A0617
Title: Penalized regression models informed by physics
Authors: Michelle Carey - Univerity College Dublin (Ireland) [presenting]
James Ramsay - McGill University (Canada)
Abstract: Linear partial differential equations (PDEs) are powerful tools for modeling complex spatial autocorrelation in irregularly shaped domains. However, estimating parameters for these equations is a challenging task. To address this, a penalized regression framework is introduced. This method uses partially observed and noisy data to estimate PDE parameters and quantify the uncertainty of these estimates and the resulting PDE solution. Simulations demonstrate that this approach significantly outperforms existing methods, achieving a three-fold improvement in parameter estimation accuracy. The method is also applied to Croatian temperature data to showcase its effectiveness in spatial data analysis. By leveraging the PDE, estimates of the spatial process are generated in complex domains with irregular data sampling and intricate spatial dependencies.
