قارن الطرق

	متروبوليس-هاستينغز لمقارنة النماذج	MCMC للمقارنة بين النماذج
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	1970 (extended 1995)	1995
صاحب الطريقة	W. K. Hastings (1970); extended for model comparison by P. J. Green (1995)	Peter J. Green (reversible-jump MCMC); Meng & Wong (bridge sampling)
النوع	MCMC-based model comparison	Bayesian computational method
المصدر التأسيسي	Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97-109.	Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82(4), 711–732.
الأسماء البديلة	MH model comparison, Metropolis-Hastings Bayes factor estimation, reversible-jump Metropolis-Hastings, MH model selection	reversible-jump MCMC, RJMCMC, marginal likelihood estimation via MCMC, Bayesian model selection via MCMC
ذات صلة	4	5
الملخص	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.	MCMC for model comparison uses Markov chain Monte Carlo algorithms to estimate the marginal likelihoods and Bayes factors needed to formally compare competing statistical models. Techniques such as reversible-jump MCMC and bridge sampling allow exploration across model spaces of different dimensionality, enabling fully Bayesian model selection and averaging.