1932

Abstract

In the postgenome era, multiple types of molecular data for the same set of samples are often available and should be analyzed jointly in an integrative analysis in order to maximize the information gain. Bayesian methods are particularly well suited for integrating different biological data sources. In this article, we cover crucial tasks and corresponding methods with a focus on integrative analyses. We emphasize gene prioritization, model-based cluster approaches for subgroup identification, regression modeling, and prediction, as well as structure learning using network models. Our review introduces prior concepts for sparsity and variable selection and concludes with some aspects on validation and computation.

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2018-03-07
2024-06-20
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Literature Cited

  1. Anders S, Huber W. 2010. Differential expression analysis for sequence count data. Genome Biol 11:R106 [Google Scholar]
  2. Beaumont MA, Zhang W, Balding DJ. 2002. Approximate Bayesian computation in population genetics. Genetics 162:2025–35 [Google Scholar]
  3. Benjamini Y, Hochberg Y. 1995. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. B 57:289–300 [Google Scholar]
  4. Berger J. 2006. The case for objective Bayesian analysis. Bayesian Anal 1:385–402 [Google Scholar]
  5. Bergersen LC, Glad IK, Lyng H. 2011. Weighted lasso with data integration. Stat. Appl. Genet. Mol. Biol. 10:1–29 [Google Scholar]
  6. Bové DS, Held L. 2011. Hyper-g priors for generalized linear models. Bayesian Anal 6:387–410 [Google Scholar]
  7. Box GEP, Draper NR. 1987. Empirical Model-Building and Response Surfaces New York: Wiley [Google Scholar]
  8. Brisbin A, Fridley BL. 2013. Bayesian genomic models for the incorporation of pathway topology knowledge into association studies. Stat. Appl. Genet. Mol. Biol. 12:505–16 [Google Scholar]
  9. Brown PJ, Vannucci M, Fearn T. 2002. Bayes model averaging with selection of regressors. J. R. Stat. Soc. B 64:519–36 [Google Scholar]
  10. Carbonetto P, Stephens M. 2012. Scalable variational inference for Bayesian variable selection in regression, and its accuracy in genetic association studies. Bayesian Anal 7:73108 [Google Scholar]
  11. Carvalho CM, Polson NG, Scott JG. 2010. The horseshoe estimator for sparse signals. Biometrika 97:465–80 [Google Scholar]
  12. Cassese A, Guindani M, Vannucci M. 2016. iBATCGH: integrative Bayesian analysis of transcriptomic and CGH data. Statistical Analysis for High-Dimensional Data: The Abel Symposium 2014 A Frigessi, P Bühlmann, I Glad, M Langaas, S Richardson, M Vannucci 105–24 New York: Springer [Google Scholar]
  13. Chu J. 2007. Bayesian function estimation using overcomplete dictionaries with application in genomics PhD Thesis, Duke Univ. [Google Scholar]
  14. Chung L, Ferguson J, Zheng W, Qian F, Bruno V. et al. 2013. Differential expression analysis for paired RNA-seq data. BMC Bioinformat 14:110 [Google Scholar]
  15. Corander J, Fraser C, Gutmann M, Arnold B, Hanage W. et al. 2017. Frequency-dependent selection in vaccine-associated pneumococcal population dynamics. Nat. Ecol. Evol. 1:1950–60 [Google Scholar]
  16. Crick F. 1970. Central dogma of molecular biology. Nature 227:561–63 [Google Scholar]
  17. Crick FH. 1958. On protein synthesis. Symp. Soc. Exp. Biol. 12:138–63 [Google Scholar]
  18. Dahl DB. 2006. Model-based clustering for expression data via a Dirichlet process mixture model. Bayesian Inference for Gene Expression and Proteomics KA Do, P Müller, M Vannucci 201–18 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  19. Do KA, Müller P, Tang F. 2005. A Bayesian mixture model for differential gene expression. Appl. Stat. 54:627–44 [Google Scholar]
