قارن الطرق

	آليات البيانات المفقودة: MCAR، MAR، و MNAR	خوارزمية التوقع-تعظيم (EM)
المجال	الإحصاء	الإحصاء
العائلة	Process / pipeline	Machine learning
سنة النشأة	1976	1977
صاحب الطريقة	Donald Rubin	Dempster, Laird & Rubin
النوع	Diagnostic / classification framework	Iterative optimization algorithm
المصدر التأسيسي	Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3), 581–592.	Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B, 39(1), 1–38.
الأسماء البديلة	Missing Data Typology, Rubin's Missing Data Framework, Missingness Mechanisms, Kayıp Veri Mekanizmaları	EM, Expectation-Maximization, Maximum Likelihood via Incomplete Data, BM Algoritması
ذات صلة	3	2
الملخص	Missing data mechanisms, introduced by Donald Rubin in 1976, provide a formal taxonomy for classifying why observations are absent from a dataset. The three categories — Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR) — describe the relationship between the probability of missingness and the observed or unobserved values. Identifying the correct mechanism is essential because it determines which analytical strategies preserve valid and unbiased inference.	The Expectation-Maximization (EM) algorithm is an iterative optimization procedure for finding maximum likelihood or maximum a posteriori estimates of parameters in statistical models with latent variables or missing data. Introduced by Dempster, Laird, and Rubin in their landmark 1977 paper, EM alternates between computing the expected complete-data log-likelihood (E-step) and maximizing it with respect to the parameters (M-step), guaranteeing monotone non-decreasing likelihood at each iteration.