It’s clearly not enough that Bayesian already has it’s own page, but we HAD to write a blog on it, too. Not that we’re obsessed or anything.

You may have heard a lot about Bayesian modelling, but wondered what it is and whether you need it. I’ll try to explain.

Perhaps unsurprisingly, our stock image provider didn’t have much in the way of ‘Bayesian’

What is it?

There are many flavours of Bayesian modelling, some to do with conjoint analysis or other methodologies, but we are going to think about its specific application to econometric modelling. The main concept to grapple with here is the notion of a Prior. What this means is that you aren’t going to believe 100% what the data tells you.

A student pays careful attention whilst her teacher explains the finer points of Bayesian statistics

Why would you not believe your data 100%?

Many reasons, but the main one being that your data may not be very good. And, in fact, probably isn’t. This issue is often ducked in the world of econometrics. A strict statistician will probably tell you that many of the variables you’d like to put into the model fail the basic tests that data should pass. Think of this like the MOT of data. So, it should be independent, not heteroscedastic, uncorrelated with other variables and so on and so forth.

Sadly, the real world is not like this. This is all YOUR fault because you didn’t set up your activity to be modelled econometrically. You didn’t set up scientifically designed structures. What you did is a bunch of stuff and now you want to know which bits of it worked.

Now in some cases this might be a lot worse than others. You should in many cases, working with a good experienced modeller with decent quality data, get a decent result. However, in cases where the data is poor you have a decision to make, namely this: believe it, or ignore it. Which is fine. But do we believe there is ANY value in this data at all? Possibly.

This is where the Bayesian part comes in. We can tell the model we think there is a high likelihood that the price elasticity should be in this range, and to model around this assumption. This is our “Prior”. We re-run the model, now incorporating our Prior, and the results make sense.

Nobody does this for real though, do they?

The thing is that we are all Bayesians without knowing it. The weather forecast says its going to pour with rain. You look outside. It’s sunny. You say, well the weather forecast is often wrong, and go out in your shorts, but you pack a lightweight rain top. You’ve taken in data (it will rain), blended it with your Prior (that the forecast is often wrong, and it looks sunny) and come up with a sensible solution. You do it at work too. You read a research report from a company you have never heard of. “I don’t believe that!”. It doesn’t fit with everything else you know. So, you discount it. You’re putting heavy emphasis on your Prior. What if the research was conducted by the most respectable university over a period of 30 years and validated by 3 other internationally renowned professors? Hmm you might say, I’ll sleep on it. So now your information is starting to balance your prior.

Ok, it’s a man… he’s on the beach. And he has an umbrella. Is he a Bayesian or just British?

So why doesn’t everybody do this all the time?

It’s difficult. The method used to build conventional econometric models (Ordinary Least Squares, or OLS) doesn’t work here, and we must turn to advanced estimation and computational methods. These take much more skill, time and effort, and so therefore cost significantly more.

Practical applications

Here are some situations where Bayesian econometrics may help.

  1. We have data for one country that is poorer quality than data for another, similar country. We can just not bother and all go home, or we can set priors to say, “I think that Country A should act broadly like Country B but be a bit different.” Traditional econometrics doesn’t let you do this. It can only model them both together to say they behave exactly the same or model them independently, so they are totally different. Bayesian econometrics can handle this.
  1. We believe that 6 different creative executions should behave broadly similarly to each other but be somewhat different from each other. Again, Bayesian econometrics can deal with this type of question where traditional econometrics can’t.
  1. Data is correlated. So, when we do a price promotion we almost always get point of sale display. A traditional econometric model looks to have as few variables in as possible so will say, “Aha I can explain everything here with price and so I’ll ignore the POS data”. You’ll get an inflated Price elasticity and report to the business that POS does nothing. By applying a Bayesian Prior to our price impact, we can allow the POS effect to enter the model.

 

Summary

But…you’re just…making things up! No, not really. We’re applying past experience, other data and common sense to the imperfect data you have to come up with a sensible useful recommendation. The point is that our Priors have – should have – value in themselves, being the product of many years of experience and observation themselves.

When we put it like that, then it doesn’t sound too crazy.

Crazy-sounding or otherwise, for a chat about Bayesian or any other aspect of marketing analytics, feel free to get in touch.

Tom Lloyd