### Abstract

We derive methods for enumerating the distinct junction tree representations for any given decomposable graph. We discuss the relevance of the method to estimating conditional independence graphs of graphical models and give an algorithm that, given a junction tree, will generate uniformly at random a tree from the set of those that represent the same graph. Programs implementing these methods are included as supplemental material.

Original language | English |
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Pages (from-to) | 930-940 |

Number of pages | 11 |

Journal | Journal of Computational and Graphical Statistics |

Publication status | Published - 2009 |

### Keywords

- Chordal graphs, triangulated graphs, graphical models, Markov chain Monte Carlo methods.

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## Cite this

Thomas, A., & Green, P. J. (2009). Enumerating the junction trees of a decomposable graph.

*Journal of Computational and Graphical Statistics*, 930-940.