Sequential sampling of junction trees for decomposable graphs
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The junction tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present a novel stochastic algorithm which we call the Christmas tree algorithm (CTA) for sequential sampling of junction trees of decomposable graphs. We show that, by incrementally expanding the underlying graph with one vertex at a time, the CTA is able to construct all junction trees for any given number of underlying vertices. The relevance of our suggested algorithm is justified from a sequential Monte Carlo (SMC) perspective for approximating distributions over decomposable graphs, where the transition kernel from the CTA is employed as proposal kernel; for more details see the companion paper Olsson et al. [14]. A numerical study of the SMC approximation illustrates the utility of our approach from a Bayesian inference perspective.
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