مقایسهٔ روش‌ها

	علّیت گرنجر بیزی	مدل تصحیح خطای برداری بیزی (Bayesian VECM)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	1969 (frequentist); 1984 (Bayesian treatment)	2002–2005
پدیدآور	Clive W. J. Granger (frequentist basis, 1969); Bayesian extension by Geweke (1984) and subsequent literature	Kleibergen & Paap; Villani
نوع	Bayesian causal inference test	Bayesian multivariate time series model
منبع بنیادین	Geweke, J. (1984). Inference and causality in economic time series models. Handbook of Econometrics, 2, 1101-1144. Elsevier.	Kleibergen, F., & Paap, R. (2002). Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration. Journal of Econometrics, 111(2), 223–249.
نام‌های دیگر	Bayesian Granger test, Bayesian predictive causality, BGC, Bayesian causality in mean	Bayesian VECM, B-VECM, Bayesian cointegrated VAR, Bayesian vector error correction
مرتبط	6	5
خلاصه	Bayesian Granger causality tests whether past values of one time series carry predictive information about another, framing the hypothesis through Bayesian inference rather than frequentist p-values. It combines a vector autoregressive (VAR) structure with prior distributions over coefficients and evaluates causal claims via posterior probabilities or Bayes factors, providing a probabilistic and nuanced alternative to the classical Granger test.	The Bayesian VECM combines the classical Vector Error Correction Model — which captures both short-run dynamics and long-run cointegrating relationships among non-stationary multivariate time series — with Bayesian prior distributions over the cointegrating rank and coefficient matrices. This allows principled uncertainty quantification, incorporation of economic theory as priors, and coherent inference even in small samples.