Post-Bayesian B: The Collapse of Fixed-Structure Presuppositions—The Limitations of Bayesian Inference in Domains of Structural Evolution
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2026
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| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| contents | <p>Bayesian inference, as a normative framework for reasoning under uncertainty,<br>derives its optimality within a fixed measure space from a set of structural pre<br>suppositions guaranteed by the Kolmogorov axioms of probability. However, when<br>the cognitive system faces an environment that demands not only the updating of<br>probability masses but also the reorganization of the belief structure itself, these<br>presuppositions cease to be neutral background conditions and instead become im<br>plicit boundaries that constrain inferential capacity. This paper systematically<br>examines five key structural presuppositions of the Bayesian machinery—the fix<br>ity of the σ-algebra, the anchoring of the likelihood function, the static nature of<br>the prior, the exchangeability constraint of the de Finetti representation, and the<br>pre-completeness of the model space—and demonstrates that each presupposition<br>encodes the assumption of “structural invariance” into the inferential framework in<br>a distinct way. Furthermore, the paper provides a precise definition of “structural<br>evolution” as the non-stationary, endogenously generated variation of the genera<br>tors of the measure space over time, and analyzes how this variation systematically<br>undermines the foundational presuppositions of Bayesian inference. It is shown<br>that in domains of structural non-stationarity, the Bayesian updating operator for<br>feits the guarantee of asymptotic consistency that it enjoys under fixed structures,<br>because the measurable space in which the limit point would reside is not defined<br>in the initial setup. This claim not only delineates a boundary of applicability for<br>the Bayesian paradigm but also furnishes a principled motivation for a shift toward<br>a cognitive dynamics grounded in discrete constraint satisfaction problems.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19512638 |
| institution | Zenodo |
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| publishDate | 2026 |
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| spellingShingle | Post-Bayesian B: The Collapse of Fixed-Structure Presuppositions—The Limitations of Bayesian Inference in Domains of Structural Evolution zhou, changzheng zhou, ziqing Bayesian inference; structural presuppositions; σ-algebra; structural evolution; constraint satisfaction problem; cognitive dynamics <p>Bayesian inference, as a normative framework for reasoning under uncertainty,<br>derives its optimality within a fixed measure space from a set of structural pre<br>suppositions guaranteed by the Kolmogorov axioms of probability. However, when<br>the cognitive system faces an environment that demands not only the updating of<br>probability masses but also the reorganization of the belief structure itself, these<br>presuppositions cease to be neutral background conditions and instead become im<br>plicit boundaries that constrain inferential capacity. This paper systematically<br>examines five key structural presuppositions of the Bayesian machinery—the fix<br>ity of the σ-algebra, the anchoring of the likelihood function, the static nature of<br>the prior, the exchangeability constraint of the de Finetti representation, and the<br>pre-completeness of the model space—and demonstrates that each presupposition<br>encodes the assumption of “structural invariance” into the inferential framework in<br>a distinct way. Furthermore, the paper provides a precise definition of “structural<br>evolution” as the non-stationary, endogenously generated variation of the genera<br>tors of the measure space over time, and analyzes how this variation systematically<br>undermines the foundational presuppositions of Bayesian inference. It is shown<br>that in domains of structural non-stationarity, the Bayesian updating operator for<br>feits the guarantee of asymptotic consistency that it enjoys under fixed structures,<br>because the measurable space in which the limit point would reside is not defined<br>in the initial setup. This claim not only delineates a boundary of applicability for<br>the Bayesian paradigm but also furnishes a principled motivation for a shift toward<br>a cognitive dynamics grounded in discrete constraint satisfaction problems.</p> |
| title | Post-Bayesian B: The Collapse of Fixed-Structure Presuppositions—The Limitations of Bayesian Inference in Domains of Structural Evolution |
| topic | Bayesian inference; structural presuppositions; σ-algebra; structural evolution; constraint satisfaction problem; cognitive dynamics |
| url | https://doi.org/10.5281/zenodo.19512638 |