A Polynomial-Time Perfect Sampler for the Q-Ising with a Vertex-Independent Noise

We present a polynomial-time perfect sampler for the Q-Ising with a vertex-independent noise. The Q-Ising, one of the generalized models of the Ising, arose in the context of Bayesian image restoration in statistical mechanics. We study the distribution of Q-Ising on a two-dimensional square lattice over n vertices, that is, we deal with a discrete state space {1, . . . , Q}n for a positive integer Q. Employing the Q-Ising (having a parameter β) as a prior distribution, and assuming a Gaussian noise (having another parameter α), a posterior is obtained from the Bayes’ formula. Furthermore, we generalize it: the distribution of noise is not necessarily a Gaussian, but any vertex-independent noise. We first present a Gibbs sampler from our posterior, and also present a perfect sampler by defining a coupling via a monotone update function. Then, we show O(n log n) mixing time of the Gibbs sampler for the generalized model under a condition that β is sufficiently small (whatever th...

• Type: Conference
• Year: 2009
• Where: COCOON
• Authors: Masaki Yamamoto, Shuji Kijima, Yasuko Matsui
• Keywords: COCOON 2009, Combinatorics, Perfect Sampler, Polynomial-time Perfect Sampler, Vertex-independent Noise