  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.
