1. 11/5/2006A 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

2. 11/5/2006A Bayesian Network Model...2 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”?

3. 11/5/2006A Bayesian Network Model...3 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

4. 11/5/2006A Bayesian Network Model...4 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.]

5. 11/5/2006A Bayesian Network Model...5 Some results (sensitivity of Origin to evidence variables) Evidence VariableMutual Information Quadratic Score Absent from deep water 0.531000.1600000 Similar to biotic mats 0.531000.1600000 Cone surface0.531000.1600000 Enhanced REE0.531000.1600000 Constant cone depth0.531000.1600000 Non-uniform cone spacing 0.531000.1600000 Types syndepositional0.246660.0766751

6. 11/5/2006A Bayesian Network Model...6 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)