Apr 29, 2013

What model is a good-enough model?

There is so much talk about models and it is seems they could do anything and give precise answers to many questions. This is almost true and many organizations build and models for their operations or planning. However, we often fail to realize that a good accuracy is matter of time, efforts and ultimately - money. As with everything else, the better and the more expensive the model is the more money, analysts and time is required. We usually face limited resources and we need to draw a line somewhere. One of the overlooked points in the process of planning for a model development is the level of accuracy we expect from it. So what model is a good enough?

It is entirely dependent on the model purpose. I will resource to the physics text-book example of a cannon-ball trajectory and use it to explain some major points. The classic problem is where will a cannon ball land if launched with a specific speed at a specific angle. This is the simplest case. All we need to answer it are some basic physics formulas and few simple calculations that could be done by hand in two minutes. Making it more complex we could add a wind with a certain speed and directions. The calculations again are simple and just a basic understanding of mechanics required. Then we could include reality and include in the problem some data about the altitude above sea level for the area surrounding the gun. The math is basically the same but there are few more factors we have to account in. Further making it more realistic we could include the alternating wind speed. Then the math is getting more complex and the initial simple model has to be scrapped and new one built. We can go further by introducing humidity, air density and the direction of the trajectory (for the coriolis effect if you wonder). The accuracy could be increased by accounting for the uncertainty coming from the gun powder or the barrel temperature. Each next step adds more complex math and more time for calculation. However, after first couple of improvements of the model the accuracy level starts to increase less by every step. In addition we need to know more and more parameters. Each one of them comes with some uncertainty in its value and resources to obtain it which means more people and equipment involved and longer time for getting model results. Where is the line? If you are a school teacher then the simplest case is the best one to use for making the demonstration of some basic principles and power of science. If you are artillery officer on the battle field you would account for few more parameters but would not go deeper as you could employ one of the many methods for correcting the artillery fire to reach your goals. The most complex case with all possible parameters involved exists probably only in some math excercises run on a super computer.

The analogy with the all sorts of models is direct. Where do you draw the line? The purpose of the model plays an important role in answering this question. It could be at the simplest case when estimating a ball-park figure or a rough probability of something happening. You could go further if a deeper understanding is necessary by employing more complex math and including more factors in  the model. A model could be designed to be a starting point of a discussion in the organization and then complexity and accuracy maybe not that important so stick to simpler cases.

Beyond a certain point the increased complexity does not contribute to better accuracy of the results and we have to stop. The account for further complexity could be done by methods like rule of thumb, expert adjustment or other. For example, artillery uses set of precalculated tables to account for altitude and humidity and the expertize of the battery commander to reduce the tome to hit the targets.

The problem with the good-enough model is tightly related to the natural level of accuracy the measure that is modeled. It is also related to to the accuracy and reliability of the input data that is used in the calculations - a very complex model based on unreliable data is waste of time.

I believe the model complexity and level of accuracy have to be in the focus of planning for the model and it seems to me it an overlooked topic. Questions that should persist in this phase include "How accurate do we need it to be?" and  "Is this accuracy achievable in the time and budget we have?". The best approach would be to start with simplest and smallest possible model and with the reality check to adjust by increasing complexity until the model answers to all the needs.

Good-enough models have always been something very interesting to me and I will be coming back on this subject.

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