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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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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 A Bayesian Network Model ...
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”? A Bayesian Network Model ...
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 A Bayesian Network Model ...
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.] A Bayesian Network Model ...
Some results (sensitivity of Origin to evidence variables) A Bayesian Network Model ...
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 methodallows 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) A Bayesian Network Model ...