# Modeling Uncertainty

Options Magazine, Summer 1995:

If you build a mathematical model to answer the question, “What is the cleanest energy technology?” a so-called deterministic model will typically yield the answer—for example—“solar power.” But without knowing the future, investing all research resources in solar power may represent too much risk.

Moreover, large-scale problems, such as how to manage a nation’s economy, energy policy, population, or environment, share several general features—complexity, dynamics, and uncertainty. Standard analytical methods go a long way toward adequately modeling complexity and dynamics, but incorporating uncertainty presents additional difficulties. Missing or inaccurate data, errors in forecasting future data, external uncontrollable occurrences, such as weather or the actions of independent data—all introduce uncertainty.

Ignoring uncertainty and its potential costs can prove perilous, and to make decision models effective, analysts must actively take account of it. One promising way is to model uncertain quantities by random variables and to formulate the decision model mathematically as a “stochastic optimization problem.” Flexibility, the ability to respond to an uncertain future, and the idea of diversification as insurance against uncertainty all emerge from stochastic models. We ask, for example, “Which is the best mix of energy technologies to protect the environment and ensure sufficient energy?” rather than “What is the cleanest technology?”

Uncertainty can be approximated in a problem by constructing a finite number of scenarios, a scenario being a set of data that can be used in the model to fully determine its output. Finding a solution that suits many such datasets can produce an approximate solution to the overall problem of uncertainty. Fundamental questions remain regarding the relationship between these approximations and reality, however. In particular, as the number of scenarios grows, does the approximation touch upon the real problem? Should analysts select sample scenarios at random or determine certain critical scenarios?

Using finite scenario approximations, analysts can present decision makers with several possible solutions, each produced by a single scenario. But an implementable policy may not result from such a multiplicity of solutions. To narrow the field of possibilities, the model can be modified until several scenarios yield the same solution, the so-called coordinating solutions approach. This often takes the form of adding costs and benefits to a model to account for the hidden effects of uncertainty. This approach is successful, especially for large problems, as it allows a problem to be broken down into subproblems that are better understood and also provide important insights into the structure of the problem.

Clearly, although the techniques developed at IIASA have been successfully applied to a number of environmental problems, the theoretical approaches and applications mentioned here do not fully exploit the wealth of possible questions. Optimization problems appear over and over again in different applications, and uncertainty is one of the key difficulties in long-term planning models.

Last edited: 06 February 2017

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