Abstract
A geological map is the representation, on a two-dimensional plane, of the disposition of three-dimensional rock bodies exposed on the earth's surface. The problem of mapping is essentially that of dividing an area into “homogeneous” subregions on the basis of the exposed rock types. Automatic Bayesian methods of model selection using default Bayes factors have been employed to solve the problem of choosing a set of boundaries between “homogeneous” subregions, assuming no complication excepting low-angle tilting affected rock bodies. The method is tested on two data sets. A sampling scheme for optimum allocation of observation points is also presented.
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REFERENCES
Aitchison, J., 1986, The statistical analysis of compositional data: Chapman and Hall, London, 416 p.
Atkinson, A. C., 1978, Posterior probabilities for choosing a regression model: Biometrika, v. 65, p. 39–48.
Berger, J. O., and Pericchi, L. R., 1996, The intrinsic Bayes factor for model selection and prediction: J. Am. Stat. Assoc., v. 91, p. 109–122.
Berger, J. O., Pericchi, L. R., and Varshavsky, J. A., 1998, Bayes factors and marginal distributions in invariant situations: Sankhya, Ser. A, v. 60, p. 307–321.
Fishman, G. S., 1978, Principles of discrete event simulation: JohnWiley and Sons, New York, 514 p.
Geisser, S., and Eddy, W. F., 1979, A predictive approach to model selection: J. Am. Stat. Assoc., v. 74, p. 153–160.
Gelfand, A. E., Dey, D. K., and Chang, H., 1992, Model determination using predictive distributions with implementation via sampling-based methods (with discussion), in Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M., eds., Bayesian statistics, Vol. 4: Oxford University Press, London, p. 147–167.
Ghosh, J. K., Saha, M. R., and Sengupta, S., 1981, Gondwana stratigraphic classification by statistical method, in Merriam, D. F., ed., Down-to-earth statistics: Solutions looking for geological problems: Syracuse University Geology Contributions, Syracuse, New York, p. 47–62.
O'Hagan, A., 1995, Fractional Bayes factor for model comparisons: J. R. Stat. Soc., Ser. B, v. 57, p. 99–138.
San Martini, A., and Spezzaferri, F., 1984, A Predictive model selection criterion: J. R. Stat. Soc., Ser. B, v. 46, p. 296–303.
Sengupta, S., 1970, Gondwana sedimentation around Bheemaram (Bhimaram), Pranhita-Godavari valley, India: J. Sed. Pet., v. 40, p. 140–170.
Sengupta, S., Ghosh, J. K., and Mazumder, B. S., 1991, Experimental-theoretical approach to interpretation of grain size frequency distributions, in Syvitski, J. P. M., ed., Principles, methods, and application of particle size analysis: Cambridge University Press, Cambridge, UK, p. 264–279.
Spiegelhalter, D. J., and Smith, A. F. M., 1982, Bayes factor for linear and log-linear models with vague prior information: J. R. Stat. Soc., Ser. B, v. 44, p. 377–387.
Switzer, P., 1967, Reconstructing patterns from sample data: Ann. Math. Stat., v. 38, p. 138–154.
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Ghosh, J.K., Bhanja, J., Purkayastha, S. et al. A Statistical Approach to Geological Mapping. Mathematical Geology 34, 505–528 (2002). https://doi.org/10.1023/A:1016038710777
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DOI: https://doi.org/10.1023/A:1016038710777