Lesson 12 - Unit 12 Summary
The first half of this Unit focused on how GoldSim can be used to represent stochastic processes. A stochastic process is a process that is inherently random, but changes over time according to some probabilistic rules. That is, the temporal behavior of the system cannot be predicted precisely, but can be described statistically. Examples of such processes include stock market fluctuations, rainfall, and Brownian motion.
After first focusing on how GoldSim can be used to represent stochastic processes, we concluded the Unit by discussing several advanced probabilistic modeling topics.
In particular, the key points that we covered were as follows:
- Many (if not most) complex, real-world processes behave stochastically to some extent. In many systems, it is critical to represent this “noisy” behavior (particularly when carrying out risk analysis), as ignoring it (by assuming the system behaves in an “averaged” or “smoothed” manner) can often lead to poor decision making.
- A Stochastic element can be used to represent a stochastic process. In such a case, the distribution represents a frequency distribution in time (e.g., the hourly flow rate in a river), and the distribution is resampled throughout the simulation (e.g., every simulated hour). Resampling a distribution means that instead of picking a random value only at the beginning of the simulation, we will pick new random values throughout the realization (according to some logic/schedule that we specify).
- A Stochastic element is resampled by using its triggering dialog. The triggering dialog is used to define one or more triggering events.
- Misinterpreting what a probability distribution is intended to represent when using it in a simulation can lead to drastically different results. Hence, if you are provided with a probability distribution as input, you must very clearly understand if it represents uncertainty due to lack of knowledge (and hence should be sampled and left constant) or random temporal variation (and hence represents a stochastic process and should be resampled).
- In many stochastic processes, successive values (e.g., yesterday’s and today’s) are correlated (i.e., if the value is very high today, it is unlikely, but not impossible, to be extremely low tomorrow). You can represent this in a resampled Stochastic element by autocorrelating it.
- In many models, what you are interested in is the highest or lowest values of some specific outputs over the course of a simulation. The Extrema element provides a straightforward way to compute this for any output in your model.
- Although representing a stochastic process by resampling a Stochastic element is powerful and useful for many situations, in some cases it may not be the most appropriate. As a result, GoldSim provides several other methods to represent stochastic processes. One of the most frequently used of these is time-shifting and randomly sampling a Time Series element.
- In order to carry out Monte Carlo simulation, GoldSim (and any Monte Carlo simulator) needs to consistently generate a series of random numbers. By understanding conceptually how GoldSim generates the random numbers it needs during a simulation, you can clearly understand why different simulations may give different answers and how you can control the manner in which GoldSim carries out its random sampling by using options on the Monte Carlo tab of the Simulation Settings dialog.
- The number of realizations required is a function of what specific question(s) you are trying to answer with the model. If you are interested only in the median or the mean, you may not need a large number of realizations to achieve high confidence in that value. On the other hand, if you were interested in a high percentile (e.g., if you wanted to know the 99th percentile with high confidence), you would need a larger number of realizations.
- When carrying out probabilistic simulations, you may run hundreds or thousands of realizations. In order to analyze the results, it is often quite useful to classify the realizations into categories. The power of categories is that once you have defined them, you can use them in two ways: 1) within certain kinds of result charts, realizations from each category can be displayed in a different color (and/or symbol); and 2) within all result displays, you can choose to screen out one or more categories, so that the results that are displayed only include those realizations in the categories which you have chosen to include.
- Probabilistic result displays (e.g., distribution results) display the results at the end of the simulation. By defining capture points, you can display results at other times in the simulation.
- While you are constructing and testing the logic of your model, viewing probabilistic results can make it difficult to ensure that your model is behaving properly. In general, the only way to properly test your model is to examine one realization at a time. To address this, GoldSim provides you with the ability to precisely control the values that will be used for your uncertain components when you want to run a single realization for testing purposes. This is done by telling GoldSim to run a deterministic simulation.