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       Handbook of Graphical Models (2018).  Chapman & Hall.
       Marloes Maathuis, Mathias Drton, Steffen Lauritzen, Martin Wainwright.

  1. Lectures on Algebraic Statistics (2009).  Oberwolfach Seminars, Vol. 39.

  2. Mathias Drton, Bernd Sturmfels, Seth Sullivant.

Working papers:

  1. a)Nested Covariance Determinants and Restricted Trek Separation in Gaussian Graphical Models
    (with Elina Robeva, Luca Weihs)

  2. b)High-Dimensional Causal Discovery Under non-Gaussianity
    (with Y. Samuel Wang)

  3. c)On Causal Discovery with Equal Variance Assumption
    (with Wenyu Chen, Y. Samuel Wang)

  4. d)Graphical models for zero-inflated single cell gene expression
    (with Andrew McDavid, Raphael Gottardo, Noah Simon)



  1. a)The maximum likelihood threshold of a path diagram
    (with Chris Fox, Andreas Käufl, Guillaume Pouliot).  Annals of Statistics, to appear.

  2. b)Algebraic problems in structural equation modeling
    The 50th Anniversary of Grobner Bases, Advanced Studies in Pure Mathematics, Mathematical Society of Japan, to appear.

  3. c)Computation of maximum likelihood estimates in cyclic structural equation models
    (with Chris Fox, Sam Wang). Annals of Statistics, to appear.

  4. d)Symmetric rank covariances: a generalised framework for nonparametric measures of dependence
    (with Luca Weihs, Nicolai Meinshausen). Biometrika, to appear.

  5. e)Graphical models for non-negative data using generalized score matching
    (with Shiqing Yu, Ali Shojaie). Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research 84: 1781-1790.

  6. f)Determinantal generalizations of instrumental variables
    (with Luca Weihs, Bill Robinson, Emilie Dufresne, Jennifer Kenkel, Kaie Kubjas, Reginald L. McGee II, Nhan Nguyen, Elina Robeva). Journal of Causal Inference 6, no. 1.

  7. g)Robust and sparse Gaussian graphical modeling under cell-wise contamination
    (with Shota Katayama, Hironori Fujisawa). Stat 7(1): e181.

  8. h)Testing independence in high dimensions with sums of squares of rank correlations
    (with Dennis Leung). Annals of Statistics 46(1): 280-307.


  1. a)A Bayesian information criterion for singular models
    (with Martyn Plummer).  Journal of the Royal Statistical Society Series B 79: 323-380 (with discussion).

  2. b)Structure learning in graphical modeling
    (with Marloes Maathuis).  Annual Review of Statistics and Its Application, to appear.

  3. c)Empirical likelihood for linear structural equation models dependent errors
    (with Y. Samuel Wang).  Stat 6(1): 434-447.

  4. d)Covariate-adaptive clustering of exposures for air pollution epidemiology cohorts
    (with Joshua Keller, Timothy Larson, Joel Kaufman, Dale Sandler, Adam Szpiro).  Annals of Applied Statistics 11(1): 93-113.

  5. e)Marginal likelihood and model selection for Gaussian latent tree and forest models
    (with Shaowei Lin, Luca Weihs, Piotr Zwiernik).  Bernoulli 23(2):  1202-1232.


  1. a)Large-sample theory for the Bergsma-Dassios sign covariance
    (with Preetam Nandy, Luca Weihs).  Electronic Journal of Statistics 10(2):  2287-2311.

  2. b)Estimation of high-dimensional graphical models using regularized score matching
    (with Lina Lin, Ali Shojaie).  Electronic Journal of Statistics 10(1):  806-854.

  3. c)Identifiability of directed Gaussian graphical models with one latent source
    (with Dennis Leung, Hisayuki Hara).  Electronic Journal of Statistics 10(1):  394-422.

  4. d)Order-invariant prior specification in Bayesian factor analysis
    (with Dennis Leung).  Statistics and Probability Letters 111: 60-66.

  5. e)Generic identifiability of linear structural equation models by ancestor decomposition
    (with Luca Weihs).  Scandinavian Journal of Statistics 43: 1035-1045.

  6. f)Efficient computation of the Bergsma-Dassios sign covariance
    (with Luca Weihs, Dennis Leung).  Computational Statistics 31(1): 315-328.

  7. g)Laplace approximation in high-dimensional Bayesian regression
    (with Rina Foygel Barber, Kean Ming Tan).  Statistical Analysis for High-Dimensional Data: The Abel Symposium 2014, Springer  International Publishing, Cham,  pp. 15-36.

  8. h)Wald tests of singular hypotheses
    (with Han Xiao).  Bernoulli 22(1): 38-59.

  9. i)Maximum likelihood estimates for Gaussian mixtures are transcendental
    (with Carlos Amendola, Bernd Sturmfels). In Mathematical Aspects of Computer and Information Sciences, Eds. I. Kotsireas, S. Rump and C. Yap, LNCS 9582, Springer, 579-590.


