We would like to hear some of your ideas on bridging the gap between pure mathematics and statistics.
I can suggest quantum statistics and anions
For topics of recent interest..
Such a potential bridge : Algebraic -Differential- Geometry
Geometry studies the properties and relationships between shapes, figures, and other geometric objects. The expressions of moments establish a formal link between the geometry of shapes and statistics:
- Samejima et al., "Methods of Moments as Least Squares Solution for Fitting a Polynomial", 1979 - https://apps.dtic.mil/sti/citations/ADA072357
- Gonzalez-Ochoa et al., "Computing Moments of Objects Enclosed by Piecewise Polynomial Surfaces", 1998 -
Article Computing Moments of Objects Enclosed by Piecewise Polynomia...
- Khan et al.,"Shape-supervised Dimension Reduction: Extracting Geometry and Physics Associated Features with Geometric Moments", 2022 -
Article Shape-supervised Dimension Reduction: Extracting Geometry an...
Statistics is concerned with methods of inference, from observed data, revealing the probabilistic structure underlying such data. Thus, estimating the shape of a statistical model in the whole of probability distributions (geometry of statistical model) is of great interest:
- N.H. Abdel-All, "Computer geometry and encoding the information on a manifold", 2011 -
Article Computer geometry and encoding the information on a manifold
- Abdel-All et al., "Information geometry and statistical manifold", 2003 - https://www.sciencedirect.com/science/article/abs/pii/S096007790200142X?via%3Dihub
- Barndorff-Nielsen et al., "The Role of Differential Geometry in Statistical Theory", 1986 - https://www.jstor.org/stable/1403260
- X. Pennec, "Probabilities and Statistics on Riemannian Manifolds: A Geometric approach", 2004 - http://yaroslavvb.com/papers/pennec-probabilities.pdf
Subject to certain conditions, shape may even be reconstructed from moments:
- Milanfar et al., "Shape Reconstruction From Moments: Theory, Algorithms, and Applications", 2000 - https://web.math.ucsb.edu/~mputinar/spie2000.pdf
In addition, You may refer to:
- Julius Ross' web page about the links between Algebraic Geometry and Complex Analysis: https://gtr.ukri.org/projects?ref=EP%2FJ002062%2F1#/tabOverview
- https://uwaterloo.ca/pure-mathematics/about-pure-math/what-is-pure-math/what-is-geometry
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