A possibilistic analogue of the Bernstein-von Mises theorem shows that inferential models are asymptotically efficient, with credal sets shrinking to the smallest set containing the Gaussian distribution at the Cramer-Rao lower bound.
Convergence to the Truth
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abstract
This article reviews and develops an epistemological tradition in the philosophy of science, known as convergentism, which holds that inference methods should be assessed based on their ability to converge to the truth across a range of possible scenarios. Emphasis is placed on its historical origins in the work of C. S. Peirce and its recent developments in formal epistemology and data science (including statistics and machine learning). Comparisons are made with three other traditions: (1) explanationism, which holds that theory choice should be guided by a theory's overall balance of explanatory virtues, such as simplicity and fit with data; (2) instrumentalism, which maintains that scientific inference should be driven by the goal of obtaining useful models rather than true theories; and (3) Bayesianism, which shifts the focus from all-or-nothing beliefs to degrees of belief.
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Asymptotic efficiency of inferential models and a possibilistic Bernstein--von Mises theorem
A possibilistic analogue of the Bernstein-von Mises theorem shows that inferential models are asymptotically efficient, with credal sets shrinking to the smallest set containing the Gaussian distribution at the Cramer-Rao lower bound.