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Markov models—Markov chains

You can look back there to explain things, but the explanation disappears. You’ll never find it there. Things are not explained by the past. They’re explained by what happens now. –Alan Watts

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Fig. 1: State transition models, transition matrices T, and the number of transitions required to approximate the steady-state limiting distributions, Tn (n→∞), to the displayed number of decimal places.
Fig. 2: Effect of the initial state (G, M) on the state evolution of 5,000 Markov chains with 20% and 40% chances of arrest.


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Correspondence to Martin Krzywinski.

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Grewal, J.K., Krzywinski, M. & Altman, N. Markov models—Markov chains. Nat Methods 16, 663–664 (2019).

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