Motivated by a multimodal neuroimaging study for Alzheimer's disease, in this article, we study the inference problem, that is, hypothesis testing, of sequential mediation analysis. The existing sequential mediation solutions mostly focus on sparse estimation, while hypothesis testing is an utterly different and more challenging problem. Meanwhile, the few mediation testing solutions often ignore the potential dependency among the mediators or cannot be applied to the sequential problem directly. We propose a statistical inference procedure to test mediation pathways when there are sequentially ordered multiple data modalities and each modality involves multiple mediators. We allow the mediators to be conditionally dependent and the number of mediators within each modality to diverge with the sample size. We produce the explicit significance quantification and establish theoretical guarantees in terms of asymptotic size, power, and false discovery control. We demonstrate the efficacy of the method through both simulations and an application to a multimodal neuroimaging pathway analysis of Alzheimer's disease.
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.
more » « less- NSF-PAR ID:
- 10530786
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- ISSN:
- 1369-7412
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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