This paper studies the consistency and statistical inference of simulated Ising models in the high dimensional background. Our estimators are based on the Markov chain Monte Carlo maximum likelihood estimation (MCMC-MLE) method penalized by the Elastic-net. Under mild conditions that ensure a specific convergence rate of MCMC method, the $\ell_{1}$ consistency of Elastic-net-penalized MCMC-MLE is proved. We further propose a decorrelated score test based on the decorrelated score function and prove the asymptotic normality of the score function without the influence of many nuisance parameters under the assumption that accelerates the convergence of the MCMC method. The one-step estimator for a single parameter of interest is purposed by linearizing the decorrelated score function to solve its root, as well as its normality and confidence interval for the true value, therefore, be established. Finally, we use different algorithms to control the false discovery rate (FDR) via traditional p-values and novel e-values.

翻译：本文研究了高维背景中模拟的Ising模型的一致性和统计推论。 我们的估测依据是受到Elistric-net惩罚的Markov链 Monte Carlo最大可能性估计法(MCMC-MLE),在确保MCMC方法具体趋同率的温和条件下,Elastic-net-penal MCMC-MLE的美元一致性得到了证明。我们进一步提议根据与分数有关的分数函数进行一个与装饰相关的评分评分测试,并证明分数的无症状正常性,而不受许多干扰参数的影响,假设是加速MCMCM方法的趋同。一个单一利益参数的单步估测算符,目的是通过将与分数有关的分数的线化来解决其根,以及其真实价值的正常性和信任度间隔。最后,我们使用不同的算法来控制通过传统的p-val值和新的电子价值来控制错误的发现率。