Integrating Bayesian Model Averaging for Uncertainty Reduction in Permeability Modeling

Abstract This paper describes a new procedure of model selection in linear regression analysis to efficiently model and predict the formation permeability in non-cored intervals. The simplest way of model selection in regression model is to adopt stepwise elimination that depends on the probability of null hypotheses. However, the new method is the Bayesian Model Averaging (BMA) that selects the most appropriate model for a given outcome variable based on Bayes factors. Model selection process in BMA considers model's posterior probability and Bayesian Information Criterion (BIC). BMA produces a posterior distribution of the outcome factor that represents the weighted average of the posterior distributions of that factor for each likely model. Only five models are selected that their posterior probabilities sum to be equal to one. The best model selection has the maximum posterior probability and minimum Bayesian Information Criterion; nevertheless, the model subset selection is determined when the probability of a non-zero predictor's coefficient is more than 90 % for the best sampled model. That means this predictor has an effect on the outcome and should be included in the regression model. All these variables are shown in the computed Occam's window. The results showed that MBA algorithm has to achieve perfect t-test and analysis of variance especially regarding the rejection of null hypotheses for all the subselected independent variables. In addition, the reduced BMA model has been evaluated through Mean Square Prediction Error (MSPE) and residual analysis that clearly shows uncertainty reduction in permeability estimation. Therefore, the predicted permeability values for the entire formation depth are much more compatible with the measured data than the linear regression model.