# Lesson 12 - Unit 11 Summary

For most real-world systems, at least some of the controlling parameters, processes and events are often uncertain (i.e., randomly variable and/or poorly understood). A probabilistic simulation attempts to represent this uncertainty explicitly and quantitatively.

Because uncertainty is inherent in all real-world systems, the entire GoldSim framework was designed from the outset with probabilistic simulation in mind.  This was the first of two Units that discuss how probabilistic simulations can be carried out in GoldSim.

In this Unit we began by discussing some fundamental concepts, and concluded by starting to introduce how these concepts are supported in GoldSim.

In particular, the key points that we covered were as follows:

• When quantifying the uncertainty in a system, there are two fundamental causes of uncertainty that it is important to distinguish between: 1) that due to inherent (temporal) randomness; and 2) that due to ignorance or lack of knowledge. A fundamental difference between these two types of uncertainty is that uncertainty resulting from lack of knowledge can theoretically be reduced by studying the parameter or system, whereas uncertainty due to inherent randomness cannot.
• When uncertainty is quantified, it is expressed in terms of probability distributions. A probability distribution is a mathematical representation of the relative likelihood of an uncertain parameter having specific values. Probability distributions can be continuous or discrete, and can be displayed as probability density or mass functions (PDF/PMF), cumulative distributions functions (CDF), or complementary cumulative distributions functions (CCDF).
• Probability distributions are defined in GoldSim using the Stochastic element.
• If the inputs describing a system are uncertain, the prediction of the future performance of the system is necessarily uncertain. That is, the result of any analysis based on inputs represented by probability distributions is itself a probability distribution. In order to compute the probability distribution of predicted simulation results, it is necessary to propagate (translate) the input uncertainties into uncertainties in the results. The most common (and most flexible) technique for propagating the uncertainty in the inputs to the uncertainty in the outputs (and the one used by GoldSim) is the Monte Carlo method.
• Just as we can create a Time History Result element, we can also create a Distribution Result element to view results that are probability distributions.
• For multi-realization simulations, time history results can only be displayed using a Time History Result element that was created prior to running the simulation.  That is, you can only plot time histories for elements that you have specifically indicated that you want to save and view.  There are multiple options for displaying probabilistic time history results.
• Defining probability distributions must be done with great care.  Three of the most common misunderstandings and errors that are made when defining probability distributions to describe your uncertainty in parameters are 1) underestimating your uncertainty; 2) combining variability and uncertainty; and 3) ignoring correlations.
• One way to express correlations in a system is to directly specify correlation coefficients between various model parameters. In practice, however, assessing and quantifying correlations in this manner can be difficult. A more practical way of representing correlations is to explicitly represent the underlying functional relationship causing the correlation.

Having discussed these fundamental concepts, and having introduced how these concepts are supported in GoldSim, in the next Unit we will continue our discussion of probabilistic simulation by describing how GoldSim allows you to represent stochastic processes (which are uncertain due to inherent randomness). Toward the end of the Unit, we will also discuss several advanced probabilistic modeling features.