Confronta i metodi

	Metropolis-Hastings per il confronto di modelli	Campionamento di Gibbs per il Confronto di Modelli
Campo	Bayesiano	Bayesiano
Famiglia	Bayesian methods	Bayesian methods
Anno di origine	1970 (extended 1995)	1995
Ideatore	W. K. Hastings (1970); extended for model comparison by P. J. Green (1995)	Carlin and Chib
Tipo	MCMC-based model comparison	Bayesian model selection via MCMC
Fonte seminale	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.
Alias	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
Correlati	4	3
Sintesi	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.