Tag
Probability
Probability theory measures uncertainty, built on a measure space of total mass one, with random variables as measurable functions and expectation as an integral. That framing is what lets limit theorems be proved rather than asserted, and what connects probability to analysis. Writing here uses probability where it meets geometry and estimation, and where a distribution is treated as a point on a manifold rather than a table of numbers.
Blog
August 9, 2026
Semantic Segmentation: Resolving a Domain and Typing its Pieces
Every segmentation method resolves a domain into pieces and then assigns each piece a type. Reading the field through those two operations puts pixels, point clouds, meshes and shape spaces on one axis, recovers the primal-dual mesh pair on which discrete exterior calculus is built, and gives a precise reason why a message-passing network may place its dual vertices where a discrete Hodge star may not.
April 8, 2026
Probability and Statistics: A Geometric Foundation
A measure-theoretic construction of probability and statistics, from sigma-algebras through estimation theory and hypothesis testing to the Riemannian geometry of statistical manifolds.