Methoden vergleichen

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