  Economic assessment in environmental science concerns the measurement or
valuation of environmental impacts, adaptation, and vulnerability. Integrated
assessment modeling is a unifying framework of environmental economics, which
attempts to combine key elements of physical, ecological, and socioeconomic
systems. Uncertainty characterization in integrated assessment varies by
component models: uncertainties associated with mechanistic physical models are
often assessed with an ensemble of simulations or Monte Carlo sampling, while
uncertainties associated with impact models are evaluated by conjecture or
econometric analysis. Manifold sampling is a machine learning technique that
constructs a joint probability model of all relevant variables which may be
concentrated on a low-dimensional geometric structure. Compared with
traditional density estimation methods, manifold sampling is more efficient
especially when the data is generated by a few latent variables. The
manifold-constrained joint probability model helps answer policy-making
questions from prediction, to response, and prevention. Manifold sampling is
applied to assess risk of offshore drilling in the Gulf of Mexico.