  1. a)High-dimensional Ising model selection with Bayesian information criteria
    (with Rina Foygel).  Electronic Journal of Statistics 9: 567-607.

  2. b)On the causal interpretation of acyclic mixed graphs under multivariate normality
    (with Chris Fox, Andreas Kaufl).  Linear Algebra and Its Applications 473:  93-113.

  3. c)Adaptive rhythm sequencing: A method for dynamic rhythm classification during CPR
    (with Heemun Kwok, Jason Coult, Thomas Rea, Lawrence Sherman).  Resuscitation 91: 26-31.


  1. a)Robust Bayesian graphical modeling using Dirichlet t-distributions
    (with Michael Finegold).  Bayesian Analysis 9(3): 521-550, with discussion, rejoinder pp. 591-596.


  1. a)PC algorithm for nonparanormal graphical models
    (with Naftali Harris).  Journal of Machine Learning Research 14(Nov): 3365-3383.


  1. a)Half-trek criterion for generic identifiability of linear structural equation models
    (with Rina Foygel, Jan Draisma).  Annals of Statistics 40(3): 1682-1713.

  2. b)Maximum likelihood degree of variance component models
    (with Elizabeth Gross, Sonja Petrovic).  Electronic Journal of Statistics 6: 993-1016.

  3. c)Nonparametric reduced rank regression
    (with Rina Foygel, Michael Horrell, John Lafferty).  Advances in Neural Information Processing Systems 25: 1637-1645.
    Slightly expanded and improved version:

  4. d)SPIn: model selection for phylogenetic mixtures via linear invariants
    (with Anna Kedzierska, Roderic Guigo, and Marta Casanellas).  Molecular Biology and Evolution 29(3): 929-937.

  5. e)Wisdom of crowds for robust gene network inference
    (as part of the `DREAM5 Consortium’).  Nature Methods 8: 796-804.


  1. a)Global identifiability of linear structural equation models
    (with Rina Foygel, Seth Sullivant).  Annals of Statistics 39(2): 865-886. arXiv:math.ST/1003.1146

  2. b)Robust graphical modeling of gene networks using classical and alternative t-distributions
    (with Michael Finegold).  Annals of Applied Statistics 5(2A): 1057-1080.

  3. c)Quantifying the failure of bootstrap likelihood ratio tests
    (with Ben Williams).  Biometrika 98(4): 919-934.


  1. a)A geometric interpretation of the characteristic polynomial of reflection arrangements
    (with Carly Klivans).  Proceedings of the American Mathematical Society 138: 2873-2887. arXiv:math.CO/0906.2208

  2. b)Smoothness of Gaussian conditional independence models
    (with Han Xiao).  In Algebraic Methods in Statistics and Probability II, Contemporary Mathematics, vol. 516, Amer. Math. Soc., Providence, RI, 2010, pp. 155-177. arXiv:math.ST/0910.5447

  3. c)Finiteness of small factor analysis models
    (with Han Xiao).  Annals of the Institute of Statistical Mathematics 62(4): 775-783. arXiv:math.ST/0908.1736

  4. d)On a parametrization of positive semidefinite matrices with zeros
    (with Josephine Yu).  SIAM Journal on Matrix Analysis and Applications 31(5): 2665-2680. arXiv:math.ST/1001.3195

  5. e)Extended Bayesian information criteria for Gaussian graphical models
    (with Rina Foygel).  Advances in Neural Information Processing Systems 23: 2020-2028.

  6. f)Exact block-wise optimization in group lasso for linear regression
    (with Rina Foygel).  arXiv:stat.ML/1010:3320.


  1. a)Likelihood ratio tests and singularities.
    Annals of Statistics 37(2):979-1012. arXiv:math.ST/0703360.

  2. b)Computing maximum likelihood estimates in recursive linear models with correlated errors
    (with Michael Eichler, Thomas S. Richardson).  Journal of Machine Learning Research 10(Oct): 2329-2348.

  3. c)Discrete chain graph models.
    Bernoulli 15(3): 736-753.  arXiv:math.ST/0909.0843.


  1. a)Moments of minors of Wishart matrices
    (with Hélène Massam, Ingram Olkin).  Annals of Statistics 36(5): 2261-2283. arXiv:math.PR/0604488.  
    Correction: The formula in Theorem 5.7 in the published paper is incorrect.

  2. b)Graphical methods for efficient likelihood inference in Gaussian covariance models
    (with Thomas S. Richardson).  Journal of Machine Learning Research 9(May): 893-914. arXiv:0708.1321.

  3. c)Binary models for marginal independence
    (with Thomas S. Richardson).  Journal of the Royal Statistical Society Series B 70(2): 287-309. arXiv:0707.3794.
    Supporting material:
    software and data.

  4. d)Multiple solutions to the likelihood equations in the Behrens-Fisher problem.
    Statistics & Probability Letters 78(18): 3288-3293. arXiv:0705.4516.

