High-dimensional inference and FDR control for simulated Markov random fields
Abstract
Identifying important features associated with a response variable is fundamental across various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional regimes. We introduce a novel Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization. Under mild conditions with the MCMC method, our penalized MCMC-MLE estimate achieves $\ell_1$ consistency. The corresponding decorrelated score test and one-step estimator establish the asymptotic normality and the associated confidence interval. Furthermore, we construct two false discovery rate control procedures via the asymptotic behaviors for both p-values and e-values. Comprehensive numerical simulations further confirm the theoretical validity of the proposed methods.
Fields of Study & Subjects
Advanced Control Systems Optimization
Fault Detection and Control Systems
Publication details
- Journal / source
- Statistics and Its Interface
- Publisher
- International Press of Boston
- Volume
- 19
- Issue
- 3
- Pages
- 369–391
- Publication date
- 1 January 2026
- Language
- EN