0:25

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

3:40

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.

5:13

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.

7:12

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