Imagine you are a company selling a fast-moving consumer good in the market.
Now, how to find out in which state the customers would be after 6 months?
Markov Chain comes to the rescue!!
Let’s first understand what Markov Chain is.
A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event
Markov Chain – States, Probabilities and Transition Matrix
Let’s delve a little deeper.
A Markov Chain provides:
Using the above two information, we can predict the next state.
In mathematical terms, the current state is called Initial State Vector.
So, what we get is:
Final State = Initial State *Transition Matrix
A classic example of Markov Chain is predicting the weather. We have two different weather conditions: Sunny and Rainy. Let’s assume today it is sunny. We have the following probabilities:
Here the initial vector is =
Transition Matrix =
Recollect the Final State = Initial State *Transition Matrix? The above represents the same.
So, what is the inference?
There is a 90% chance that the weather will be sunny on Day 2 and 10% chance that it will rain.
Back to the Problem
Coming back to the problem where we need to know what the state the customer is after 6 months of launching the product.
We can assume there are 4 states in which the customer can be at any point in time.
We have the following information:
The Marketing Analytics objective:
So, lets dive into the math part.
Note: A – Awareness, C – Consideration, P – Purchase, NP – No Purchase
Initial State Vector =
It would be clearer to see the movements among all 4 states diagrammatically.
Final States of Customers = Initial State Vector * Transition Matrix
Evaluation of the Result
Now let’s evaluate our results.
We can notice that the number of people under ‘Awareness’ and ‘Consideration’ have decreased. This is a good thing because, the people actually shifted from the state of ‘Awareness’ and ‘Consideration’ to the state of ‘Purchase’ (an increase of nearly 34% !!) Also notice that the number of people in ‘No Purchase’ states decreased (a decrease of 11%).
Overall our analysis goes to show that the campaign/ads has worked!!
Markov Chain has many other applications in Marketing Analytics and other fields such as NLP.
Stay tuned for more articles….