Model averaging and dimension selection for the singular value decomposition

2006/09/01 by Peter D. Hoff, Hoff, Peter D. · 2 citations
Mathematics · #62F15 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62F15 #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0609042

arxiv created 2006/09/01 · arxiv updated 2009/12/01

Abstract

Many multivariate data analysis techniques for an m× n matrix \m Y are related to the model \m Y = \m M +\m E, where \m Y is an m× n matrix of full rank and \m M is an unobserved mean matrix of rank K< (m\wedge n). Typically the rank of \m M is estimated in a heuristic way and then the least-squares estimate of \m M is obtained via the singular value decomposition of \m Y, yielding an estimate that can have a very high variance. In this paper we suggest a model-based alternative to the above approach by providing prior distributions and posterior estimation for the rank of \m M and the components of its singular value decomposition. In addition to providing more accurate inference, such an approach has the advantage of being extendable to more general data-analysis situations, such as inference in the presence of missing data and estimation in a generalized linear modeling framework.

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• Robust Rank Estimation for Noisy Matrices
• Bayesian Mixed-Effects Models for Multilevel Two-way Functional Data: Applications to EEG Experiments

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