As a digital marketer, you’d be forgiven if you’ve never heard of Bayes’ theorem. However, in many of the predictive and machine learning technologies you interact with, it’s likely that Bayes’ theorem is involved. This is because it’s a very important way to calculate and predict the probability of an event. It uses prior knowledge or experience to do this, and is very easily executed in machine learning. It’s named after Thomas Bayes, a British mathematician from the 18th century.
In mathematical notation, Bayes’ theorem is commonly expressed as:
P(A|B) = (P(B|A) x P(A)) / P(B)
Let’s break this down in plain English so that it’s easier to understand for non-maths folk. We’ll start with the left hand side of the equation, where we are calculating the probability of event A happening, given that another event B has happened. Notice the vertical pipe character, that represents the “given that” part of the phrase. The theorem states that this probability is equal to the right hand side of the equation.
It’s a bit long, so let’s take a look at the first part in brackets. Here, we have the probability of event B happening given that event A has happened. This is then multiplied by the probability of event A taking place. All of this is divided by the probability of event B happening.
Bayes’ theorem is often used in statistics and machine learning to update beliefs or hypotheses based on new evidence. It is also commonly used in product recommendations, spam filtering, and retargeting ads.
For example, let’s say we want to calculate the probability of a user adding a product to the basket after they have viewed the product details. We could run this through Bayes’ theorem, so long as we know information such as typical product add to basket rate, and product details page view rate.
By inputting these metrics into Bayes’ theorem, we can update our initial belief about the likelihood of the user adding to basket based on their behaviour of viewing the product details. This can in turn help marketers and UX designers, as they’ll be able to update their ecommerce store layouts to help facilitate a user’s experience..
Overall, Bayes’ theorem provides a useful framework for reasoning about uncertain events and making predictions based on available data. For marketing purposes, using Bayes’ theorem can provide a statistical hint on how to proceed with optimisation decisions. With the right type of data set, it could be applied to predict if a user will add to basket if they first view a certain page. Because nothing is guaranteed, probabilities will help with your decision making, rather than telling you what to do.