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Markov models—Markov chains

Nature Methods volume 16, pages 663–664 (2019)Cite this article

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

To model biological systems that undergo change, it is not strictly necessary to know the details of the underlying mechanisms. Instead, we can model change as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another. Together with the states, these transition probabilities define a stochastic model with the Markov property: transition probabilities depend on only the current state—the future can be considered independently of the past if the present is known.

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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.

References

  1. Skewes, A. D. & Welch, R. D. PeerJ 1, e127 (2013).

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Authors and Affiliations

  1. PhD candidate, Canada’s Michael Smith Genome Sciences Centre, Vancouver, BC, Canada

    Jasleen K. Grewal

  2. Staff scientist, Canada’s Michael Smith Genome Sciences Centre, Vancouver, BC, Canada

    Martin Krzywinski

  3. Professor of Statistics, The Pennsylvania State University, University Park, PA, USA

    Naomi Altman

Authors
  1. Jasleen K. Grewal
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  2. Martin Krzywinski
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  3. Naomi Altman
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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). https://doi.org/10.1038/s41592-019-0476-x

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