Sampo ya Gibbs kwa Ulinganishaji wa Modeli
Nyanja	Mbinu za Bayes	Mbinu za Bayes
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1970 (extended 1995)	1995
Mwanzilishi	W. K. Hastings (1970); extended for model comparison by P. J. Green (1995)	Carlin and Chib
Aina	MCMC-based model comparison	Bayesian model selection via MCMC
Chanzo asilia	Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97-109.	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.
Majina mbadala	MH model comparison, Metropolis-Hastings Bayes factor estimation, reversible-jump Metropolis-Hastings, MH model selection	Gibbs-based model selection, MCMC model comparison via Gibbs, Bayesian model comparison with Gibbs sampling, Gibbs sampler model selection
Zinazohusiana	4	3
Muhtasari	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.	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.