قارن الطرق

	متروبوليس-هاستينغز متعدد المستويات	الاستدلال البايزي الهرمي
المجال	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods
سنة النشأة	1953 (core); 1990s (multilevel application)	1972 (Lindley & Smith); consolidated 1995–2013
صاحب الطريقة	Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature	Lindley & Smith; Gelman et al.
النوع	MCMC sampling algorithm	Bayesian multilevel model
المصدر التأسيسي	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955
الأسماء البديلة	hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
ذات صلة	6	6
الملخص	Multilevel Metropolis-Hastings applies the Metropolis-Hastings MCMC algorithm to hierarchical (multilevel) Bayesian models, sampling jointly from group-level parameters and hyperparameters by proposing candidate values and accepting or rejecting them via a ratio that respects the full joint posterior across all levels of the model.	Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.