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Statisticians are largely focused on developing methods that perform well ina frequentist sense -- even the Bayesians. But the widely-publicizedreplication crisis suggests that these performance guarantees alone are notenough to instill confidence in scientific discoveries. In addition to reliablydetecting hypotheses that are (in)compatible with data, investigators requiremethods that can probe for hypotheses that are actually supported by the data.In this paper, we demonstrate that valid inferential models (IMs) achieve bothperformance and probativeness properties and we offer a powerful new resultthat ensures the IM's probing is reliable. We also compare and contrast theIM's dual performance and probativeness abilities with that of Deborah Mayo'ssevere testing framework.

Possibility-theoretic statistical inference offers performance and probativeness assurances