1. Markov Chain analysis
So far, we've explored how multivariate distributions help us analyze business relationships and how conditional probability refines our predictions. Now, we'll take these concepts further by introducing Markov Chains, used for modeling customer behavior and decision-making over time.
2. What are Markov Chains?
Markov Chains are a framework used to model systems with different states they can be in. Transitioning between states is based on probabilities.
The idea behind Markov Chains is that the probability of moving to the next state depends only on the current state, not on how the system arrived at that state. This memoryless property makes Markov Chains a practical way to model sequential decisions and behaviors.
Markov Chains are particularly applied for understanding customer journeys, as customers often move through different stages, such as browsing, adding items to their cart, making a purchase, or leaving.
3. The elements of a Markov Chain
The basic building blocks of Markov chains are states. These are different conditions a system can be in. For example, sunny or cloudy.
4. The elements of a Markov Chain
States are linked through transitions. These are the probabilities of moving from one state to another.
For example, if it is sunny, there is 20% chance the next day will be cloudy.
A transition can also refer to staying in the same state. This is denoted by a self-loop. For example, if it's a sunny day, there is an 80% chance the next day will be sunny as well.
5. The elements of a Markov Chain
We also have steady-state probabilities. These are the long-term probabilities of being in a particular state after many transitions. They need to be calculated based on the transition matrix - a table of all transition probabilities using a specific formula. Statistical software or BI tools can handle this for you.
For example, if we were to input this matrix into statistical software to calculate the steady-state probability for sunny, the result would be 66.67%. This means that, in the long run, about two-thirds of the days will be sunny.
6. Applications of Markov Chains
Some common applications of Markov chains include:
Customer retention, by identifying transition probabilities between engagement and churn states to reduce attrition.
Conversion optimization: Understanding the likelihood of users progressing through a sales funnel.
Product recommendations, like predicting future customer interactions based on past behaviors.
7. Example: e-commerce$^1$
Markov Chains help businesses understand and predict customer movement through different stages by modeling the likelihood of transitions between various points in the customer journey. Let's explore this through an e-commerce case study.
Imagine an online retailer wants to improve its conversion rate by analyzing customer behavior on its website. The company identifies the following states for visitors:
C for Coupon: The visitor uses a coupon code.
P for Purchase: The visitor buys something.
E for Exit: The visitor leaves the website without purchasing.
8. Example: e-commerce
Using Markov Chains, the retailer can identify critical points where customers drop off and implement strategies to improve retention.
This leads us for example to the following insight:
9. Example: e-commerce
60% of customers who use a coupon complete a purchase, showing that discounts are effective in converting customers.
However, 30% still exit, meaning that not all coupon users are convinced to buy. And once a customer has left, 80% don't come back.
An actionable strategy could be to improve messaging around coupon use or reduce friction in the checkout process.
10. Let's practice!
In the next chapter, we'll shift our focus to measuring and managing uncertainty. For now, let's practice!