  20. Dobra A, Hans C, Jones B, Nevins JR, Yao G, West M. 2004. Sparse graphical models for exploring gene expression data. J. Multivar. Anal. 90:196–212 [Google Scholar]
  21. Efron B. 2004. Large-scale simultaneous hypothesis testing: the choice of a null hypothesis. J. Am. Stat. Assoc. 99:96–104 [Google Scholar]
  22. Efron B. 2012. Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  23. Efron B, Tibshirani R, Storey JD, Tusher V. 2001. Empirical Bayes analysis of a microarray experiment. J. Am. Stat. Assoc. 96:1151–60 [Google Scholar]
  24. Ein-Dor L, Kela I, Getz G, Givol D, Domany E. 2005. Outcome signature genes in breast cancer: Is there a unique set?. Bioinformatics 21:171–78 [Google Scholar]
  25. Ferkingstad E, Frigessi A, Rue H, Thorleifsson G, Kong A. 2008. Unsupervised empirical Bayesian multiple testing with external covariates. Ann. Appl. Stat. 2:714–35 [Google Scholar]
  26. Fridley BL, Lund S, Jenkins GD, Wang LA. 2012. Bayesian integrative genomic model for pathway analysis of complex traits. Genet. Epidemiol. 36:352–59 [Google Scholar]
  27. Gelman A, Jakulin A, Pittau MG, Su YS. 2008. A weakly informative default prior distribution for logistic and other regression models. Ann. Appl. Stat. 2:1360–83 [Google Scholar]
  28. George E, McCulloch R. 1993. Variable selection via Gibbs sampling. J. Am. Stat. Assoc. 88:881–89 [Google Scholar]
  29. George E, McCulloch R. 1997. Approaches for Bayesian variable selection. Stat. Sin. 7:339–73 [Google Scholar]
  30. Gong W, Koyano-Nakagawa N, Li T, Garry DJ. 2015. Inferring dynamic gene regulatory networks in cardiac differentiation through the integration of multi-dimensional data. BMC Bioinformat 16:74 [Google Scholar]
  31. Griffin JE, Brown PJ. 2010. Inference with normal-gamma prior distributions in regression problems. Bayesian Anal 5:171–88 [Google Scholar]
  32. Guan D, Shao J, Deng Y, Wang P, Zhao Z. et al. 2014. CMGRN: a web server for constructing multilevel gene regulatory networks using ChIP-seq and gene expression data. Bioinformatics 30:1190–92 [Google Scholar]
  33. Guindani M, Sepúlveda N, Paulino CD, Müller P. 2014. A Bayesian semiparametric approach for the differential analysis of sequence counts data. J. R. Stat. Soc. C 63:385–404 [Google Scholar]
  34. Hardcastle TJ, Kelly KA. 2010. baySeq: empirical Bayesian methods for identifying differential expression in sequence count data. BMC Bioinformat 11:422 [Google Scholar]
  35. Hein AM, Richardson S, Causton H, Ambler G, Green P. 2005. BGX: a fully Bayesian gene expression index for Affymetrix GeneChip data. Biostatistics 6:3349–73 [Google Scholar]
  36. Hill S, Neve R, Bayani N, Kuo W, Ziyad S. et al. 2012. Integrating biological knowledge into variable selection: an empirical Bayes approach with an application in cancer biology. BMC Bioinformat 13:94 [Google Scholar]
  37. Holmes I, Harris K, Quince C. 2012. Dirichlet multinomial mixtures: generative models for microbial metagenomics. PLOS ONE 7:e30126 [Google Scholar]
  38. Ickstadt K, Bornkamp B, Grzegorczyk M, Wieczorek J, Sheriff M. et al. 2011. Nonparametric Bayesian networks (with discussion). In Bayesian Statistics 9. JM Bernardo, MJ Bayarri, JO Berger, AP Dawid, D Heckerman et al.283–316 Oxford, UK: Oxford Univ. Press
  39. Imoto S, Higuchi T, Goto T, Tashiro K, Kuhara S, Miyano S. 2003. Combining microarrays and biological knowledge for estimating gene networks via Bayesian networks. Proc. IEEE Comput. Soc. Bioinform. Conf. 2:104–13 [Google Scholar]
  40. Jaenisch R, Bird A. 2003. Epigenetic regulation of gene expression: how the genome integrates intrinsic and environmental signals. Nat. Genet. 33:245–54 [Google Scholar]
  41. Jiang Y, He Y, Zhang H. 2016. Variable selection with prior information for generalized linear models via the prior lasso method. J. Am. Stat. Assoc. 111:355–76 [Google Scholar]
