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## Robust Bayesian Inference of Networks Using Dirichlet t-Distributions (2014)

### Citations

1208 |
A bayesian analysis of some nonparametric problems. The annals of statistics
- Ferguson
- 1973
(Show Context)
Citation Context ...∼ DP (α, P0). The Dirichlet process possesses a clustering property due to the fact that if P ∼ DP (α, P0) then P is discrete with probability 1. This holds even if the base measure P0 is continuous (=-=Ferguson, 1973-=-). Let pi1, . . . , pin be independent draws from a random measure P ∼ DP (α, P0). 9 P0 P α τ1 τ2 τ3 X1 X2 X3 Y1 Y2 Y3 Figure 1: Representation of the process generating a tα-random vector Y from a la... |

1067 | Core Team 2010. R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing. Available at: http://www.Rproject.org (accessed 20 - Development - 2011 |

941 | Hierarchical dirichlet processes - Teh, Jordan, et al. - 2006 |

773 |
Probabilistic Networks and Expert Systems. Statistics for Engineering and Information Science.
- Cowell, Dawid, et al.
- 1999
(Show Context)
Citation Context ...obability min { 1, P (Y | G′) P (Y | G) } , (2.7) setting Gt+1 = G if the move is rejected or G ′ is not decomposable. Decomposability of the inputG0 can be tested with the Max-Cardinality algorithm (=-=Cowell et al., 1999-=-). Given the decomposable graph G0, the set of all decomposable graphs can be traversed following simple rules for edge addition and deletion (Giudici and Green, 1999). 5 3 Bayesian Graphical Models f... |

741 | Genomic expression programs in the response of yeast cells to environmental changes. - Gasch, Spellman, et al. - 2000 |

651 | Bayesian density estimation and inference using mixtures,” - Escobar, West - 1995 |

642 | Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The Annals of Statistics, - Antoniak - 1974 |

201 | Sparse graphical models for exploring gene expression data,
- Dobra, Hans, et al.
- 2004
(Show Context)
Citation Context ... prior on the covariance matrix, which allows for exact local computation (Dawid and Lauritzen, 1993). In particular, a closed form marginal likelihood permits treatment of high-dimensional datasets (=-=Dobra et al., 2004-=-; Jones et al., 2005). Exact computations for non-decomposable graphs are much more involved (Roverato, 2002; Dellaportas et al., 2003; Atay-Kayis and Massam, 2005); for an approximate treatment see L... |

185 |
Hyper-Markov laws in the statistical analysis of decomposable graphical models.
- Dawid, Lauritzen
- 1993
(Show Context)
Citation Context ...e graph. Giudici and Green (1999), for instance, use a uniform prior on decomposable graphs and place a Hyper Inverse Wishart prior on the covariance matrix, which allows for exact local computation (=-=Dawid and Lauritzen, 1993-=-). In particular, a closed form marginal likelihood permits treatment of high-dimensional datasets (Dobra et al., 2004; Jones et al., 2005). Exact computations for non-decomposable graphs are much mor... |

106 | Decomposable graphical Gaussian model determination.
- Giudici, Green
- 1999
(Show Context)
Citation Context ...d with the Max-Cardinality algorithm (Cowell et al., 1999). Given the decomposable graph G0, the set of all decomposable graphs can be traversed following simple rules for edge addition and deletion (=-=Giudici and Green, 1999-=-). 5 3 Bayesian Graphical Models for t-Distributions 3.1 Classical and Alternative Multivariate t-Distributions The classical multivariate t-distribution tp,ν(µ,Ψ) in Rp has density fν(y | µ,Ψ) = Γ(ν+... |

83 | Experiments in stochastic computation for high-dimensional graphical models.
- Jones, Carvalho, et al.
- 2005
(Show Context)
Citation Context ...ance matrix, which allows for exact local computation (Dawid and Lauritzen, 1993). In particular, a closed form marginal likelihood permits treatment of high-dimensional datasets (Dobra et al., 2004; =-=Jones et al., 2005-=-). Exact computations for non-decomposable graphs are much more involved (Roverato, 2002; Dellaportas et al., 2003; Atay-Kayis and Massam, 2005); for an approximate treatment see Lenkoski and Dobra (2... |

