Points of Significance: Bayesian networks

Journal name:
Nature Methods
Volume:
12,
Pages:
799–800
Year published:
DOI:
doi:10.1038/nmeth.3550
Published online

Abstract

For making probabilistic inferences, a graph is worth a thousand words.

At a glance

Figures

  1. Bayesian network of regulation between five genes.
    Figure 1: Bayesian network of regulation between five genes.

    (a) A five-gene regulation pathway. A and B activate C. C and B inhibit E, and B inhibits D. (b) Bayesian network representation of the regulation pathway with interactions parameterized as probabilities of the active state. Conditional probabilities for nodes C, D and E describe dependencies on parent nodes. A bar plot of the probability table helps with quantitative comparisons. (c) Prior probabilities calculated from the conditional probabilities in b. All values are probabilities of the active state expressed in percent and rounded to the nearest integer.

  2. Observing the state of a node can change the estimate of the states of other nodes.
    Figure 2: Observing the state of a node can change the estimate of the states of other nodes.

    Shown are posterior probabilities updated from the priors from Figure 1c (and the difference computed using rounded probabilities except for D, for which these differences are small) using observations about nodes. (a) Observations propagate along serial chains, such as Aright arrowCright arrowE. By observing A active, C's posterior P(C|A) = 76% increases by 13% from the prior P(C) = 63%. B and D are unaffected. (b) Effect of observation can propagate backwards along a path. Observing C affects posteriors of all nodes—its causes and effects. (c) Propagation of information can be altered by observations. Once C is observed, observations about A now influence B and D but no longer influence E. (d) Observing something about an effect changes our estimates of all of its causes.

  3. Observation about child nodes creates conditional dependencies and independencies between its parent nodes on different paths.
    Figure 3: Observation about child nodes creates conditional dependencies and independencies between its parent nodes on different paths.

    (a) Observation about A and D does not create new conditional relationships. (b) Observation about B, C and E generates both dependencies and independencies. Observing C or E causes A and B (or D) to influence each other. Observing B or C splits the model and blocks propagation (e.g., D and E become independent).

References

  1. Needham, C.J., Bradford, J.R., Bulpitt, A.J. & Westhead, D.R. PLoS Comput. Biol. 3, e129 (2007).
  2. Beaumont, M.A. & Rannala, B. Nat. Rev. Genet. 5, 251261 (2004).
  3. Puga, J.L., Krzywinski, M. & Altman, N. Nat. Methods 12, 277278 (2015).
  4. Nagarajan, R., Scutari, M. & Lèbre, S. Bayesian Networks in R with Applications in Systems Biology (Springer, 2013).

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Author information

Affiliations

  1. Jorge López Puga is a Professor of Research Methodology at Universidad Católica de Murcia (UCAM).

  2. Martin Krzywinski is a staff scientist at Canada's Michael Smith Genome Sciences Centre.

  3. Naomi Altman is a Professor of Statistics at The Pennsylvania State University.

Competing financial interests

The authors declare no competing financial interests.

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