title: Significance evaluation in factor graphs.
abstract: BACKGROUND
  Factor graphs provide a flexible and general framework for specifying probability distributions. They can capture a range of popular and recent models for analysis of both genomics data as well as data from other scientific fields. Owing to the ever larger data sets encountered in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models.
  
  
  RESULTS
  Two novel numerical approximations for evaluation of statistical significance are presented. First a method using importance sampling. Second a saddlepoint approximation based method. We develop algorithms to efficiently compute the approximations and compare them to naive sampling and the normal approximation. The individual merits of the methods are analysed both from a theoretical viewpoint and with simulations. A guideline for choosing between the normal approximation, saddle-point approximation and importance sampling is also provided. Finally, the applicability of the methods is demonstrated with examples from cancer genomics, motif-analysis and phylogenetics.
  
  
  CONCLUSIONS
  The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets in the general factor graph framework.
authors.affiliation: Department of Molecular Medicine, Aarhus University, Palle Juul-Jensens Boulevard 99, Aarhus, Denmark. tobias.madsen@clin.au.dk.|Bioinformatics Research Center, Aarhus University, C.F. Møllers Allé 8, Aarhus, Denmark. tobias.madsen@clin.au.dk.
authors.forename: Tobias
authors.identifier: http://orcid.org/0000-0002-6846-4384
authors.initials: T
authors.lastname: Madsen
authors.affiliation: Bioinformatics Research Center, Aarhus University, C.F. Møllers Allé 8, Aarhus, Denmark.
authors.forename: Asger
authors.initials: A
authors.lastname: Hobolth
authors.affiliation: Department of Mathematics, Aarhus University, Ny Munkegade 118, Aarhus, Denmark.
authors.forename: Jens Ledet
authors.initials: JL
authors.lastname: Jensen
authors.affiliation: Department of Molecular Medicine, Aarhus University, Palle Juul-Jensens Boulevard 99, Aarhus, Denmark.|Bioinformatics Research Center, Aarhus University, C.F. Møllers Allé 8, Aarhus, Denmark.
authors.forename: Jakob Skou
authors.initials: JS
authors.lastname: Pedersen
mesh_terms: D000465:Algorithms; D000595:Amino Acid Sequence; D000076246:CCCTC-Binding Factor; D019295:Computational Biology / Q000379:methods*; D023281:Genomics; D006801:Humans; D061986:MCF-7 Cells; D008962:Models, Theoretical; D009369:Neoplasms / Q000175:diagnosis / Q000235:genetics; D010802:Phylogeny; D011336:Probability; D054730:Protein Interaction Domains and Motifs; D012097:Repressor Proteins; D016415:Sequence Alignment
chemical_list: D000076246:CCCTC-Binding Factor; C000619697:CTCF protein, human; D012097:Repressor Proteins
keywords: Factor graph; Importance sampling; Saddlepoint approximation; Significance evaluation