## Experiments in Stochastic Computation for High-Dimensional Graphical Models (2004)

### Cached

### Download Links

Citations: | 50 - 19 self |

### BibTeX

@MISC{Jones04experimentsin,

author = {Beatrix Jones and Carlos Carvalho and Adrian Dobra and Chris Hans and Chris Carter and Mike West},

title = {Experiments in Stochastic Computation for High-Dimensional Graphical Models},

year = {2004}

}

### OpenURL

### Abstract

### Citations

1103 |
Numerical Modelling of the
- S, ERRAUD, et al.
- 2000
(Show Context)
Citation Context ...presentations of the conditional independence structure of a multivariate distribution as well as access to efficient algorithms for computation of conditional and marginal densities (Whittaker 1990, =-=Lauritzen 1996-=-, Andersson, Madigan, Perlman, and Richardson 1998, Cowell, Dawid, Lauritzen, and Spiegelhalter 1999) . The computational efficiencies arise through decompositions of the sample space into subsets of ... |

739 | Using Bayesian networks to analyze expression data - Friedman, Linial, et al. - 2000 |

624 | Probabilistic networks and expert systems - Cowell, Dawid, et al. - 1999 |

441 | Graphical models in applied multivariate statistics - Whittaker - 1990 |

226 | Bayesian graphical models for discrete data
- Madigan, York
- 1995
(Show Context)
Citation Context ...o a single prime component; there is no cancellation in the likelihood ratio. 19s7 Markov Chain Monte Carlo Algorithms MCMC is a much used tool for exploring the space of graphical structures, (e. g. =-=Madigan and York 1995-=-, Dellaportas and Forster 1999, Giudici and Castelo 2003). In the context of Gaussian graphical models, Wong and Carter (2002) use their results to construct a fixed scan Gibbs sampler for decomposabl... |

192 | 2001, ‘Predicting the Clinical Status of Human Breast Cancer by Using Gene Expression Profiles - West, Blanchette, et al. |

187 | Covariance selection - Dempster - 1972 |

156 | Dependency networks for inference, collaborative filtering, and data - Heckerman, Chickering, et al. - 2000 |

132 | Sparse graphical models for exploring gene expression data - Dobra, Hans, et al. - 2004 |

120 |
Hyper Markov laws in the statistical analysis of decomposable models
- DAWID, LAURITZEN
- 1993
(Show Context)
Citation Context ..., and prior and posterior densities, can be computed separately on the subsets of vertices and then reassembled into a likelihood or density incorporating all variables (Hammersley and Clifford 1971, =-=Dawid and Lauritzen 1993-=-). Subsets of variables that are complete (have all possible edges between them filled in, or equivalently have no conditional independencies between them) play a special role. The basic terminology a... |

107 |
Markov fields on finite graphs and lattices. Unpublished manuscript
- Hammersley, Clifford
- 1971
(Show Context)
Citation Context ...over its graph, so likelihoods, and prior and posterior densities, can be computed separately on the subsets of vertices and then reassembled into a likelihood or density incorporating all variables (=-=Hammersley and Clifford 1971-=-, Dawid and Lauritzen 1993). Subsets of variables that are complete (have all possible edges between them filled in, or equivalently have no conditional independencies between them) play a special rol... |

74 | Positive definite completions of partial hermitian matrices - Grone, Johnson, et al. - 1984 |

63 | Decomposable graphical Gaussian model determination
- Giudici, Green
- 1999
(Show Context)
Citation Context ...ere Sy is the sum of products matrix, � n i=1 yiy ′ i. In examples below, we use Φ = τI for specified constants τ (other choices for Φ, such as an intra-class correlation structure, are consid=-=ered in Giudici and Green 1999-=-). This choice is consistent with problems in which variables represent measures of similarly defined quantities on a common scale. The form of the posterior makes it clear that it is important to cho... |

56 | Advances to Bayesian network inference for generating causal networks from observational biological data - Yu, Smith, et al. - 2004 |

54 | Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models
- DELLAPORTAS, FORSTER
- 1999
(Show Context)
Citation Context ...ent; there is no cancellation in the likelihood ratio. 19s7 Markov Chain Monte Carlo Algorithms MCMC is a much used tool for exploring the space of graphical structures, (e. g. Madigan and York 1995, =-=Dellaportas and Forster 1999-=-, Giudici and Castelo 2003). In the context of Gaussian graphical models, Wong and Carter (2002) use their results to construct a fixed scan Gibbs sampler for decomposable graphs, where each edge was ... |

