11/5/2006 A Bayesian Network Model ... 1

A Bayesian Network Model of Stromatolite Formation

[Figure adapted from A. C. Allwood et al. Stromatolite reef from the Early Archaean era of Australia. Nature 441 (8 June 2006), 714-718.]

Jack K. Horner

Science Applications International Corporation

jhorner@cybermesa.com

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Problem statement

• Stromatolites are attached, lithified sedimentary growth structures, accretionary away from a point or limited surface of initiation.

• Whether stromatolites have a biotic origin is vigorously debated

• If biotic in origin, the oldest (~3.5 billion years before present) were created by some of the first forms of terrestrial life

• Because no single piece of evidence at present could decide whether stromatolites are of biotic origin, the debate depends significantly on how to interpret the “evidence as a whole”

• How do we rigorously represent the notion of the “evidence as a whole”?

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Some requirements (Abstracted from Allwood et al., op. cit.)

• Cone surfaces have a consistent/inconsistent vertical depth• There are systematic differences/similarities between the

texture of the cone surfaces and the texture of the laminae between the cones

• The cones are heterogeneously/homogeneously spaced• The cones are absent_from/present_in deep water • The cone surfaces exhibit/don’t_exhibit 250-fold enhanced

rare earth element (REE) composition• The structure of the cone surfaces is consistent/inconsistent

with the mat structure of several biotic sources• At many sites, individual instances of a given type of cone

share/don’t_share common depositional characteristics, over an extended geographic region

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Implementation (Bayesian network)[Origin is the only hypothesis variable, all others are evidence variables. P(Origin = Biotic | X = “upper value”) = 0.9, where X ≠ Types_syndepositional is an evidence

variable; else P(Origin = Biotic | X) ~ 0.1N, where N is number of types syndepositional. Argument from Allwood et al., op. cit., is shown.]

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Some results (sensitivity of Origin to evidence variables)

Evidence Variable Mutual Information

Quadratic Score

Absent from deep water

0.53100 0.1600000

Similar to biotic mats

0.53100 0.1600000

Cone surface 0.53100 0.1600000

Enhanced REE 0.53100 0.1600000

Constant cone depth 0.53100 0.1600000

Non-uniform cone spacing

0.53100 0.1600000

Types syndepositional 0.24666 0.0766751

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Discussion

• Many inference topologies are possible– at present, the literature does not motivate anything more

complicated than the model shown above– the Bayesian network method can naturally accommodate

more complexity if needed• Requirements do not uniquely determine the

conditional probabilities – this is a common feature of scientific explanations– the Bayesian network method allows us to rigorously

compare effects of probability assignments (e.g., results are almost identical if P(Origin = Biotic | X = “upper value on Slide 4”) = 0.7 (instead of 0.9)