74 |
Multivariate t Distributions and Their Applications.
- Kotz, Nadarajah
- 2004
(Show Context)
Citation Context ...sts and is equal to ν/(ν − 2) times Ψ. If X ∼ Np(0,Ψ) is a multivariate normal random vector independent of the Gamma-random variable τ ∼ Γ(ν/2, ν/2), then Y = µ +X/ √ τ has a tp,ν(µ,Ψ)-distribution (=-=Kotz and Nadarajah, 2004-=-, Chap. 1). The heavy tails of the distribution are related to small values of the divisor τ . The classical t-distribution is useful for robust inference when only a handful of the observations are c... |

62 |
Hyper inverse Wishart distribution for non-decomposable graphs and its application to Bayesian inference for Gaussian graphical models.
- Roverato
- 2002
(Show Context)
Citation Context ...ular, a closed form marginal likelihood permits treatment of high-dimensional datasets (Dobra et al., 2004; Jones et al., 2005). Exact computations for non-decomposable graphs are much more involved (=-=Roverato, 2002-=-; Dellaportas et al., 2003; Atay-Kayis and Massam, 2005); for an approximate treatment see Lenkoski and Dobra (2011). Other recent literature providing different extensions to the basic Gaussian model... |

50 | ML estimation of the t distribution using EM and its extensions, - Liu, Rubin - 1995 |

48 | Outlier models and prior distributions in Bayesian linear regression. - West - 1984 |

35 | Objective Bayesian model selection in Gaussian graphical models - CARVALHO, SCOTT - 2009 |

32 |
A Monte Carlo method for computing the marginal likelihood in nondecomposable Gaussian graphical models. Biometrika
- Atay-Kayis, Massam
- 2005
(Show Context)
Citation Context ...rmits treatment of high-dimensional datasets (Dobra et al., 2004; Jones et al., 2005). Exact computations for non-decomposable graphs are much more involved (Roverato, 2002; Dellaportas et al., 2003; =-=Atay-Kayis and Massam, 2005-=-); for an approximate treatment see Lenkoski and Dobra (2011). Other recent literature providing different extensions to the basic Gaussian model includes Rajaratnam et al. (2008) and Carvalho and Sco... |

32 | Simulation of hyperinverse Wishart distributions in graphical models. - Carvalho, Massam, et al. - 2007 |

30 | Graphical Models, volume 17 of Oxford Statistical Science Series. - Lauritzen - 1996 |

29 | Flexible covariance estimation in graphical Gaussian models - Rajaratnam, Massam, et al. - 2008 |

22 | Computational aspects related to inference in gaussian graphical models with the g-wishart prior. - Lenkoski, Dobra - 2011 |

19 | Bayesian inference for nondecomposable graphical Gaussian models
- Dellaportas, Giudici, et al.
(Show Context)
Citation Context ...orm marginal likelihood permits treatment of high-dimensional datasets (Dobra et al., 2004; Jones et al., 2005). Exact computations for non-decomposable graphs are much more involved (Roverato, 2002; =-=Dellaportas et al., 2003-=-; Atay-Kayis and Massam, 2005); for an approximate treatment see Lenkoski and Dobra (2011). Other recent literature providing different extensions to the basic Gaussian model includes Rajaratnam et al... |

12 | Bayesian covariance matrix estimation using a mixture of decomposable graphical models - Armstrong, Carter, et al. - 2008 |

12 | The Bayesian approach to the rejection of outliers - FINETTI - 1961 |

4 | An empirical Bayes procedure for the selection of Gaussian graphical models, arXiv:1003.5851 - Donnet, Marin |

4 |
Robust Graphical Modeling with Classical and Alternative T-Distributions,” preprint available in arXiv:1009.3669
- Finegold, Drton
(Show Context)
Citation Context ... we term the alternative t-distribution has independent Gamma scalars for each component of the latent Gaussian vector. This construction has been used in a frequentist treatment of graphical models (=-=Finegold and Drton, 2011-=-), but seems to have received little attention otherwise. While better suited to higher-dimensional analysis, the distribution’s use comes at increased computational cost and imposes constraints on th... |

1 | Rejection sampling for an extended Gamma distribution - Liu, Wichura, et al. - 2012 |