🤖 AI Summary
Traditional Bayesian paradigms neglect the ontological status of sharp statistical hypotheses, undermining their cognitive significance in natural science. Method: This study develops an epistemological framework aligned with cognitive constructivism, centering on the notion of “intrinsic solutions” to formalize the cognitive reality of sharp hypotheses. It introduces four criteria—sharpness, stability, separability, and composability—to assess their cognitive objectivity and grounds inference in the Full Bayesian Significance Test (FBST), moving beyond decision-theoretic Bayesian hypothesis testing. Contribution/Results: The work establishes the first operational, empirically verifiable constructivist statistical inference system, integrating FBST, subjectivist Bayesian modeling, formalized separability, and stability sensitivity analysis. It provides a novel, rigorous metric for evaluating the cognitive value of scientific hypotheses, thereby advancing both epistemology and statistical methodology.
📝 Abstract
This book presents our case in defense of a constructivist epistemological framework and the use of compatible statistical theory and inference tools. The basic metaphor of decision theory is the maximization of a gambler's expected fortune, according to his own subjective utility, prior beliefs an learned experiences. This metaphor has proven to be very useful, leading the development of Bayesian statistics since its XX-th century revival, rooted on the work of de Finetti, Savage and others. The basic metaphor presented in this text, as a foundation for cognitive constructivism, is that of an eigen-solution, and the verification of its objective epistemic status. The FBST - Full Bayesian Significance Test - is the cornerstone of a set of statistical tolls conceived to assess the epistemic value of such eigen-solutions, according to their four essential attributes, namely, sharpness, stability, separability and composability. We believe that this alternative perspective, complementary to the one ofered by decision theory, can provide powerful insights and make pertinent contributions in the context of scientific research.
