Markov Chain
A Markov Chain is a mathematical system that undergoes transitions from one state to another according to a certain probabilistic rule.The defining characteristic of a Markov chain is that no matter what the processarriveThe current state and possible future states are fixed. It is a stochastic model that describes a series of possible events, where the probability of each event depends only on the state reached by the previous event. This can be thought of as "what happens next depends only on the current state of things." For example, the probability of x at step n+1 depends only on step n, not on the complete sequence of steps before n. This property is called the Markov property or memorylessness.
Applications of Markov Chains
Markov chains make the study of many real-world processes much simpler and easier to understand. Using Markov chains, we can derive some useful results, such as stationary distributions, etc.
- MCMC (Markov Chain Monte Carlo) is a method for solving the normalization factor problem based on Markov chain.
- Markov chains are used in information theory, search engines, speech recognition, etc.
- Markov chains have great possibilities, future and importance in the field of data science. Interested readers are requested to learn these things properly and become competent people in the field of data science.
Assumptions of Markov Chains
- A statistical system contains a finite number of states.
- These states are mutually exclusive and collectively exhaustive.
- The probability of transitioning from one state to another is constant over time.
Markov processes are quite common in real-life problems, and Markov chains are easy to implement due to their memoryless properties. Using Markov chains, we can simplify the problem without affecting its accuracy.