Partially Recursive Acceptance Rejection

TL;DR

This paper introduces a new perfect simulation protocol that operates in linear time for high-dimensional distributions, extending previous methods and applicable to models like Strauss, Ising, and random cluster.

Contribution

It presents a partially recursive acceptance rejection algorithm that improves the efficiency of perfect simulation for complex models, expanding the range of parameters.

Findings

Runs in O(n) time for various models

Applicable to a wider parameter range than previous methods

Extends Wilson's popping algorithms

Abstract

Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary distribution, but most require $O(n \ln(n))$ time, where $n$ measures the size of the input. In this work a new protocol for creating perfect simulation algorithms that runs in $O(n)$ time for a wider range of parameters on several models (such as Strauss, Ising, and random cluster) than was known previously. This work represents an extension of the popping algorithms due to Wilson.