Ergodic Theory in Classical and Bayesian Inference

Artur O. Lopes

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arXiv · 2606.07901

Ergodic Theory in Classical and Bayesian Inference

Artur O. Lopes

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Abstract

We begin by presenting the mathematical rationale underlying classical deductive inference. We then introduce the foundational ideas of the Bayesian inference framework. Results lying at the interface of Statistics and Ergodic Theory are outlined, providing a theoretical framework applicable to the prediction and analysis of real-world phenomena from random data. This text is expository in nature - no new results are presented; rather, recently published results are described in a didactic manner. Throughout, we work with H\"older equilibrium measures, which encompass a substantially more general class of processes than i.i.d. ones.

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Artur O. Lopes. 2026-06-05. Ergodic Theory in Classical and Bayesian Inference. https://arxiv.org/abs/2606.07901

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