title: Empirical Bayes method for reducing false discovery rates of correlation matrices with block diagonal structure.
abstract: BACKGROUND
  Correlation matrices are important in inferring relationships and networks between regulatory or signalling elements in biological systems. With currently available technology sample sizes for experiments are typically small, meaning that these correlations can be difficult to estimate. At a genome-wide scale estimation of correlation matrices can also be computationally demanding.
  
  
  RESULTS
  We develop an empirical Bayes approach to improve covariance estimates for gene expression, where we assume the covariance matrix takes a block diagonal form. Our method shows lower false discovery rates than existing methods on simulated data. Applied to a real data set from Bacillus subtilis we demonstrate it's ability to detecting known regulatory units and interactions between them.
  
  
  CONCLUSIONS
  We demonstrate that, compared to existing methods, our method is able to find significant covariances and also to control false discovery rates, even when the sample size is small (n=10). The method can be used to find potential regulatory networks, and it may also be used as a pre-processing step for methods that calculate, for example, partial correlations, so enabling the inference of the causal and hierarchical structure of the networks.
authors.affiliation: CCBI, Department Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK. cep46@cam.ac.uk.|Cambridge Systems Biology Centre, University of Cambridge, Tennis Court Road, Cambridge, CB2 1QR, UK. cep46@cam.ac.uk.
authors.forename: Clare
authors.identifier: http://orcid.org/0000-0001-7791-0940
authors.initials: C
authors.lastname: Pacini
authors.affiliation: Department of Pathology, University of Cambridge, Tennis Court Road, Cambridge, CB2 1QP, UK.
authors.forename: James W
authors.initials: JW
authors.lastname: Ajioka
authors.affiliation: CCBI, Department Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK.|Cambridge Systems Biology Centre, University of Cambridge, Tennis Court Road, Cambridge, CB2 1QR, UK.
authors.forename: Gos
authors.initials: G
authors.lastname: Micklem
mesh_terms: D001412:Bacillus subtilis / Q000235:genetics*; D001499:Bayes Theorem; D003198:Computer Simulation; D018401:Sample Size; D012984:Software; D014158:Transcription, Genetic
keywords: Correlation; Empirical Bayes