Deep Uncertainty Quantification: with an Application to Integrated Assessment Models

Abstract

This paper presents a comprehensive method for efficiently solving stochastic Integrated Assessment Models (IAMs) and performing parametric uncertainty quantification. Our approach consists of two main components: a deep learning-based algorithm designed to globally solve IAMs as a function of endogenous and exogenous state variables as well as uncertain parameters within a single model evaluation. Additionally, we develop a Gaussian process-based surrogate model to facilitate the efficient analysis of key metrics, such as the social cost of carbon, with respect to uncertain model parameters. Our approach enables a rapid estimation of Sobol’ indices, Shapley values, and univariate effects, which would otherwise be computationally very challenging. To demonstrate the effectiveness of our method, we posit a high-dimensional stochastic IAM that aligns with cutting-edge climate science. This model incorporates a social planner with recursive preferences, iterative belief updates of equilibrium climate sensitivity using Bayes’ rule, and stochastic climate tipping. Our computations reveal that most of the variability in the social cost of carbon stems from the parametric uncertainty in the equilibrium climate sensitivity and in the damage function. We also show that the uncertainty about the equilibrium climate sensitivity resolves in about a decade, which in turn leads to higher optimal temperatures and a slightly decreased social cost of carbon compared to a modeling set-up without Bayesian learning. Joint paper with Aleksandra Friedl, Felix Kübler and Takafumi Usui.