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## NetLogo User Community Models(back to the NetLogo User Community Models) ## Marble-Fall-Icosystem-4by Paolo Gaudiano (Submitted: 03/24/2008)
This is a simulation of falling marbles to illustrate certain points about statistics and modeling.
Marbles fall from the top and bounce over pegs to the left or to the right. At the bottom they are collected into bins. The distribution of marbles across bins can be observed and modified by applying a "bias" to some of the pegs.
When there are no biases, the resulting distribution approximates a Gaussian (or "Bell-shaped" or "Normal" distribution). Groups of pegs can be biased to the left or to the right by varying degrees.
=== Main Control Buttons ===
=== Marble Settings ===
=== Bias Settings ===
=== Distribution Settings ===
- Use the "d-mean" "d-amp" and "d-stdev" sliders to set the mean, amplitude and standard deviation of the Gaussian distribution.
=== Additional controls ===
The main point of this demo is to illustrate the difference between statistical approaches and agent-based or "bottom-up" approaches to modeling.
When there are no biases, it can be shown mathematically that the distribution of falling marbles should approach a Gaussian distribution. In fact, if you run this with about 250 marbles and no biases, you should be able to fit the resulting distribution with a Gaussian with mean 0, amplitude 1 and standard deviation 10.
However, suppose now that someone shows you a distribution which is not Gaussian. Perhaps it is skewed to one side, or even bimodal. A statistical modeling approach would try to find a different mathematical function (perhaps a gamma or beta distribution) and adjust parameters until it minimizes the error between theoretical and empirical distributions. However, this approach doesn't really say anything about WHY the distribution should be the way it is, nor is there any relationship between the mathematical expression for the distribution and the underlying behavior.
In contrast, using a bottom-up modeling approach, we can make speculations about WHY a certain distribution arises. For instance, if you see a distribution where most marbles end up on the right, you can assume that some pegs must be biased to the right. By selecting different pegs you can make adjustments until you get close to the observed distribution.
Conversely, you can make hypotheses about the impact of different biases. For instance, what happens if all the pegs on the right are biased to the right and all the pegs on the left are biased to the left? Is there a difference between biasing the first five rows of pegs versus biasing the bottom five rows of pegs?
Now imagine the pegs representing people expressing opinions about a product. Each "person" decides whether he or she thinks the product is good (right) or bad (left). Each person then expresses that opinion to another person. Now imagine one person is biased in one direction. If that person can also influence many of its friends through word-of-mouth, a big cluster of biased individuals can cause the opinion of the entire population to shift.
Modeling these kinds of effects is nearly impossible with statistical approaches. You might even imagine a more complex situation, in which the bias of individuals is changed gradually over time by watching what other people decided. Bottom-up modeling gives you the ability to test different conditions, and to do so based on direct, intuitive terms, such as "what happens if this group is biased?" or "where is the most effective group to bias?"
By comparison, with a statistical approach you might be able to ask questions like "what if the standard deviation of the distribution increases?" or "what if I use a Gamma distribution instead of a Gaussian?"
In a nutshell, bottom-up modeling gives you the power to explore and understand causality, while statistical approaches at best can tell you about correlations between variables.
The "manual" distribution should place dots at the average between the highest marbles on the left and right sides.
It would be nice to let the bias change as a function of several other factros, such as what other patches are doing, or what information the marbles carry.
This work was created by Paolo Gaudiano and is copyright of Icosystem Corporation. This may not be used for commercial purposes without prior consent of Icosystem. For additional information please visit our web site (http://www.icosystem.com) or send mail to info@icosystem.com |

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