Adaptive Online Monitoring of the Ising model

Ising model is a general framework for capturing the dependency structure among random variables. It has many interesting real-world applications in the fields of medical imaging, genetics, disease surveillance, etc. Nonetheless, literature on the online change-point detection of the interaction parameter in the model is rather limited. This might be attributed to following two challenges: 1) the exact evaluation of the likelihood function with the given data is computationally infeasible due to the presence of partition function and 2) the post-change parameter usually is unknown. In this paper, we overcome these two challenges via our proposed adaptive pseudo-CUSUM procedure, which incorporates the notion of pseudo-likelihood function under the CUSUM framework. Asymptotic analysis, numerical simulation, and case study corroborate the statistical efficiency and the practicality of our proposed scheme.