Simultaneous Inference Under the Vacuous Orientation Assumption

TL;DR

This paper introduces a new simultaneous inference method that relaxes isotropic error assumptions, using Dempster-Shafer calculus to produce calibrated posterior inference among dependent hypotheses.

Contribution

It proposes a vacuous orientation assumption for simultaneous inference, enabling calibration without specifying error correlation structures, and employs Dempster-Shafer calculus for posterior inference.

Findings

Produces calibrated posterior inference with dependent hypotheses

Outperforms Bonferroni correction in conservativeness

Uses Dempster-Shafer calculus for three-valued logic inference

Abstract

I propose a novel approach to simultaneous inference that alleviates the need to specify a correlational structure among marginal errors. The vacuous orientation assumption retains what the normal i.i.d. assumption implies about the distribution of error configuration, but relaxes the implication that the error orientation is isotropic. When a large number of highly dependent hypotheses are tested simultaneously, the proposed model produces calibrated posterior inference by leveraging the logical relationship among them. This stands in contrast to the conservative performance of the Bonferroni correction, even if neither approaches makes assumptions about error dependence. The proposed model employs the Dempster-Shafer Extended Calculus of Probability, and delivers posterior inference in the form of stochastic three-valued logic.