## Addressing Risk and Uncertainty Using Probabilistic Simulation

Although simulation can be a valuable tool for better understanding the underlying mechanisms that control the behavior of a system, using simulation to make **predictions** of the future behavior of a system can be difficult. This is because, for most real-world systems, at least some of the controlling parameters, processes and events are often stochastic, uncertain and/or poorly understood. The objective of many simulations is to identify and quantify the risks associated with a particular option, plan or design. Simulating a system in the face of such uncertainty and computing such risks requires that the uncertainties be quantitatively included in the calculations.

Many simulation tools and approaches are deterministic. In a deterministic simulation, the input parameters for a model are represented using single values (which typically are described either as "the best guess" or "worst case" values). Unfortunately, this kind of simulation, while it may provide some insight into the underlying mechanisms, is not well-suited to making predictions to support decision-making, as it cannot quantitatively address the risks and uncertainties that are inherently present.

However, it is possible to quantitatively represent uncertainties in simulations. **Probabilistic simulation** is the process of explicitly representing these uncertainties by specifying inputs as probability distributions. If the inputs describing a system are uncertain, the prediction of future performance is necessarily uncertain. That is, the result of any analysis based on inputs represented by probability distributions is itself a probability distribution. Hence, whereas the result of a deterministic simulation of an uncertain system is a *qualified statement* ("if we build the dam, the salmon population could go extinct"), the result of a probabilistic simulation of such a system is a *quantified probability* ("if we build the dam, there is a 20% chance that the salmon population will go extinct"). Such a result (jn this case, quantifying the risk of extinction) is typically much more useful to decision-makers who might utilize the simulation results.

In order to compute the probability distribution of predicted performance, it is necessary to *propagate* (translate) the input uncertainties into uncertainties in the results. A variety of methods exist for propagating uncertainty. One common technique for propagating the uncertainty in the various aspects of a system to the predicted performance (and the one used by GoldSim) is Monte Carlo simulation. In Monte Carlo simulation, the entire system is simulated a large number (e.g., 1000) of times. Each simulation is equally likely, and is referred to as a realization of the system. For each realization, all of the uncertain parameters are sampled (i.e., a single random value is selected from the specified distribution describing each parameter). The system is then simulated through time (given the particular set of input parameters) such that the performance of the system can be computed. This results in a large number of separate and independent results, each representing a possible “future” for the system (i.e., one possible path the system may follow through time). The results of the independent system realizations are assembled into probability distributions of possible outcomes.