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Perfect sampling methods for random forests

Part of: Probabilistic methods, simulation and stochastic differential equations Graph theory

Published online by Cambridge University Press:  01 July 2016

Hongsheng Dai
Hongsheng Dai*
Affiliation:
Lancaster University
*
∗ Postal address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, UK. Email address: [email protected]
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Abstract

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A weighted graph G is a pair (V, ℰ) containing vertex set V and edge set ℰ, where each edge e ∈ ℰ is associated with a weight We. A subgraph of G is a forest if it has no cycles. All forests on the graph G form a probability space, where the probability of each forest is proportional to the product of the weights of its edges. This paper aims to simulate forests exactly from the target distribution. Methods based on coupling from the past (CFTP) and rejection sampling are presented. Comparisons of these methods are given theoretically and via simulation.

Keywords

Coupling from the pastMCMCperfect samplingrejection samplingtrees and forests

MSC classification

Primary: 65C05: Monte Carlo methods 65C50: Other computational problems in probability
Secondary: 05C80: Random graphs
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 3 , September 2008 , pp. 897 - 917
Copyright
Copyright © Applied Probability Trust 2008 

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