Methoden vergleichen

	Gibbs-Sampling für Modellvergleich	Metropolis-Hastings zur Modellvergleich
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1995	1970 (extended 1995)
Urheber	Carlin and Chib	W. K. Hastings (1970); extended for model comparison by P. J. Green (1995)
Typ	Bayesian model selection via MCMC	MCMC-based model comparison
Wegweisende Quelle	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.
Aliasnamen	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
Verwandt	3	4
Zusammenfassung	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.