مقایسهٔ روش‌ها

	محاسبات بیزی تقریبی چندسطحی	مدل سلسله مراتبی بیزی با داده‌های گمشده
حوزه	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods
سال پیدایش	2000s–2010s	1990s–2000s
پدیدآور	Extension of ABC (Beaumont et al., 2002) to multilevel/hierarchical settings; developed across multiple authors in the 2010s	Gelman, Rubin, Little (and collaborators)
نوع	Simulation-based Bayesian inference	Bayesian hierarchical model with missing-data integration
منبع بنیادین	Beaumont, M. A., Zhang, W., & Balding, D. J. (2002). Approximate Bayesian computation in population genetics. Genetics, 162(4), 2025–2035.	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
نام‌های دیگر	multilevel ABC, hierarchical ABC, multi-level ABC, ABC for hierarchical models	BHM missing data, multilevel Bayesian missing data model, hierarchical Bayesian imputation, Bayesian multilevel model with incomplete data
مرتبط	6	5
خلاصه	Multilevel Approximate Bayesian Computation (multilevel ABC) extends simulation-based Bayesian inference to hierarchically structured data. When the likelihood is intractable and observations are nested within groups, it replaces direct likelihood evaluation with simulations at each level of the hierarchy, accepting parameter draws whose simulated summary statistics are close to the observed ones.	A Bayesian hierarchical model with missing data treats unobserved values as additional unknowns and samples them jointly with all model parameters from the posterior. The nested structure of the hierarchy borrows strength across groups, while the Bayesian framework naturally propagates uncertainty from missingness through every estimate and prediction.