Linganisha mbinu

	Modelu ya Bayesian Autoregressive (AR)	Muundo wa Bayesian ARIMA
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1971	1970s (ARIMA); Bayesian extension prominent from 1990s
Mwanzilishi	Arnold Zellner; foundational Bayesian time-series work by West & Harrison	Pole, West & Harrison (Bayesian treatment); Box & Jenkins (ARIMA foundation)
Aina	Bayesian time-series model	Bayesian time series model
Chanzo asilia	Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. Wiley. ISBN: 978-0471169376	Pole, A., West, M., & Harrison, J. (1994). Applied Bayesian Forecasting and Time Series Analysis. Chapman & Hall. ISBN: 978-0412416903
Majina mbadala	Bayesian autoregressive model, BAR model, Bayesian AR, Bayesian time-series autoregression	Bayesian ARIMA, BARIMA, Bayesian Box-Jenkins model, Bayesian integrated time series model
Zinazohusiana	6	6
Muhtasari	The Bayesian AR model estimates an autoregressive time-series process by combining a likelihood derived from the AR structure with prior distributions over the lag coefficients and error variance. Rather than producing single point estimates, it yields full posterior distributions, enabling principled uncertainty quantification and probabilistic forecasting.	The Bayesian ARIMA model combines the classical Box-Jenkins ARIMA framework with Bayesian inference. Instead of obtaining single point estimates for autoregressive and moving average parameters, it places prior distributions over them and uses observed data to update beliefs into a full posterior distribution, enabling coherent uncertainty quantification and probabilistic forecasting.