50 |
Conjugate priors for exponential families
- Diaconis, Ylvisaker
- 1979
(Show Context)
Citation Context ...shart as a prior density for ΣP P (thus we will call the prior over Σ a hyper-inverse Wishart distribution just as in the decomposable case). The prior is derived as the Diaconis-Ylvisaker conjugate=-= (Diaconis and Ylvisaker 1979) o-=-f the likelihood for Ω. In this density, some of the non-free elements of ΣP P will appear; however, the true dimension of the density corresponds to the number of free elements. The free elements ... |

47 |
Improving Markov Chain Monte Carlo Model Search for Data Mining
- Giudici, Castelo
- 2003
(Show Context)
Citation Context ...in the likelihood ratio. 19s7 Markov Chain Monte Carlo Algorithms MCMC is a much used tool for exploring the space of graphical structures, (e. g. Madigan and York 1995, Dellaportas and Forster 1999, =-=Giudici and Castelo 2003-=-). In the context of Gaussian graphical models, Wong and Carter (2002) use their results to construct a fixed scan Gibbs sampler for decomposable graphs, where each edge was updated according to its f... |

44 | Bounds for cell entries in contingency tables given marginal totals and decomposable - Dobra, Fienberg - 2000 |

39 | Efficient Estimation of Covariance Selection Models - Wong, Carter, et al. - 2003 |

32 | Decomposition of maximum likelihood in mixed graphical interaction models - Frydenberg, Lauritzen - 1989 |

32 | Hyper inverse Wishart distribution for non-decomposable graphs and its application to Bayesian inference for Gaussian graphical models - Roverato - 2002 |

30 | Efficient Stepwise Selection in Decomposable Models - Deshpande, Garofalakis, et al. - 2001 |

28 | The weighted likelihood ratio, linear hypotheses on Normal location parameters. The annals of Statistics 42 - Dickey - 1971 |

28 | Graphical models for genetic analyses - Lauritzen, Sheehan - 2003 |

14 | Bayesian inference for nondecomposable graphical Gaussian models - Dellaportas, Giudici, et al. |

13 | Incremental Compilation of Bayesian networks - Flores, Gámez, et al. - 2003 |

12 | Model search among multiplicative models - WERMUTH - 1976 |

11 | Learning in graphical Gaussian models - Giudici - 1996 |

8 | The marginal likelihood for decomposable and nondecomposable graphical gaussian models. Biometrika - Atay-Kayis, Massam - 2006 |

5 | Fienberg (2000). Bounds for cell entries in contingency tables given marginal totals and decomposable graphs - E |

5 | Bayesian covariance matrix estimation using a mixture of decomposable graphical models - Armstrong, Carter, et al. - 2009 |

4 | Graphical Markov models in multivariate analysis - Andersson, Madigan, et al. - 1998 |

3 | Learning in graphical Gaussian models - Guidici - 1996 |

2 |
Graphical Modles in Applied Multivariate Statistics
- Whittaker
- 1990
(Show Context)
Citation Context ...odels provide representations of the conditional independence structure of a multivariate distribution as well as access to efficient algorithms for computation of conditional and marginal densities (=-=Whittaker 1990-=-, Lauritzen 1996, Andersson, Madigan, Perlman, and Richardson 1998, Cowell, Dawid, Lauritzen, and Spiegelhalter 1999) . The computational efficiencies arise through decompositions of the sample space ... |

2 | An efficient sampler for decomposable covariance selection models. preprint. A Building the Junction Forest A.1 Maximum Cardinality Search and Decomposable Graphs In this section we will consider how to obtain a junction tree representation of a connected - Wong, Carter - 2002 |

2 | One edge changes that maintain decomposability It has long been known that an edge deletion maintains decomposability if that edge is contained in exactly one clique (see, for example, Frydenberg and Lauritzen - unknown authors - 1989 |

2 | Bayesian covariance selection. Available as Discussion Paper 04-23 at www.isds.duke - DOBRA, M - 2004 |

1 | Efficient estimation of covariance selection models - F, Kohn - 2003 |