Probability Aggregation Methods in Geoscience

Allard D, D’Or D, Froidevaux R (2011) An efficient maximum entropy approach for categorical variable prediction. Eur J Soil Sci 62(3):381–393

Bacharach M (1979) Normal Bayesian dialogues. J Am Stat Assoc 74:837–846

Benediktsson J, Swain P (1992) Consensus theoretic classification methods. IEEE Trans Syst Man Cybern 22:688–704

Bordley RF (1982) A multiplicative formula for aggregating probability assessments. Manag Sci 28:1137–1148

Brier G (1950) Verification of forecasts expressed in terms of probability. Mon Weather Rev 78:1–3

Bröcker J, Smith LA (2007) Increasing the reliability of reliability diagrams. Weather Forecast 22:651–661

Cao G, Kyriakidis P, Goodchild M (2009) Prediction and simulation in categorical fields: a transition probability combination approach. In: Proceedings of the 17th ACM SIGSPATIAL international conference on advances in geographic information systems, GIS’09. ACM, New York, pp 496–499

Christakos G (1990) A Bayesian/maximum-entropy view to the spatial estimation problem. Math Geol 22:763–777

Chugunova T, Hu L (2008) An assessment of the tau model for integrating auxiliary information. In: Ortiz JM, Emery X (eds) VIII international geostatistics congress, Geostats 2008. Gecamin, Santiago, pp 339–348

Clemen RT, Winkler RL (1999) Combining probability distributions from experts in risk analysis. Risk Anal 19:187–203

Clemen RT, Winkler W (2007) Aggregating probability distributions. In: Edwards W, Miles RF, von Winterfeldt D (eds) Advances in decision analysis. Cambridge University Press, Cambridge, pp 154–176

Comunian A (2010) Probability aggregation methods and multiple-point statistics for 3D modeling of aquifer heterogeneity from 2D training images. PhD thesis, University of Neuchâtel, Switzerland

Comunian A, Renard P, Straubhaar J (2011) 3D multiple-point statistics simulation using 2D training images. Comput Geosci 40:49–65

Cover TM, Thomas JA (2006) Elements of information theory, 2nd edn. Wiley, New York

Dietrich F (2010) Bayesian group belief. Soc Choice Welf 35:595–626

Genest C (1984) Pooling operators with the marginalization property. Can J Stat 12:153–165

Genest C, Wagner CG (1987) Further evidence against independence preservation in expert judgement synthesis. Aequ Math 32:74–86

Genest C, Zidek JV (1986) Combining probability distributions: a critique and an annotated bibliography. Stat Sci 1:114–148

Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J Am Stat Assoc 102:359–378

Heskes T (1998) Selecting weighting factors in logarithmic opinion pools. In: Jordan M, Kearns M, Solla S (eds) Advances in neural information processing systems, vol 10. MIT Press, Cambridge, pp 266–272

Journel A (2002) Combining knowledge from diverse sources: an alternative to traditional data independence hypotheses. Math Geol 34:573–596

Krishnan S (2008) The Tau model for data redundancy and information combination in earth sciences: theory and application. Math Geosci 40:705–727

Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22:76–86

Lantuéjoul C (2002) Geostatistical simulations. Springer, Berlin

Lehrer K, Wagner C (1983) Probability amalgamation and the independence issue: a reply to Laddaga. Synthese 55:339–346

Mariethoz G, Renard P, Froidevaux R (2009) Integrating collocated auxiliary parameters in geostatistical simulations using joint probability distributions and probability aggregation. Water Resour Res 45(W08421):1–13

Okabe H, Blunt MJ (2004) Prediction of permeability for porous media reconstructed using multiple-point statistics. Phys Rev E 70(6):066135

Okabe H, Blunt MJ (2007) Pore space reconstruction of vuggy carbonates using microtomography and multiple-point statistics. Water Resour Res 43(W12S02):1–5

Polyakova EI, Journel AG (2007) The nu expression for probabilistic data integration. Math Geol 39:715–733

Ranjan R, Gneiting T (2010) Combining probability forecasts. J R Stat Soc B 72:71–91

Schwartz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464

Stone M (1961) The opinion pool. Ann Math Stat 32:1339–1348

Strebelle S, Payrazyan K, Caers J (2003) Modeling of a deepwater turbidite reservoir conditional to seismic data using principal component analysis and multiple-point geostatistics. SPE J 8:227–235

Tarantola A (2005) Inverse problem theory. Society for Industrial and Applied Mathematics, Philadelphia

Tarantola A, Valette B (1982) Inverse problems = quest for information. J Geophys 50:159–170

Wagner C (1984) Aggregating subjective probabilities: some limitative theorems. Notre Dame J Form Log 25:233–240

Winkler RL (1968) The consensus of subjective probability distributions. Manag Sci 15:B61–B75