قارن الطرق

	الاستدلال الإحصائي البايزي	النمذجة متعددة المستويات
المجال	إحصاء البحث	إحصاء البحث
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1763	1992
صاحب الطريقة	Thomas Bayes	Anthony Bryk and Stephen Raudenbush
النوع	Method	Method
المصدر التأسيسي	Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society, 53, 370–418.	Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE Publications.
الأسماء البديلة	Bayes theorem, Bayesian inference, posterior probability	HLM, mixed-effects models, random effects models, MLM
ذات صلة	3	3
الملخص	Bayesian inference is a statistical framework using Bayes' theorem to update beliefs about parameters or hypotheses as data accumulate. Published posthumously in 1763, Thomas Bayes' work lay dormant until the 20th century, when computational advances (Gibbs sampling, Markov Chain Monte Carlo) made Bayesian methods practical. Unlike frequentist inference (which treats parameters as fixed unknowns), Bayesian analysis treats parameters as random variables with probability distributions, enabling direct probability statements about parameters, incorporation of prior knowledge, and sequential updating. Essential in precision medicine, adaptive trials, complex hierarchical models, and any context where prior information enriches inference.	Multilevel modeling (also called hierarchical linear modeling, mixed-effects modeling) is a statistical framework for analyzing data organized in nested or clustered structures—students within schools, patients within hospitals, repeated measures within individuals. Developed by Bryk and Raudenbush (1992), it accounts for dependency among observations and partitions variance into levels (within-cluster and between-cluster), enabling valid inference and revealing context effects. Essential in education, medicine, organizational research, and any field where data have natural hierarchies.