Regression on Ice: Function approximation for the mathematically-inclined glaciologist.

I am writing a mini-textbook on the mathematics of regression in the context of glaciology research. The motivation is to bring awareness of mathematical methods and mindsets to practicing scientists and scientists-in-training.

[Link to working document]

Topics include: definition and basics of regression (Bayes optimal regressor), linear regression and generalizations, Gaussian processes (including Kriging estimation), and foundations of functional analysis (including Hilbert spaces and kernel theory),

Each chapter features both examples from relevant glaciology research and mathematical “curios” which invoke some higher-level themes in the theory of statistics and computation.

Affiliations include: the NSF-sponsored GHub Program at University of Buffalo; the Laidlaw Scholarship; and the NSF VERSEIM REU at Tufts University.