Our knowledge of the way things work, in society or nature, comes trailing clouds of vagueness. Vast ills have followed a belief in certainty.Kenneth Arrow

# Unit 11 Overview

In the previous Units we have started to show (through simple models) how simulation can be a valuable tool for better understanding the underlying mechanisms that control the behavior of a system and making predictions of future behavior. However, 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).

Simulating a system and making predictions in the face of
such uncertainty requires that the uncertainties be quantitatively included in
the calculations. In fact, the objective of many predictive simulation models of
complex, real-world systems is to identify and quantify the ** risks**
associated with a particular alternative, plan or design (e.g., what is the
probability of a bad outcome?), and then based on that analysis, determine what
can be done to mitigate that risk and/or choose the most appropriate
alternative. This type of analysis is referred to as

**(or in some arenas,**

*risk analysis**,*

**probabilistic risk assessment****or**

*performance assessment***).**

*safety analysis*As we first discussed in Unit 2, there are two fundamental
types of simulations: ** deterministic** and

**. 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 perhaps "the worst case" values). The result of running one or more deterministic simulations is a**

*probabilistic*__qualitative__statement such as this:

"If I don’t change my spending habits, it is possible under some circumstances or scenarios that my account balance may go negative."

Unfortunately, this kind of simulation, while it can provide insight into the underlying mechanisms, often is not well-suited to making predictions to support decision-making, as it does not quantitatively address the uncertainties that are inherently present.

A probabilistic simulation recognizes that the controlling
parameters, processes and events for any system you are trying to simulate are
never completely certain or well understood, and it therefore attempts to
represent this uncertainty explicitly and quantitatively. Hence, the result of a
probabilistic simulation of a system is a __quantitative__ statement such as
this:

"If I don’t change my spending habits, there is a 50% chance that my account balance will go negative."

A quantitative statement such as this is much more useful to a decision-maker than a simple qualitative statement.

Because uncertainty is inherent in all real-world systems, the entire GoldSim framework was designed from the outset with probabilistic simulation (and risk analysis) in mind. However, other than the introductory Units, we have not yet discussed probabilistic simulation! Why? In order to truly understand and appreciate the power of probabilistic simulation in GoldSim, it is first necessary to be very comfortable with deterministic dynamic simulation (and to understand the basic mechanics of using GoldSim). We have spent the previous ten Units laying that groundwork, and we are now ready to tackle this important topic. The topic is so important, in fact, that we will spend two Units discussing it (there is too much material to cover in a single Unit). This is the first of those two Units.

In this Unit we begin by discussing some fundamental concepts, and conclude by starting to introduce how these concepts are supported in GoldSim. In particular, in this Unit we will discuss the following:

• Understanding uncertainty;

• Quantifying uncertainty using probability distributions;

• The Stochastic element;

• Propagating uncertainty using Monte Carlo simulation;

• Running a probabilistic simulation and viewing distribution results;

• Viewing time histories of probabilistic results;

• Selecting probability distributions; and

• Creating correlations and displaying multi-variate results.

This Unit also includes two Exercises (in addition to several Examples that we will work through together). This Unit has a total of 12 Lessons (including this overview and a summary at the end).

Before proceeding, however, it is important to make one key point. Some people may be intimidated by the concept of probabilistic simulation, thinking that in order to do this, you have to be an expert in statistics and applied probability. Although it is true that probabilistic analysis must be carried out with care (as we shall see, there are several errors that you can make that would result in very misleading models), probabilistic analysis itself is in fact conceptually simple to understand (and explain), and straightforward to carry out.