markov chains - explained #maths #statistics #mathematics #machinelearning #datascience

2026-02-08 · Source: DataMListic · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Novice, quick

Summary

Markov chains are probabilistic systems where the future state depends solely on the current state, not on past states. These systems are defined by a set of states, such as "sunny" or "rainy" for weather prediction, and transition probabilities that dictate the likelihood of moving from one state to another. For example, if it's sunny today, there might be an 80% chance it stays sunny and a 20% chance it becomes rainy. These probabilities are organized into a transition matrix P, where each row represents a starting state and each column an ending state, with each row summing to one. When combined with an initial state distribution, a Markov chain's probabilities evolve over time, eventually converging to a steady-state distribution, regardless of the initial conditions.

Key takeaway

For data scientists modeling sequential events, understanding Markov chains is crucial for predicting long-term behavior. You should define your system's states and their transition probabilities to construct a transition matrix, then simulate its evolution to identify steady-state distributions, which reveal the system's inherent long-term tendencies irrespective of initial conditions.

Key insights

Markov chains model systems where future states depend only on the present state, defined by transition probabilities.

Principles

• Future state depends only on present state.
• Probabilities leaving a state sum to one.

Method

Define states, assign transition probabilities between them, encode these in a transition matrix, and apply iteratively with an initial state distribution to observe convergence to a steady state.

In practice

• Predict weather patterns.
• Analyze stock price movements.

Topics

• Markov Chains
• Transition Probabilities
• Transition Matrix
• Steady State Analysis
• Stochastic Processes

Best for: AI Student, Data Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by DataMListic.