Stochastic simulation of patterns using Bayesian pattern modeling
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In this paper, a Bayesian framework is introduced for pattern modeling and multiple point statistics simulation. The method presented here is a generalized clustering-based method where the patterns can live on a hyper-plane of very low dimensionality in each cluster. The provided generalizationallows a remarkable increase in variability of the model and a significant reduction in the number of necessary clusters for pattern modeling which leads to more computational efficiency compared with clustering-based methods. The Bayesian model employed here is a nonlinear model which is composed of a mixture of linear models. Therefore, the model is stronger than linear models for data modeling and computationally more effective than nonlinear models. Furthermore, the model allows us to extract features from incomplete patterns and to compare patterns in feature space instead of spatial domain. Due to the lower dimensionality of feature space, comparison in feature space results in more computational efficiency as well. Despite most of the previously employed methods, the feature extraction filters employed here are customized for each training image (TI). This causes the features to be more informative and useful. Using a fully Bayesian model, the method does not require extensive parameter setting and tunes its parameters itself in a principled manner. Extensive experiments on different TIs (either continuous or categorical) show that the proposed method is capable of better reproduction of complex geostatistical patterns compared with other clustering-based methods using a very limited number of clusters.
KeywordsMultiple point statistics Geostatistics Stochastic simulation Bayesian pattern modeling Mixture modeling
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- 2.Isaaks, E.: The application of Monte Carlo methods to the analysis of spatially correlated data. Ph.D. thesis, Stanford University (1990)Google Scholar
- 5.Mariethoz, G., Renard, P., Straubhaar, J.: The Direct Sampling method to perform multiple-points geostatistical simulations. Water Resour. Res. (2010) doi: 10.1029/2008WR007621
- 7.Tjelmeland, H., Eidsvik, J.: Directional Metropolis–Hastings updates for posteriors with nonlinear likelihood. In: Leuangthong, O., Deutsch, C.V. (eds.) Geostatistics, pp. 195–104. Springer, Banff (2004)Google Scholar
- 8.Tjelmeland, H.: Stochastic models in reservoir characterization and Markov random fields for compact objects. Doctoral dissertation, Norwegian University of Science and Technology, Trondheim (1996)Google Scholar
- 9.Kjønsberg, H., Kolbjørnsen, O.: Markov mesh simulations with data conditioning through indicator kriging. In: Proceedings of the 8th International Geostatistics Congress. Santiago, Chile (2008)Google Scholar
- 10.Lyster, S., Deutsch, C.V.: MPS simulation in a Gibbs sampler algorithm. In: Proceedings of the 8th International Geostatistics Congress. Santiago, Chile (2008)Google Scholar
- 17.Bishop, C.M., Winn, J.: Non-linear Bayesian image modeling. In: Proceedings of the 6th European Conference on Computer Vision. Dublin, Ireland (2000)Google Scholar
- 22.Caers, J., Journel, A.G.: Stochastic reservoir simulation using neural networks trained on outcrop data. SPE paper 49026 (1998)Google Scholar
- 23.Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Prentice Hall, Upper Saddle River (2008)Google Scholar
- 24.Jolliffe, I.T.: Principal Component Analysis, 2nd edn. Springer, Heidelberg (2002)Google Scholar
- 31.Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)Google Scholar