Vertaile menetelmiä

	Bayesiläinen mallikeskiarvoistus	Bayesiläinen hierarkkinen malli
Tieteenala	Bayesilainen tilastotiede	Bayesilainen tilastotiede
Menetelmäperhe	Bayesian methods	Bayesian methods
Syntyvuosi	1999	2006
Kehittäjä	Hoeting, Madigan, Raftery & Volinsky	Gelman & Hill (2006); Bayesian multilevel tradition
Tyyppi	Bayesian model averaging	hierarchical probabilistic model
Alkuperäislähde	Hoeting, J. A., Madigan, D., Raftery, A. E. & Volinsky, C. T. (1999). Bayesian Model Averaging: A Tutorial. Statistical Science, 14(4), 382–401.	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
Rinnakkaisnimet	BMA, Bayesian model combination, Bayesian Model Ortalaması (BMA)	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model
Liittyvät	5	4
Tiivistelmä	Bayesian Model Averaging (BMA), formalised as a tutorial by Hoeting, Madigan, Raftery and Volinsky in 1999, addresses model uncertainty by averaging over all plausible model specifications rather than selecting a single best model. Each candidate model receives a posterior probability that reflects how well it fits the data given a prior, and predictions or coefficient estimates are formed as weighted averages across the entire model space. This approach reduces the bias and overconfidence that arise when a single selected model is treated as the true one.	Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations.