Algorithms - Markov Models : Markov Chain
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Markov chain
A Markov chain is the simplest Markov model. It is a discrete random process with the property that the next state depends only on the current state:
$$P(X_n | X_1, X_2, \ldots X_n-1) = P(X_n | X_{n-1})$$Markov chain example
Let's think about the weather. Suppose, the weather follows Markov chain model: The weather of today can be predicted by only using yesterday's weather information.
Let's assume we have only two kinds of weather: Rainy and Sunny.
- When it is rainy on one day the next day is Sunny with probability 0.3 => $P(S|R) = 0.3$, $P(R|R) = 0.7$
- When it is Sunny, the probability for Rain next day is 0.4 => $P(R|S) = 0.4$, $P(S|S) = 0.6$
Question: Today Sunny, what's the weather of the day after tomorrow look like?
Sunny: 0.4*0.3 + 0.6*0.6 = 0.48, Rainly: 1-0.48 = 0.52
So, the weather for the day after tomorrow - 48% chance of sunny day, and 52% chance of rainy day.
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