Spatial regression with partial differential equation regularization

32/2021

Spatial regression with partial differential equation regularization

Wednesday 2nd June 2021

Sangalli, L.M.

This work gives an overview of an innovative class of methods for the analysis of spatial and of functional data observed over complicated two-dimensional domains. This class is based on regression with regularizing terms involving partial differential equations. The associated estimation problems are solved resorting to advanced numerical analysis techniques. The synergical interplay of approaches from statistics, applied mathematics and engineering endows the methods with important advantages with respect to the available techniques, and makes them able to accurately deal with data structures for which the classical techniques are unfit. Spatial regression with differential regularization is illustrated via applications to the analysis of eco-color doppler measurements of blood-flow velocity, and to functional magnetic resonance imaging signals associated with neural connectivity in the cerebral cortex.

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International Statistical Review, DOI: 10.1111/insr.12444 Published version available at https://doi.org/10.1111/insr.12444