What Markov is
In statistics, Markov is a type of probabilistic model that describes a system which changes over time and evolves according to a set of rules. It is used to study the evolution of a process over time and to predict future outcomes.
The Markov process consists of the following steps:
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Define the states: The first step is to define the states of the system. These states can be anything from a number of different variables or objects.
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Define the transition probabilities: The second step is to define the transition probabilities from one state to another. This is done by defining the probability of transitioning from one state to another.
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Define the initial state: The third step is to define the initial state of the system. This is the starting point of the process and is usually determined by the initial conditions of the system.
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Calculate the probabilities: The fourth step is to calculate the probabilities of transitioning from one state to another. This is done by examining the transition probabilities and the initial state of the system.
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Predict the future states: The fifth step is to predict the future states of the system. This is done by using the transition probabilities and the initial state of the system to calculate the probability of transitioning from one state to another over time.
Examples
- Markov Chain Monte Carlo (MCMC) is a statistical technique used to generate samples from a probability distribution.
- Markov Chain is used to model a sequence of events, such as stock prices or weather.
- Markov Chain can be used to predict future behavior based on past data.
- Markov Decision Processes are used to model decision making under uncertainty.
- Markov Models are used to analyze the transition probabilities between states in a process.
- Markov Chains are used to analyze the probability of a given outcome based on a sequence of events.