  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 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
$\mathrm{CO}_2$ 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.
