High-dimensional Inference and FDR Control for Simulated Markov Random Fields

TL;DR

This paper develops a new statistical inference framework for high-dimensional simulated Markov random fields, introducing MCMC-MLE with Elastic-net regularization, decorrelated score tests, and FDR control procedures, validated through simulations.

Contribution

It presents a novel penalized MCMC-MLE approach with Elastic-net regularization and FDR control methods for high-dimensional Markov random fields, with theoretical guarantees and simulation validation.

Findings

Achieves $ ext{l}_1$-consistency under mild conditions

Establishes asymptotic normality of the score test and estimator

Validates methods through comprehensive simulations

Abstract

Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a methodology based on Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization. Under mild conditions on the MCMC method, our penalized MCMC-MLE method achieves $\ell_{1}$-consistency. We propose a decorrelated score test, establishing both its asymptotic normality and that of a one-step estimator, along with 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 confirm the theoretical validity of the proposed methods.