  42. Johnson VE, Rossell D. 2010. On the use of non-local prior densities in Bayesian hypothesis tests. J. R. Stat. Soc. B 72:143–70 [Google Scholar]
  43. Johnson VE, Rossell D. 2012. Bayesian model selection in high-dimensional settings. J. Am. Stat. Assoc. 107:649–60 [Google Scholar]
  44. Joshi A, van de Peer Y, Michoel T. 2008. Analysis of a Gibbs sampler method for model-based clustering of gene expression data. Bioinformatics 24:176–83 [Google Scholar]
  45. Kim S, Tadesse MG, Vannucci M. 2006. Variable selection in clustering via Dirichlet process mixture models. Biometrika 93:877–93 [Google Scholar]
  46. Kirk P, Griffin JE, Savage RS, Ghahramani Z, Wild DL. 2012. Bayesian correlated clustering to integrate multiple datasets. Bioinformatics 28:3290–97 [Google Scholar]
  47. Klambauer G, Schwarzbauer K, Mayr A, Clevert DA, Mitterecker A. et al. 2012. cn.MOPS: mixture of Poissons for discovering copy number variations in next-generation sequencing data with a low false discovery rate. Nucleic Acids Res 40:e69 [Google Scholar]
  48. Klein HU, Schäfer M, Porse B, Hasemann M, Ickstadt K, Dugas M. 2014. Integrative analysis of histone ChIP-seq and gene expression microarray data using Bayesian mixture models. Bioinformatics 30:1154–62 [Google Scholar]
  49. Kormaksson M, Booth JG, Figueroa ME, Melnick A. 2012. Integrative model-based clustering of microarray methylation and expression data. Ann. Appl. Stat. 6:1327–47 [Google Scholar]
  50. Kpogbezan GB, Vaart AW, Wieringen WN, Leday GG, Wiel MA. 2017. An empirical Bayes approach to network recovery using external knowledge. Biometrical J 59:932–47 [Google Scholar]
  51. Law CW, Chen Y, Shi W, Smyth GK. 2014. Voom: precision weights unlock linear model analysis tools for RNA-seq read counts. Genome Biol 15:R29 [Google Scholar]
  52. Leng N, Dawson JA, Thomson JA, Ruotti V, Rissman AI. et al. 2013. EBSeq: an empirical Bayes hierarchical model for inference in RNA-seq experiments. Bioinformatics 29:1035–43 [Google Scholar]
  53. Lewin A, Richardson S, Marshall C, Glazier A, Aitman T. 2006. Bayesian modeling of differential gene expression. Biometrics 62:10–18 [Google Scholar]
  54. Li C, Li H. 2008. Network-constrained regularization and variable selection for analysis of genomic data. Bioinformatics 24:1175–82 [Google Scholar]
  55. Li GW, Xie XS. 2011. Central dogma at the single-molecule level in living cells. Nature 475:308–15 [Google Scholar]
  56. Liang F, Paulo R, Molina G, Clyde MA, Berger JO. 2008. Mixtures of g priors for Bayesian variable selection. J. Am. Stat. Assoc.410–23 [Google Scholar]
  57. Liu X, Jessen WJ, Sivaganesan S, Aronow BJ, Medvedovic M. 2007. Bayesian hierarchical model for transcriptional module discovery by jointly modeling gene expression and ChIP-chip data. BMC Bioinformat 8:283 [Google Scholar]
  58. Liu X, Sivaganesan S, Yeung KY, Guo J, Bumgarner RE, Medvedovic M. 2006. Context-specific infinite mixtures for clustering gene expression profiles across diverse microarray dataset. Bioinformatics 22:1737–44 [Google Scholar]
  59. Liu Y, Qiao N, Zhu S, Su M, Sun N. et al. 2013. A novel Bayesian network inference algorithm for integrative analysis of heterogeneous deep sequencing data. Cell Res 23:440–43 [Google Scholar]
  60. Lock EF, Dunson DB. 2013. Bayesian consensus clustering. Bioinformatics 29:2610–16 [Google Scholar]
  61. Love MI, Huber W, Anders S. 2014. Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biol 15:1–21 [Google Scholar]
  62. Mattick JS. 2003. Challenging the dogma: the hidden layer of non-protein-coding RNAs in complex organisms. Bioessays 25:930–39 [Google Scholar]
  63. Mattick JS. 2004. RNA regulation: a new genetics?. Nat. Rev. Genet. 5:316–23 [Google Scholar]
