Mixed Models, Posterior Means and Penalized Least-Squares

• Published in: Lecture notes-monograph series Vol. 57; pp. 216 - 236
• Main Author: Maldonado, Yolanda Muñoz
• Format: Journal Article
• Language: English
• Published: Institute of Mathematical Statistics 01.01.2009
• Subjects: Bayesian networks; Coefficients; Confidence interval; Data smoothing; Estimation methods; Estimators; Kalman filters; Matrices; Maximum likelihood estimation; Modeling
• ISSN: 0749-2170

This paper reviews the connections between estimators that derive from three different modeling methodologies: Mixed-effects models, Bayesian models and Penalized Least-squares. Extension of classical results on the equivalence for smoothing spline estimators and best linear unbiased prediction and/or posterior analysis of certain Gaussian signal-plus-noise models is examined in a more general setting. These connections allow for the application of an efficient, linear time algorithm, to estimate parameters, compute random effects predictions and evaluate likelihoods in a large class of model scenarios. We also show that the methods of generalized cross-validation, restricted maximum likelihood and unbiased risk prediction can be used to estimate the variance components or adaptively select the smoothing parameters in any of the three settings.