Marios' Thoughts

What if We Identified Causes From Their Effects? — Assimilative Causal Inference

A concise introduction to assimilative causal inference, a new mathematical framework in which causes are traced backwards from their observed effects, bridging prediction, attribution, and causal discovery while shifting the classical paradigm of predictive causality.

🖈Posted on: March 02, 2026 || 🖎 Last Update: March 02, 2026 || Category: Causal Inference, Stochastic Differential Equations, High-Dimensional Complex Systems, Data Assimilation, Information Theory, Nonlinear Geophysics

Information-Theoretic Structures of Filtering in Conditional Gaussian Nonlinear Systems

An entropy balance/budget law and an input–output signal-to-noise ratio evolution equation are derived for conditional Gaussian nonlinear systems, extending the classical information-theoretic theory of the Kalman-Bucy filter to nonlinear, path-dependent dynamics with closed-form conditional uncertainty quantification of observation-driven information gain.

🖈Posted on: Coming soon || 🖎 Last Update: || Category: Stochastic Differential Equations, High-Dimensional Complex Systems, Data Assimilation, Information Theory, Kalman–Bucy Filter

A Brief Guide to the Informational-Content Characterisations of Stochastic Processes

A concise overview of the key properties that describe how stochastic processes encode, reveal, and organise information over time, assembling key definitions, intuitions, examples, and relationships to clarify their role in stochastic calculus.

🖈Posted on: Coming soon || 🖎 Last Update: || Category: Probability, Stocastic Processes, Information Theory

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