  64. McGuffey EJ, Morris JS, Manyam GC, Carroll RJ, Baladandayuthapani V. 2015. Bayesian models for flexible integrative analysis of multi-platform genomics data. Integrating Omics Data GC Tseng, D Ghosh, XJ Zhou 221–41 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  65. Medvedovic M, Sivaganesan S. 2002. Bayesian infinite mixture model based clustering of gene expression profiles. Bioinformatics 18:1194–206 [Google Scholar]
  66. Medvedovic M, Yeung K, Bumgarner R. 2004. Bayesian mixture model based clustering of replicated microarray data. Bioinformatics 20:1222–32 [Google Scholar]
  67. Mo Q, Shen R, Guo C, Vannucci M, Chan KS, Hilsenbeck SG. 2017. A fully Bayesian latent variable model for integrative clustering analysis of multi-type omics data. Biostatistics https://doi.org/10.1093/biostatistics/kxx017 [Crossref] [Google Scholar]
  68. Newton MA, Kendziorski CM, Richmond CS, Blattner FR, Tsui KW. 2001. On differential variability of expression ratios: improving statistical inference about gene expression changes from microarray data. J. Comput. Biol. 8:37–52 [Google Scholar]
  69. Newton MA, Noueiry A, Sarkar D, Ahlquist P. 2004. Detecting differential gene expression with a semiparametric hierarchical mixture method. Biostatistics 5:155–76 [Google Scholar]
  70. O'Hagan A. 2003. HSSS model criticism. Highly Structured Stochastic Systems PJ Green, NL Hjort, S Richardson 423–44 Oxford, UK: Oxford University Press [Google Scholar]
  71. O'Hara R, Sillanpää M. 2009. A review of Bayesian variable selection methods: what, how and which. Bayesian Anal 4:85–117 [Google Scholar]
  72. Park T, Casella G. 2008. Bayesian lasso. J. Am. Stat. Assoc. 103:681–86 [Google Scholar]
  73. Peng B, Zhu D, Ander B, Zhang X, Xue F. et al. 2013. An integrative framework for Bayesian variable selection with informative priors for identifying genes and pathways. PLOS ONE 8:e67672 [Google Scholar]
  74. Peterson C, Stingo FC, Vannucci M. 2015. Bayesian inference of multiple Gaussian graphical models. J. Am. Stat. Assoc. 110:159–74 [Google Scholar]
  75. Peterson C, Stingo FC, Vannucci M. 2016. Joint Bayesian variable and graph selection for regression models with network-structured predictors. Stat. Med. 35:1017–31 [Google Scholar]
  76. Piironen J, Vehtari A. 2017. Comparison of Bayesian predictive methods for model selection. Stat. Comput. 27:711–35 [Google Scholar]
  77. Polson NG, Scott JG. 2010. Shrink globally, act locally: sparse Bayesian regularization and prediction. Bayesian Stat 9:501–38 [Google Scholar]
  78. Polson NG, Scott JG, Windle J. 2013. Bayesian inference for logistic models using Pólya–Gamma latent variables. J. Am. Stat. Assoc. 108:1339–49 [Google Scholar]
  79. Porzelius C, Johannes M, Binder H, Beißbarth T. 2011. Leveraging external knowledge on molecular interactions in classification methods for risk prediction of patients. Biometrical J 53:190–201 [Google Scholar]
  80. Quintana M, Conti D. 2013. Integrative variable selection via Bayesian model uncertainty. Stat. Med. 32:4938–53 [Google Scholar]
  81. Rasmussen CE, De la Cruz BJ, Ghahramani Z, Wild DL. 2009. Modeling and visualizing uncertainty in gene expression clusters using Dirichlet process mixtures. IEEE Trans. Comput. Biol. Bioinformat. 6:615–28 [Google Scholar]
  82. Richardson S, Bottolo L, Rosenthal JS. 2011. Bayesian models for sparse regression analysis of high dimensional data. Bayesian Statistics 9 JM Bernardo, MJ Bayarri, JO Berger, AP Dawid, D Heckerman et al.539–68 Oxford, UK: Oxford Univ. Press [Google Scholar]
  83. Richardson S, Tseng GC, Sun W. 2016. Statistical methods in integrative genomics. Annu. Rev. Stat. Appl. 3:181–209 [Google Scholar]
