Perfect sampling methods for random forests

Abstract

A weighted graphGis a pair (V, ℰ) containing vertex setVand edge set ℰ, where each edgee∈ ℰ is associated with a weightWe. A subgraph ofGis a forest if it has no cycles. All forests on the graphGform 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.