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	時系列ベイズ階層モデル	ベイズ回帰
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1989–1997	—
提唱者	West & Harrison (dynamic models); Gelman et al. (hierarchical Bayesian framework)	—
種類	Bayesian hierarchical model for time series	Bayesian linear model
原典	West, M. & Harrison, J. (1997). Bayesian Forecasting and Dynamic Models (2nd ed.). Springer. ISBN: 978-0387947259	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
別名	TSBHM, Bayesian hierarchical time series, hierarchical dynamic Bayesian model, multilevel Bayesian time series	bayesian linear regression, probabilistic regression, bayesian regresyon
関連	6	2
概要	A time series Bayesian hierarchical model combines the hierarchical (multilevel) Bayesian framework with a dynamic state-space structure to analyse temporal data collected on multiple units or groups. Priors encode beliefs about both within-unit dynamics and cross-unit variation, and the posterior is obtained via MCMC or sequential Monte Carlo, yielding full probabilistic forecasts with calibrated uncertainty.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.