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Empirical Bayes Linear Regression with Unknown Model Order
Uppsala University, Sweden.
Royal Institute of Technology.ORCID iD: 0000-0002-7599-4367
2008 (English)In: Digital signal processing (Print), ISSN 1051-2004, E-ISSN 1095-4333, Vol. 18, no 2, 236-248 p.Article in journal (Refereed) Published
Abstract [en]

We study maximum a posteriori probability model order selection for linear regression models, assuming Gaussian distributed noise and coefficient vectors. For the same data model, we also derive the minimum mean-square error coefficient vector estimate. The approaches are denoted BOSS (Bayesian order selection strategy) and BPM (Bayesian parameter estimation method), respectively. In their simplest form, both BOSS and BPM require a priori knowledge of the distribution of the coefficients. However, under the assumption that the coefficient variance profile is smooth, we derive “empirical Bayesian” versions of our algorithms which estimate the coefficient variance profile from the observations and thus require little or no information from the user. We show in numerical examples that the estimators can outperform several classical methods, including the well-known AICc and BIC for model order selection.

Place, publisher, year, edition, pages
2008. Vol. 18, no 2, 236-248 p.
Keyword [en]
Linear regression; Empirical Bayes; MMSE estimation; Parameter estimation; Order selection
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-25568DOI: 10.1016/j.dsp.2007.03.005OAI: oai:DiVA.org:liu-25568DiVA: diva2:245931
Available from: 2009-10-08 Created: 2009-10-08 Last updated: 2016-08-31

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Larsson, Erik G.

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