5 papers
Mixed Fractional Information: Consistency of Dissipation Measures for Stable Laws
William Cook
Symmetric alpha-stable (S alpha S) distributions with alpha<2 lack finite classical Fisher information. Building on Johnson's framework, we define Mixed Fractional Information (MFI…
Beyond Coordinates: Meta-Equivariance in Statistical Inference
William Cook
Optimal statistical decisions should transcend the language used to describe them. Yet, how do we guarantee that the choice of coordinates - the parameterisation of an optimisation…
A Hierarchical Decomposition of Kullback-Leibler Divergence: Disentangling Marginal Mismatches from Statistical Dependencies
William Cook
The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying…
The Resonance Bias Framework: Resonance, Structure, and Arithmetic in Quadrature Error
William Cook
We study the trapezoidal rule for periodic functions on uniform grids and show that the quadrature error exhibits a rich deterministic structure, beyond traditional asymptotic or s…
A Recursive Block Pillar Structure in the Kolakoski Sequence K(1,3)
William Cook
The Kolakoski sequence K(1,3) over {1, 3} is known to be structured, unlike K(1,2), with symbol frequency d approx. 0.397 linked to the Pisot number alpha (real root of x^3 - 2x^2…