  84. Riebler A, Menigatti M, Song JZ, Statham AL, Stirzaker C. et al. 2014. BayMeth: improved DNA methylation quantification for affinity capture sequencing data using a flexible Bayesian approach. Genome Biol 15:R35 [Google Scholar]
  85. Riebler A, Robinson M, van de Wiel M. 2014. Analysis of next generation sequencing data using integrated nested Laplace approximation (INLA). Statistical Analysis of Next Generation Sequencing Data S Datta, D Nettleton 75–91 New York: Springer [Google Scholar]
  86. Robinson MD, McCarthy DJ, Smyth GK. 2010. edgeR: a Bioconductor package for differential expression analysis of digital gene expression data. Bioinformatics 26:139–40 [Google Scholar]
  87. Ročková V, George EI. 2014. EMVS: The EM approach to Bayesian variable selection. J. Am. Stat. Assoc. 109:828–46 [Google Scholar]
  88. Rogers S, Girolami M, Kolch W, Waters KM, Liu T. et al. 2008. Investigating the correspondence between transcriptomic and proteomic expression profiles using coupled cluster models. Bioinformatics 24:2894–900 [Google Scholar]
  89. Rue H, Martino S, Chopin N. 2009. Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). J. R. Stat. Soc. B 71:319–92 [Google Scholar]
  90. Ruffieux H, Davison AC, Hager J, Irincheeva I. 2017. Efficient inference for genetic association studies with multiple outcomes. Biostatistics 18:4618–36 [Google Scholar]
  91. Savage RS, Ghahramani Z, Griffin JE, De la Cruz BJ, Wild DL. 2010. Discovering transcriptional modules by Bayesian data integration. Bioinformatics 26:i158–67 [Google Scholar]
  92. Savage RS, Ghahramani Z, Griffin JE, Kirk P, Wild DL. 2013. Identifying cancer subtypes in glioblastoma by combining genomic, transcriptomic and epigenomic data. arXiv1304.3577 [q-bio.GN]
  93. Schäfer M, Klein HU, Schwender H. 2017. Integrative analysis of multiple genomic variables using a hierarchical Bayesian model. Bioinformatics 33:3220–27 [Google Scholar]
  94. Schäfer M, Lkhagvasuren O, Klein HU, Elling C, Wüstefeld T. et al. 2012. Integrative analyses for omics data: a Bayesian mixture model to assess the concordance of ChIP-chip and ChIP-seq measurements. J. Toxicol. Environ. Health Part A 75:461–70 [Google Scholar]
  95. Scott-Boyer MP, Imholte GC, Tayeb A, Labbe A, Deschepper CF, Gottardo R. 2012. An integrated hierarchical Bayesian model for multivariate eQTL mapping. Stat. Appl. Genet. Mol. Biol. 11:1515–44 [Google Scholar]
  96. Sha K, Boyer LA. 2009. The chromatin signature of pluripotent cells. StemBook Cambridge, MA: Harv. Stem Cell Inst https://www.ncbi.nlm.nih.gov/books/NBK27041/ [Google Scholar]
  97. Smyth GK. 2004. Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Stat. Appl. Genet. Mol. Biol. 3:3 [Google Scholar]
  98. Stingo FC, Chen YA, Tadesse MG, Vannucci M. 2011. Incorporating biological information into linear models: a Bayesian approach to the selection of pathways and genes. Ann. Appl. Stat. 5:1978–2002 [Google Scholar]
  99. Stingo FC, Vannucci M. 2011. Variable selection for discriminant analysis with Markov random field priors for the analysis of microarray data. Bioinformatics 27:495–501 [Google Scholar]
  100. Storey JD. 2003. The positive false discovery rate: a Bayesian interpretation and the q-value. Ann. Stat. 31:2013–35 [Google Scholar]
  101. Sun H, Li H. 2010. A Bayesian approach for graph-constrained estimation for high-dimensional regression. Int. J. Syst. Synthet. Biol. 1:255–72 [Google Scholar]
  102. Szklarczyk D, Morris J, Cook H, Kuhn M, Wyder S. et al. 2017. The STRING database in 2017: quality-controlled protein-protein association networks, made broadly accessible. Nucleic Acids Res 45:D362–68 [Google Scholar]
  103. Tadesse MG, Sha N, Vannucci M. 2005. Bayesian variable selection in clustering high-dimensional data. J. Am. Stat. Assoc. 100:602–17 [Google Scholar]
