I'm now going to talk about some of the key steps in the modeling process. So every model is different, but they do share some common features in the way that the model was created. So I will call that the work flow. So typically we begin the modeling process by identifying and defining some inputs and outputs. What does the model trying to predict, what is the key outcome, and what are the underlying variables that are going to help us predict or understand that outcome. So an identification of the inputs and the outputs of the model, they need to be articulated, ideally defined. There's also a part where you need to think about the scope of the model and so when I talk about the scope of the model and it's like, what is it being applied to? And so going back to the diamonds example, if you have a look at the size of the diamonds that the model was trying to predict, it was little diamonds, basically between .1 and .3 of a carat. And that's what I mean by the scope. It was a model was being created to work in a particular instance. I wouldn't sit here an claim that same model would be useful for pricing diamonds that weighed one carat or two carats, so you need to think and define what the scope of. Of the model, where is it going to be applied. So those are the inputs, outputs, and the scope of the model. Then once you've got those basic building blocks defined, you're going to formulate the model and that's very much an art as well as a science. It's going to be a step that involves your understanding of the underlying business process, and it's where all of those mathematical and statistical ideas come in through the model formulation. So we have created a model. Then once you've created the model you shouldn't just go and use it. You need to think about whether or not. That model is performing well, and in particular two of the activities that we typically go through once we have created a model are a sensitivity analysis. So all of the models take inputs, their underlying assumptions. How sensitive are the outputs to those inputs. And identifying where those sensitivity lie. Helps us understand the value of the model and where, in particular, we might be reticent in using it so there's a sensitivity analysis. There's also what I would term a validation of the model forecast so oftentimes, the models are going to be used in some forecasting or prediction context. And it would be foolish to use a model that was creating forecasts without at some point looking to see whether or not those forecasts were close to the actual values that ultimately were observed. And so, sometimes that's sort of easy to do. We, When there's an election, you can look at a political poll that will try and tell you who's going to win the election. Then the election happens and you actually get a point that you can validate the initial polls against. So oftentimes there is an ultimate realization, so for example maybe we have a model for the price of oil in one year's time. So I'll make my forecast, then what I should do is in one year look to see what the price of oil actually is, and see how close my forecast is to the actual price. Now validation takes many forms. That's sort of what I've discussed was a looking out into the future. Maybe your data doesn't come over time, your model isn't a time series model. Then what one often does is withhold some of the data from the model itself. And we call that a holdout sample. And then what we might do is fit the model, train the model on a subset of the data that we have available and look to see how well it forecasts the holdout sample. So there should typically be some validation process after the model has been created. Then if you're happy with the validation and the sensitivity analysis you ask the big question. And the big question is not is the model right? Because as I've said almost every model you create is going to be a simplification. So it's not going to be perfect. That's an unrealistic assumption. And that's why I've put in here, is the model fit for purpose? And so that is a question. That the person creating the model has to decide. Is it suitable for the purpose that it's being used for. Not, is it right? But, is it helpful? And there's a very famous saying by Professor Box who said all models are wrong but some are useful, and that's the idea that I'm trying to get at when I say is the model fit for purpose rather than is the model right. Now if it's not fit for purpose, if you're not happy with your model. Then you're going to go back and revisit some of the initial steps. Maybe you need some additional inputs. Maybe you've been using your model out of scope. And so you need to redefine your scope. And certainly you might need to reformulate the model. As you realize, as I say, for example, that an important variable had been missed out of the model. And so it is an inherently iterative process, this model building. In my own experience, I have never managed to write down a model and use it the first time around. There's always this feedback component. And so you shouldn't feel that that is a failure in any sense. It's absolutely to be expected. But at some point hopefully you declare your model fit for purpose and then you go into the ultimate activity, which is to implement it. And that's the part that takes you to the spreadsheet modeling component of the specialization. So those are the key steps in the modeling process. Now, as I've alluded to, there is an iterative component to this, and so what happens if the model doesn't work? What happens if some of our forecasts are lousy, is that the end of the world. Well, I don't think so. In fact, when the observed outcome from the model differs greatly from the model's predictions, so it was a lousy predicting model, hopefully not everywhere, but maybe one or two points or observations. Then it turns out that that can be very, very informative, because if you can identify the reason why your model has not predicted or performed well, you've probably learned something new that you didn't know before. And that Is one of the great benefits of modeling, the actual ability to learn new things through the process by realizing that your current understanding isn't able to map to reality. And I've got an example in a couple of the modules coming up that will make that point more explicit. And I would certainly come back to it. So the story is not to be totally disappointed if the model isn't always working. There's an opportunity to learn something new there. It's definitely the case that modeling is continuous. It's an evolutionary process. And ultimately, as we identify the weaknesses and limitations and iterate through the modeling process, we hope to be able to overcome some of those limitations. So an initial model not working well is not the end of the world. It's a chance to learn. That's how I think about it.