  Ising models originated in statistical physics and are widely used in
modeling spatial data and computer vision problems. However, statistical
inference of this model remains challenging due to intractable nature of the
normalizing constant in the likelihood. Here, we use a pseudo-likelihood
instead to study the Bayesian estimation of two-parameter, inverse temperature,
and magnetization, Ising model with a fully specified coupling matrix. We
develop a computationally efficient variational Bayes procedure for model
estimation. Under the Gaussian mean-field variational family, we derive
posterior contraction rates of the variational posterior obtained under the
pseudo-likelihood. We also discuss the loss incurred due to variational
posterior over true posterior for the pseudo-likelihood approach. Extensive
simulation studies validate the efficacy of mean-field Gaussian and bivariate
Gaussian families as the possible choices of the variational family for
inference of Ising model parameters.