  104. Tai F, Pan W, Shen X. 2010. Bayesian variable selection in regression with networked predictors. Analysis of High Dimensional Data T Cai, X Shen 147–65 Beijing: High. Educ. Press [Google Scholar]
  105. Tang B, Hsu HK, Hsu PY, Bonneville R, Chen SS. et al. 2012. Hierarchical modularity in ER alpha transcriptional network is associated with distinct functions and implicates clinical outcomes. Sci. Rep. 2:875 [Google Scholar]
  106. Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf MP. 2009. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6:187–202 [Google Scholar]
  107. Treppmann T, Ickstadt K, Zucknick M. 2017. Integration of multiple genomic data sources in a Bayesian Cox model for variable selection and prediction. Comput. Math. Methods Med. 2017:7340565 [Google Scholar]
  108. Vehtari A, Ojanen J. 2012. A survey of Bayesian predictive methods for model assessment, selection and comparison. Stat. Surv. 6:142–228 [Google Scholar]
  109. Vitelli V, Sørensen Ø, Crispino M, Frigessi A, Arjas E. 2017. Probabilistic preference learning with the Mallows rank model. arXiv1405.7945 [stat.ME]
  110. Wang H. 2015. Scaling it up: stochastic search structure learning in graphical models. Bayesian Anal 10:351–77 [Google Scholar]
  111. Wang W, Baladandayuthapani V, Morris JS, Broom BM, Manyam G, Do KA. 2013. iBAG: integrative Bayesian analysis of high-dimensional multiplatform genomics data. Bioinformatics 29:149–59 [Google Scholar]
  112. Wei Y, Li X, Wang Q, Ji H. 2012. iASeq: integrative analysis of allele-specificity of protein-DNA interactions in multiple ChIP-seq datasets. BMC Genom 13:681 [Google Scholar]
  113. Werhli AV, Husmeier D. 2007. Reconstructing gene regulatory networks with Bayesian networks by combining expression data with multiple sources of prior knowledge. Stat. Appl. Genet. Mol. Biol. 6:15 [Google Scholar]
  114. Wieczorek J, Malik-Sheriff RS, Fermin Y, Grecco HE, Zamir E, Ickstadt K. 2015. Uncovering distinct protein-network topologies in heterogeneous cell populations. BMC Syst. Biol. 9:24 [Google Scholar]
  115. Wiel MA, Lien TG, Verlaat W, Wieringen WN, Wilting SM. 2016. Better prediction by use of co-data: adaptive group-regularized ridge regression. Stat. Med. 35:368–81 [Google Scholar]
  116. Xu Y, Lee J, Yuan Y, Mitra R, Liang S. et al. 2013. Nonparametric Bayesian bi-clustering for next generation sequencing count data. Bayesian Anal 8:759–80 [Google Scholar]
  117. Xu Y, Zhu Y, Ji Y. 2015. A Bayesian graphical model for integrative analysis of TCGA data: BayesGraph for TCGA integration. Integrating omics data GC Tseng, D Ghosh, XJ Zhou 205–20 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  118. Yuan Y, Savage RS, Markowetz F. 2011. Patient-specific data fusion defines prognostic cancer subtypes. PLOS Comput. Biol. 7:e1002227 [Google Scholar]
  119. Zablocki RW, Schork AJ, Levine RA, Andreassen OA, Dale AM, Thompson WK. 2014. Covariate-modulated local false discovery rate for genome-wide association studies. Bioinformatics 30:2098–104 [Google Scholar]
  120. Zellner A. 1986. On assessing prior distributions and Bayesian regression analysis with g-prior distributions. Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti PK Goel, A Zellner 233–43 Amsterdam: Elsevier [Google Scholar]
  121. Zellner A, Siow A. 1980. Posterior odds ratios for selected regression hypotheses. Trabajos Estadst. Invest. Oper. 31:585–603 [Google Scholar]
  122. Zhang X, Robertson G, Krzywinski M, Ning K, Droit A. et al. 2011. PICS: probabilistic inference for ChIP-seq. Biometrics 67:151–63 [Google Scholar]
  123. Zhou H, Zheng T. 2013. Bayesian hierarchical graph-structured model for pathway analysis using gene expression data. Stat. Appl. Genet. Mol. Biol. 12:393–412 [Google Scholar]
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