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I just want to understand Markov process on a deeper level. Here the rule is $P(Xt+1=xt+1| Xt=xt, ..., X1=x1) = P(Xt+1=xt+1| Xt=xt)$

But what confuses me is that those neglected events would be useful to construct a better transition matrix. I feel if I totally neglected the previous events, then I trade the known with the unknown!

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    $\begingroup$ You are mixing a probability model with stat inference. // The Markov Chain is a probability model with known prob's of movement among states. Given that info, you are trying to predict the next move given the current state. (Analogously, if you know a coin is fair, then you know the next toss has a 50-50 chance of showing Heads.) // If you have a reasonably long historical record of the sequences of past states, then you might be able to estimate transition probabilities of a MC. (Similarly, if you have a record of past H's and T's for a coin of unknown $p = $P(Heads) you can estimate $p.)$ $\endgroup$
    – BruceET
    Commented Dec 8, 2020 at 7:23
  • $\begingroup$ @BruceET thank you for your answer. But do you mean that I should not mix them! I think I need to get more deep to understand on what basis Markov chain is looking at one event! $\endgroup$
    – Omar113
    Commented Dec 8, 2020 at 9:10

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