Skip to main content
Journal cover image

Models of random sparse eigenmatrices and Bayesian analysis of multivariate structure

Publication ,  Conference
Cron, A; West, M
Published in: Abel Symposia
January 1, 2016

We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for defining distributions on sparsity structure of random eigenmatrices. We explore theoretical aspects and implications for conditional independence structures arising in multivariate Gaussian models, and discuss connections with sparse PCA, factor analysis and Gaussian graphical models. Methodology includes model-based exploratory data analysis and Bayesian analysis via reversible jump Markov chain Monte Carlo. A simulation study examines the ability to identify sparse multivariate structures compared to the benchmark graphical modelling approach. Extensions to multivariate normal mixture models with additional measurement errors move into the framework of latent structure analysis of broad practical interest. We explore the implications and utility of the new models with summaries of a detailed applied study of a 20-dimensional breast cancer genomics data set.

Duke Scholars

Altmetric Attention Stats
Dimensions Citation Stats

Published In

Abel Symposia

DOI

EISSN

2197-8549

ISSN

2193-2808

ISBN

9783319270975

Publication Date

January 1, 2016

Volume

11

Start / End Page

125 / 153
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Cron, A., & West, M. (2016). Models of random sparse eigenmatrices and Bayesian analysis of multivariate structure. In Abel Symposia (Vol. 11, pp. 125–153). https://doi.org/10.1007/978-3-319-27099-9_7
Cron, A., and M. West. “Models of random sparse eigenmatrices and Bayesian analysis of multivariate structure.” In Abel Symposia, 11:125–53, 2016. https://doi.org/10.1007/978-3-319-27099-9_7.
Cron, A., and M. West. “Models of random sparse eigenmatrices and Bayesian analysis of multivariate structure.” Abel Symposia, vol. 11, 2016, pp. 125–53. Scopus, doi:10.1007/978-3-319-27099-9_7.
Journal cover image

Published In

Abel Symposia

DOI

EISSN

2197-8549

ISSN

2193-2808

ISBN

9783319270975

Publication Date

January 1, 2016

Volume

11

Start / End Page

125 / 153