  5. e)A SINful approach to Gaussian graphical model selection
    (with Michael D. Perlman).  Journal of Statistical Planning and Inference 138(4): 1179-1200.

  6. f)Iterative conditional fitting for discrete chain graph models.
    COMPSTAT 2008 - Proceedings in Computational Statistics, pp. 93-104, Physica, Heidelberg.


  1. a)Estimation of a covariance matrix with zeros
    (with Sanjay Chaudhuri, Thomas S. Richardson).  Biometrika 94(1): 199-216. arXiv:math.ST/0508268.

  2. b)Algebraic factor analysis: tetrads, pentads and beyond
    (with Bernd Sturmfels, Seth Sullivant).  Probability Theory and Related Fields 138(3/4): 463-493. arXiv:math.ST/0509390.

  3. c)Algebraic statistical models
    (with Seth Sullivant).  Statistica Sinica 17: 1273-1297. arXiv:math.ST/0703609.

  4. d)Multiple testing and error control in Gaussian graphical model selection
    (with Michael D. Perlman).  Statistical Science 22(3): 430-449. arXiv:math.ST/0508267.

  5. e)A mutagenetic tree hidden Markov model for longitudinal clonal HIV sequence data
    (with Niko Beerenwinkel).  Biostatistics 8(1): 53-71. arXiv:q-bio.PE/0603031.


  1. a)Maximum likelihood estimation in Gaussian chain graph models under the alternative Markov property
    (with Michael Eichler).  Scandinavian Journal of Statistics 33(2): 247-257. arXiv:math.ST/0508266.

  2. b)Seat excess variances of apportionment methods for proportional representation
    (with Udo Schwingenschlögl).  Statistics & Probability Letters 76(16): 1723-1730.

  3. c)Computing all roots of the likelihood equations of seemingly unrelated regressions.
    Journal of Symbolic Computation 41(2): 245-254. arXiv:math.ST/0508437.

  4. d)Conditional independence models for seemingly unrelated regressions with incomplete data
    (with Steen A. Andersson, Michael D. Perlman).  Journal of Multivariate Analysis 97(2): 385-411.


  1. a)Asymptotic seat bias formulas
    (with Udo Schwingenschlögl).  Metrika 62(1): 23-31.

  2. b)Mutagenetic tree models
    (with Niko Beerenwinkel).  In L. Pachter and B. Sturmfels, editors, Algebraic Statistics for Computational Biology, chapter 14. Cambridge University Press.

  3. c)Ultra-conserved elements in vertebrate and fly genomes
    (with Nick Eriksson, Garmay Leung).  In L. Pachter and B. Sturmfels, editors, Algebraic Statistics for Computational Biology, chapter 22. Cambridge University Press.


  1. a)Model selection for Gaussian concentration graphs
    (with Michael D. Perlman).  Biometrika 91(3): 591-602.

  2. b)Multimodality of the likelihood in the bivariate seemingly unrelated regressions model
    (with Thomas S. Richardson).  Biometrika 91(2): 383-392.

  3. c)Iterative conditional fitting for Gaussian ancestral graph models
    (with Thomas S. Richardson).  Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence, 130-137.

  4. d)Surface volumes of rounding polytopes
    (with Udo Schwingenschlögl).  Linear Algebra and Its Applications 378: 71-91.

  5. e)Seat allocation distributions and seat biases of stationary apportionment methods for proportional representation
    (with Udo Schwingenschlögl).  Metrika 60(2): 191-202.

  6. f)Simulation of aphasic naming performance in non-brain-damaged adults
    (with JoAnn P. Silkes, Malcolm R. McNeil).  Journal of Speech, Language and Hearing Research 47(3): 610-623.

  7. g)A rediscovered Llull tract and the Augsburg web edition of Llull's electoral writings
    (with Günter Hägele, Dominik Haneberg, Friedrich Pukelsheim, and Wolfgang Reif).  Le Médiéviste et l'Ordinateur 43, online.


  1. a)A new algorithm for maximum likelihood estimation in Gaussian graphical models for marginal independence (with Thomas S. Richardson).  Proceedings of the 19th Conference on Uncertainty in Artificial Intelligence, 184-191.

  2. b)A Markov chain model of tornadic activity
    (with Caren Marzban, Peter Guttorp, Joseph T. Schaefer).  Monthly Weather Review 131(12): 2941-2953.

  3. c)Seat biases of apportionment methods for proportional representation
    (with Karsten Schuster, Friedrich Pukelsheim, Norman R. Draper).  Electoral Studies 22(4): 651-676.


  1. a)Analyse de la variance non-équirépétée hiérarchique: comparaison de cinq logiciels
    (Unbalanced hierarchical analysis of variance: comparison of five software packages) (with Jean-Marc Azaïs).  Journal de la Société Française de Statistique 140(1): 23-40.