Parameter estimation for computationally intensive nonlinear regression with an application to climate modeling
Drignei, D., Forest, C. E., & Nychka, D. W. (2008). Parameter estimation for computationally intensive nonlinear regression with an application to climate modeling. Annals Of Applied Statistics, 2, 1217-1230. doi:10.1214/08-AOAS210
Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by maximum likelihood is not feasible. The method presented... Show moreNonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by maximum likelihood is not feasible. The method presented in this paper proposes to construct a faster running surrogate for such a computationally intensive nonlinear function, and to use it in a related nonlinear statistical model that accounts for the uncertainty associated with this surrogate. A pivotal quantity in the Earth’s climate system is the climate sensitivity: the change in global temperature due to doubling of atmospheric CO₂ concentrations. This, along with other climate parameters, are estimated by applying the statistical method developed in this paper, where the computationally intensive nonlinear function is the MIT 2D climate model. Show less