Valid and efficient possibilistic fusion

2026-05-27

AI Summary

This study addresses the critical challenge of balancing provable validity and fusion efficiency when integrating multi-source information within inferential models (IMs). Focusing on possibility-measure-based IMs, the work proposes a general validity-preserving fusion framework applicable across diverse dependence structures—including independence, arbitrary dependence, and exchangeability. By employing a rank-and-calibrate construction, the framework achieves robust fusion while rigorously maintaining the theoretical validity guarantees inherent to IMs. The research establishes, for the first time, a universal mechanism for preserving validity under fusion, exposes the inefficiency of conventional fusion operators in the IM context, and offers superior alternatives that significantly enhance fusion efficiency without compromising statistical rigor.

Abstract

Besides the classical motivation of fusing evidence from multiple sources, modern inferential procedures based on randomization, resampling, and data splitting often introduce analyst-generated multiplicity, where aggregating outputs across random realizations can improve robustness and stability. This emphasizes the importance of developing principled strategies for fusing measures of evidence across different inferential settings, while preserving the key properties of the adopted inferential framework. The present paper addresses this problem in the context of inferential models (IMs), a possibilistic approach for provably valid statistical inference. Although the fusion of possibility measures has been extensively studied in the possibility-theory literature, existing methods do not, in general, preserve IM validity. We propose a general validity-preserving framework for possibilistic fusion, motivated by the ranking--validification construction underlying IMs. We study the implementation of this framework under independence, arbitrary dependence, and exchangeability of the available IMs, thereby providing a unified approach for IM fusion across a broad range of practically relevant scenarios. The proposed framework also reveals important efficiency considerations, showing that intuitive and commonly used fusion operators may become inefficient in the IM context, so that alternative choices can sometimes be advantageous, including ones that might not appear natural from a purely intuitive standpoint.

Problem

• possibilistic fusion
• inferential models
• validity preservation
• evidence aggregation
• statistical inference

Innovation

• possibilistic fusion
• inferential models
• validity-preserving
• evidence aggregation
• efficiency