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Leverage in Bayesian Regression
Author(s) -
Steece Bert M.
Publication year - 1989
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710310707
Subject(s) - leverage (statistics) , bayesian probability , statistics , mathematics , regression , econometrics , regression analysis , monotonic function , bayesian linear regression , bayesian inference , mathematical analysis
Using the concept of an extended data set (Zellner, 1986), we derived the projection or hat matrix for Bayesian regression analysis. The hat matrix shows how much influence or leverage the observed responses and the prior means have on each of the posterior fitted values. The amount of leverage associated with the observed data is shown to be a monotonically decreasing function of the ratio of the process variance to the prior variance. Additional properties of the Bayesian hat matrix are discussed. Two illustrative examples are presented.