Now it's time to talk about some of the words that people throw around when they do quantitative modelling and so being exposed to this vocabulary is helpful because it will allow you to describe to other people more accurately what you're doing and also when you hear about someone else's model, you'll have a sense of what's going on. And so, I'm going to describe some of these terms here. Okay, there's a spectrum out there and most models fit on the spectrum somewhere between empirical and theoretical. So an example of a theoretical model is an option pricing model and what I mean there is that by a theoretical model, is that someone has laid down a set of assumptions, they have written down some relationships and they really ask what are the logical consequences of those assumptions and relationships. So there could be assumption that markets are efficient, and then given that assumption, there are certain logical consequences and those logical consequences could be used for example, to come up with a model for pricing, a stock option and so that's an example of a theoretical model. The other end of the spectrum is a model that is purely based on data and that's when I've got a set of observations and I'm asking myself, how can I approximate the underlying process that generated those observations? And so I start with the data and then I try to back out the model as opposed to the theoretical one where I start with the theory and look at the consequences of that theory. So an example of a data driven model might be a set of customers that I have I have, I figured out the profitability of each of those customers and now I ask myself the question, what are the essential characteristics that separate out the profitable from unprofitable customers? That would be a useful thing to know, but my starting point here is not some grand theory of how the world works, my starting point is a spreadsheet full of data, the data being the profitability of my customers. There's a set of attributes associated with those customers, and I'm trying to figure out which of the attributes are associated with profitable customers, so that would be an example of a totally data driven model. So, that's essentially the spectrum where most modellers fit, somewhere between empirical and theoretical. You'll find that there are often arguments between people because they lie at different points on the spectrum. My own opinion here is that you really want to be able to take a piece from both of these approaches. Additional terms that you will hear thrown around by people who are making models are deterministic and probabilistic. We're going to look at these two types of models in other modules, but just to get started, what do we mean by deterministic? Well, essentially given a fixed set of inputs, the model's always going to give the identical or same output. So here's an example, you've got $1000, that's the input. You're going to invest at a 4% annual compound interest for two years. After two years, given the way the money is growing, that $1000 is always going to turn out to be equal to or will have grown to $1081.60 and it's never going to change, it's totally deterministic. The same input, always gives the same output, but what happens if you took that $1,000 and rather than putting it in to an investment that was growing at 4%, you bought lottery tickets with it? And, I could say well how much is this $1,000 going to have grown to after two years, for example, after the lottery has happened. Well, the answer now is, it fundamentally depends on whether or not one of those lottery tickets won the lottery or not. If none of the tickets won the lottery, then you're going to get an output of zero, all the money disappeared. If one of the lottery tickets was lucky enough to win the lottery, you're going to get a very, very different output. And so the output of this process or model is probabilistic, it's what we call a random variable. It all depends on whether or not the lottery was won. So that's very different from the deterministic model. And, the term stochastic is often used as really a synonym for a probabilistic model, so you'll see both of those terms used when there's uncertainty. And so those are terms deterministic and probabilistic. More terms. The next one is discrete versus continuous. Now, the analogy that I'm going to use here is the idea of a watch. Now, there are two different sorts of watches, essentially. Some watches are digital, and others are what we call analog. And so a digital watch only can show you specific times because it has the given or finite number of numbers appearing on the face and so, there's some inherent resolution beyond which you can't go in telling the time. On the other hand, if you have an analog watch, that's one where the hands are physical and sweep out the time, then it can pick up any time possible because the hands have to go through every single number. That's the idea of something that's continuous. So just as we have digital and analog, we're going to have in our modelling, the same concept happening. In the modelling world, we would call them discrete or continuous. So discrete processes are characterized by jumps in distinct values just like the digital watch, the numbers jump from one to another whereas continuous processes tend to be much smoother and more formally, you can get an infinite number of values happening in any fixed interval. And so going back to the watch here, you will see every possible time presented on the analog watch between say, 12 o'clock and 1 o'clock, because the hands are going to sweep out every single time within that period. And so, some models will be discrete and others will be continuous and it's one of the choices that the modeller gets to make. Now when you do spreadsheets, you're typically taking a rather discrete approach to the world. When you think of mat continuous variables, it tends to be a little more mathematical in nature. Final terms that we want to talk about are static and dynamic models. So, static models are those that are really trying to capture a single snapshot of a business process and so here's an example of a static model. Given a website's installed software base, what are the chances that it is compromised today? I'm just trying to make a statement about this single period in time. By contrast, a dynamic model is much more about an evolution of a process and it's the evolution that is of interest that we are trying to understand. And these dynamic models typically capture a business process moving from state to state, and we model the dynamics of those transitions. So here's an example, what I would think of as a dynamic model and this would be a sort of question that someone who was a public policy individual would be interested in, or an economist. So given a person's participation in a job training program, how long is it until he or she finds a job and then once they find one, how long can they keep it? And so I'm thinking here that a person's participation in the labor market goes through a set of states. Sometimes they're unemployed, and sometimes they're employed, and they can go from employed back to unemployed again, potentially. And so we'd be interested in modeling the transition through these states, and that would be the idea of a dynamic as opposed to a static model. So there's a whole set of terminology that I've gone through that is associated with modelling. That's what I call the lexicon of models and it's not like you can only have one of these things going on in terms of the language, you could clearly have something like a static probabilistic, discrete time model. And we're going to see one of those and it's termed a mark of chain later on. So, there's our lexicon.
