A note on p-values interpreted as plausibilities

P-values are a mainstay in statistics but are often misinterpreted. We propose a new interpretation of p-value as a meaningful plausibility, where this is to be interpreted formally within the inferential model framework. We show that, for most practical hypothesis testing problems, there exists an inferential model such that the corresponding plausibility function, evaluated at the null hypothesis, is exactly the p-value. The advantages of this representation are that the notion of plausibility is consistent with the way practitioners use and interpret p-values, and the plausibility calculation avoids the troublesome conditioning on the truthfulness of the null. This connection with plausibilities also reveals a shortcoming of standard p-values in problems with non-trivial parameter constraints.Comment: 13 pages, 1 figur

Quantifying Eulerian Eddy Leakiness in an Idealized Model

An idealized eddy‐resolving ocean basin, closely resembling the North Pacific Ocean, is simulated using MITgcm. We identify rotationally coherent Lagrangian vortices (RCLVs) and sea surface height (SSH) eddies based on the Lagrangian and Eulerian framework, respectively. General statistical results show that RCLVs have a much smaller coherent core than SSH eddies with the ratio of radius is about 0.5. RCLVs are often enclosed by SSH anomaly contours, but SSH eddy identification method fails to detect more than half of RCLVs. Based on their locations, two types of eddies are classified into three categories: overlapping RCLVs and SSH eddies, nonoverlapping SSH eddies, and nonoverlapping RCLVs. Using Lagrangian particles, we examine the processes of leakage and intrusion around SSH eddies. For overlapping SSH eddies, over the lifetime, the material coherent core only accounts for about 25% and about 50% of initial water leak from eddy interior. The remaining 25% of water can still remain inside the boundary, but only in the form of filaments outside the coherent core. For nonoverlapping SSH eddies, more water leakage (about 60%) occurs at a faster rate. Guided by the number and radius of SSH eddies, fixed circles and moving circles are randomly selected to diagnose the material flux around these circles. We find that the leakage and intrusion trends of moving circles are quite similar to that of nonoverlapping SSH eddies, suggesting that the material coherence properties of nonoverlapping SSH eddies are not significantly different from random pieces of ocean with the same size

Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive prior

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity, determining if parameters associated with correlated predictors should be shrunk together or kept apart. Under suitable conditions, we prove that this empirical Bayes posterior concentrates around the true sparse parameter at the optimal rate asymptotically. A simplified version of a shotgun stochastic search algorithm is employed to implement the variable selection procedure, and we show, via simulation experiments across different settings and a real-data application, the favorable performance of the proposed method compared to existing methods.Comment: 25 pages, 4 figures, 2 table