Imagine you are a company selling a fast-moving consumer good in the market.
Let’s assume that the customer would follow the given journey to make the final purchase: These are the states at which the customer would be at any point in the purchase journey.
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.
Markov Chains:
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
Classic Example
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:
Source: Wikipedia
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.
Initial Vector
Final Vector
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….
Comment
I think an article on how to create a transition matrix would help.
Hi Nitin, Faridat: The probabilities in the transition matrix are calculated based on ratio between: 1. The initial no. Of customers in each state 2. The no. Of customers in each state finally
Great! Another article on how to buil the transition matrix will be welcomed.
Great explanation. How do we create transition matrixes? Any intuitions or guidelines, say with your ad example?
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