 to this lecture about the art of modeling. Here actually is a follow-up to the first lecture on the course called an introduction to modeling and simulation. In that introduction, there was a little bit of modeling, a little bit of simulation, and the way that they fit together. And as far as the modeling part of it, there was some material that was specific to creating models that we're going to be studying in this lecture. There isn't only one way of creating a model. What makes a model good? Is this model better than some other model? I mean, really, it's more of an art than a science. Expertise goes a long way in this case. As we've seen in the previous lecture on modeling, models are everywhere. I'm not going to repeat what we studied already, but if you haven't looked at it yet, it actually is a very, very interesting lecture, if I say so myself. You have models in fields, in humanities, in business, in engineering, in the arts, and all of these models have things in common and things that are not in common. But no matter what model you're talking about, you're going to have abstraction, you're going to have structure, you're going to have information hiding. There's always going to be simplification and management of complexity. The world is a complex place. If we want to study something, we have to reduce the complexity, simplify, and highlight that aspect of the world that we're trying to study. That's basically what the art of modeling is all about. What do we need when we are in the modeling effort? Well, we're going to look at a problem, analyze it. That's the way a lot of things start out. Modeling is no different. The problem is going to be a complex problem, a real-world problem. We want to abstract from it the essential features that we want to study. What are the things that must be in there? And certainly whatever it is we want to study, that must be in there. Look at the assumptions. Number three, we're going to look at the assumptions. We want to test them. We want to modify them. You may want assumptions because you can't create a simple model any other way. And then finally, once we have a simple model, then we can start enriching it and making it more and more complex. And keep testing as we go along to make sure that it's still an accurate representation of reality. Once we go about modeling, there's really no one cut and dried method. But some of the things you should consider and make sure that you do when you're creating a model, when you're building a model without looking at other models at the same time. The first thing you do is you have a problem. You may want to factor it, reduce it into several simpler problems. You can create models for each of those perhaps. You definitely want to know what your objective is for this modeling effort. You need to know, what am I studying this for? What's the variable or variables that I'm studying? What's my objective? You may want to seek analogies because why reinvent the wheel? There may be something already out there that models a similar system and you can make use of it. You reduce by looking at something complex and variable and consider it not to be a variable. Let's try one specific constant, try running the problem as a model and see what happens. You can always make it more variable later on after you've got a handle on it. You want some symbols. You want to look at things that are specific and look at the problem and say, okay, wait, I need to have some symbolic representation of the complexity of this system. Don't miss out on the obvious. That's a very common mistake as we think everybody knows something and then all of a sudden we come back a few months later and say, why didn't we do this? Finally, if a tractable model is obtained like the previous slide, then you go ahead and say, okay, I can work with this. The model is good. Let me see if I can make it more complex because I just simplified it an awful lot. You can see the first and last of the guidelines here. It advises you to simplify your original problem. That begs the question, how do I simplify? Well, we already had some of this here, but it's almost like steps in the process of looking under the to simplify box. We want to take variables, turn them into constants. It's a very good way of building a model, testing the model, and then you can later on start to say, okay, fine, now I'm going to turn the constants into variables and see if it still works. And then you would do a sensitivity analysis. The next step would be further reducing the variables. Maybe take some away, combine some, just to simplify, you can always put it back later once you have a working model. Assume something, assume some kind of relationship among the variables. Why do I say assume linearity? Because it's very well studied and we could do a lot with it. We can do a prior regression to the output values of the model if it's database, if it's numeric, quantitative. And you don't have to assume linearity, but it's just one example. You can assume that the relationships in the model are log linear. Make assumptions and that'll simplify things tremendously. That's what people do with models. Make restrictions. And then finally, restrict the boundaries of the system, the scope of the system, so that you have a smaller universe to work with, because you can always spread it out and make it more universal later on. And then of course you take these suggestions for simplifying your model and once you have a simple tractable model, then just go in the opposite direction, constants to variables, increase the bounds of the system and so on. We have looked at the process of modeling without being specific about the area, even though much of what we talked about here is definitely applicable to creating simulation models. We iteratively simplify, test, enrich and then still test. We basically want to, we're doing testing to make sure that this is a valid model, that it's a good representation of the real world. When we finally have the final model that we're going to be working with, that's the best model we can come up with. It's going to be workable because it's definitely simpler than the real world and so it helps us to study the entities that we're interested in studying, or the relationships that we're interested in studying. And yet it is also about as complex as we can make it and still make sure that the model is valid to work with. Thank you very much for attending this lecture.