Analysis of Distributional Variation Through Graphical Multi-Scale Beta-Binomial Models

References

• Anderson, T. W. (1962), “On the Distribution of the Two-Sample Cramer-von Mises Criterion,” Annals of Mathematical Statistics, 33, 1148–1159.
   Google Scholar
• Barbieri, M. M., and Berger, J. O. (2004). “Optimal Predictive Model Selection,” Annals of Statistics, 32, 870–897.
   Web of Science ®Google Scholar
• Baringhaus, L., and Franz, C. (2004), “On a New Multivariate Two-Sample Test,” Journal of Multivariate Analysis, 88, 190–206.
   Web of Science ®Google Scholar
• Chen, L., Dai, P., and Dou, W. (2010), MTSKNN: Multivariate Two-Sample Tests Based on K-Nearest-Neighbors, R Package Version 0.0-5.
   Google Scholar
• Chen, Y., and Hanson, T. E. (2014), “Bayesian Nonparametric k-Sample Tests for Censored and Uncensored Data,” Computational Statistics & Data Analysis, 71, 335–346.
   Web of Science ®Google Scholar
• Crouse, M. S., Nowak, R. D., and Baraniuk, R. G. (1998), “Wavelet-Based Statistical Signal Processing using Hidden Markov Models,” IEEE Transactions on Signal Processing, 46, 886–902.
   Web of Science ®Google Scholar
• Crowder, M. J. (1978), “Beta-Binomial ANOVA for Proportions,” Journal of the Royal Statistical Society, Series C, 27, 34–37.
   Google Scholar
• De Iorio, M., Rosner, P., and MacEachern, S. N. (2004), “An ANOVA Model for Dependent Random Measures,” Journal of The American Statistical Association, 99, 205–215.
   Web of Science ®Google Scholar
• Degner, J., Pai, A., Pique-Regi, R., Veyrieras, J., Gaffney, D., Pickrell, J., De Leon, S., Michelini, K., Lewellen, N., Crawford, G., Stephens, M., Gilad, Y., and JK, P. (2012), “Dnase Sensitivity qtls are a Major Determinant of Human Expression Variation,” Nature, 482, 390–394.
   PubMed Web of Science ®Google Scholar
• Ferguson, T. S. (1973), “A Bayesian Analysis of Some Nonparametric Problems,” Annals of Statistics, 1, 209–230.
   Web of Science ®Google Scholar
• Franz, C. (2014), cramer: Multivariate Nonparametric Cramer-Test for the Two-Sample-Problem, R Package Version 0.9-1.
   Google Scholar
• Henze, N. (1988), “A Multivariate Two-Sample Test Based on The Number of Nearest Neighbor Type Coincidences,” Annals of Statistics, 16, 772–783.
   Web of Science ®Google Scholar
• Holmes, C., Caron, F., Griffin, J., and Stephens, D. A. (2015), “Two-Sample Bayesian Nonparametric Hypothesis Testing,” Bayesian Analysis, 2, 297–320.
   Web of Science ®Google Scholar
• Jara, A., Hanson, T., Quintana, F., Müller, P., and Rosner, G. (2011), “Dp-Package: Bayesian Semi- and Nonparametric Modeling in R,” Journal of Statistical Software, 40, 1–30.
   PubMed Web of Science ®Google Scholar
• Jiang, B., Ye, C., and Liu, J. S. (2015), “Nonparametric k-sample Tests via Dynamic Slicing,” Journal of the American Statistical Association, 110, 642–653.
   Web of Science ®Google Scholar
• Lavine, M. (1992), “Some Aspects of Pólya Tree Distributions for Statistical Modelling,” Annals of Statistics, 20, 1222–1235.
   Web of Science ®Google Scholar
• Ma, L. (2017), “Adaptive Shrinkage in Pólya Tree Type Models,” Bayesian Analysis, 12, 779–805.
   Web of Science ®Google Scholar
• Ma, L., and Wong, W. H. (2011), “Coupling Optional Pólya Trees and the Two Sample Problem,” Journal of the American Statistical Association, 106, 1553–1565.
   Web of Science ®Google Scholar
• Müller, P., Parmigiani, G., and Rice, K. (2007), “FDR and Bayesian Multiple Comparisons Rules,” in Bayesian Statistics 8 eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith, and M. West, Oxford: Oxford University Press, pp. 349–370.
   Google Scholar
• R Core Team (2016), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Rue, H., Martino, S., and Chopin, N. (2009), “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations,” Journal of the Royal Statistical Society, Series B, 71, 319–392.
   Google Scholar
• Rufibach, K., and Walther, G. (2010), “The Block Criterion for Multiscale Inference about a Density, with Applications to Other Multiscale Problems,” Journal of Computational and Graphical Statistics, 19, 175–190.
   Web of Science ®Google Scholar
• Schilling, M. F. (1986), “Multivariate Two-Sample Tests based on Nearest Neighbors,” Journal of the American Statistical Association, 81, 799–806.
   Web of Science ®Google Scholar
• Shim, H., and Stephens, M. (2015), “Wavelet-Based Genetic Association Analysis of Functional Phenotypes Arising from High-Throughput Sequencing Assays,” Annals of Applied Statistics, 9, 665–686.
   Web of Science ®Google Scholar
• Song, L., and Crawford, G. E. (2010), “DNase-seq: A High-Resolution Technique for Mapping Active Gene Regulatory Elements across the Genome from Mammalian Cells,” Cold Spring Harbor Protocols, 2010, pdb.prot5384+.
   PubMedGoogle Scholar
• Soriano, J., and Ma, L. (2017), “Probabilistic Multi-Resolution Scanning for Two-Sample Differences,” Journal of the Royal Statistical Society, Series B, 79, 547–572.
   Google Scholar
• The ENCODE Consortium., (2012), “An Integrated Encyclopedia of DNA Elements in the Human Genome,” Nature, 489, 57–74.
   PubMed Web of Science ®Google Scholar
• Wainwright, M. J. (2015), “Graphical Models and Message-Passing Algorithms: Some Introductory Lectures,” in Mathematical Foundations of Complex Networked Information Systems: Politecnico di Torino, Verrès, Italy 2009, Springer, pp. 51–108.
   Google Scholar
• Walther, G. (2010), “Optimal and Fast Detection of Spatial Clusters with Scan Statistics,” Annals of Statistics, 38, 1010–1033.
   Web of Science ®Google Scholar
• Willsky, A. S. (2002), “Multi-Resolution Markov Models for Signal and Image Processing,” Proceedings of the IEEE, 90, 1396–1458.
   Web of Science ®Google Scholar
• Wong, W. H., and Ma, L. (2010), “Optional Pólya Tree and Bayesian Inference,” Annals of Statistics, 38, 1433–1459.
   Web of Science ®Google Scholar