Extended fiducial inference: toward an automated process of statistical inference
提出扩展信仰推断方法，结合随机梯度马尔可夫链蒙特卡洛和稀疏深度神经网络，实现基于观测数据的参数不确定性推断，在参数估计和假设检验上优于频率学派和贝叶斯方法，尤其适用于含异常值的数据，并支持半监督学习。
While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set-'inferring the uncertainty of model parameters on the basis of observations'-has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable for big data. Extended Fiducial inference involves jointly imputing random errors realized in observations using stochastic gradient Markov chain Monte Carlo and estimating the inverse function using a sparse deep neural network (DNN). The consistency of the sparse DNN estimator ensures that the uncertainty embedded in observations is properly propagated to model parameters through the estimated inverse function, thereby validating downstream statistical inference. Compared to frequentist and Bayesian methods, EFI offers significant advantages in parameter estimation and hypothesis testing. Specifically, EFI provides higher fidelity in parameter estimation, especially when outliers are present in the observations; and eliminates the need for theoretical reference distributions in hypothesis testing, thereby automating the statistical inference process. Extended Fiducial inference also provides an innovative framework for semisupervised learning.