Heat Kernel Smoothing in Manifolds

Abstract

Physical models often contain unknown calibration parameters, which are estimated from data using least squares methods. Many simplifying assumptions are made in deriving the physical models and when these assumptions do not match satisfactorily with the reality, the calibrated model will not be a good predictive model. To overcome this problem, Gaussian process models are proposed in the literature to simultaneously capture the model bias and estimate calibration parameters. This approach can also go wrong when the data contains systematic experimental biases. In this talk, I will introduce the concept of minimal adjustment and explain how to estimate the calibration parameters and improve the physical model by accounting for both the model and experimental biases.