Anyone knows about Markov Chains?

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In summary, a Markov Chain is a mathematical model used to describe a sequence of events where the probability of each event only depends on the previous event. They are widely used in science, including fields such as physics, biology, economics, and computer science, to model systems with randomness. The key components of a Markov Chain are states, transition probabilities, and an initial state. Unlike other mathematical models, Markov Chains only consider the current state of a system and do not take into account previous states. Real-world examples of Markov Chains include predicting stock market trends, analyzing customer behavior in marketing, and predicting weather patterns, as well as being used in machine learning and artificial intelligence algorithms.
  • #1
nktvnvn
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Hi all

Does anyone in this forum have a firm understanding of Markov Chains? I searched for this thing on the Net but could not find very useful information. Most of them are very abstract.

I appreciate it if anyone can please show me an easy-to-follow example to illustrate the purpose of Markov Chains.

Thanks a lot.
 
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  • #3
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1. What is a Markov Chain?

A Markov Chain is a mathematical model that describes a sequence of events where the probability of each event depends only on the previous event. It is a type of stochastic process and is used to model systems that have a random component.

2. How are Markov Chains used in science?

Markov Chains are widely used in many scientific fields, including physics, biology, economics, and computer science. They are used to model systems that involve randomness, such as weather patterns, stock market trends, and biological processes.

3. What are the key components of a Markov Chain?

The key components of a Markov Chain include states, transition probabilities, and an initial state. States represent the different possible outcomes of a system, transition probabilities represent the likelihood of moving from one state to another, and the initial state determines where the chain starts.

4. How are Markov Chains different from other mathematical models?

Markov Chains differ from other mathematical models in that they only consider the current state of a system and do not take into account previous states. This makes them simpler to use and analyze, but also limits their application to systems with memoryless properties.

5. What are some real-world examples of Markov Chains?

Markov Chains are used in many real-world applications, such as predicting stock market trends, analyzing customer behavior in marketing, and predicting weather patterns. They are also used in machine learning and artificial intelligence algorithms.

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