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Scaling possibilistic IMs to high-dimensional settings

Develop scalable computational and methodological strategies that enable possibilistic inferential models to operate effectively in high-dimensional parameter spaces while maintaining strong validity and achieving statistical efficiency.

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Background

The paper’s validity results are finite-sample and dimension-agnostic, but high-dimensional applications pose computational and efficiency challenges.

The conclusion calls for advances that combine optimization and Monte Carlo techniques and incorporate regularization to address both statistical and computational scaling.

References

There are far too many open problems to list out here, but below are a few that seem particularly interesting, touching on theory, methods, computation, and applications. How to scale up to higher dimensions?

Possibilistic inferential models: a review (2507.09007 - Martin, 11 Jul 2025) in Section 6 (Conclusion)