Closed-skew Distributions: Simulation, Inversion and Parameter Estimation

Abstract

Bayesian closed-skew Gaussian inversion is defined as a generalization of traditional Bayesian Gaussian inversion. Bayesian inversion is often used in seismic inversion, and the closed-skew model is able to capture the skewness in the variable of interest. Different stationary prior models are presented, but the generalization comes at a cost, simulation from high-dimensional pdfs and parameter inference from data is more complicated. An efficient algorithm to generate realizations from the high-dimensional closed-skew Gaussian distribution is presented. A full-likelihood is used for parameter estimation of stationary prior models under exponential dependence structure. The simulation algorithms and estimators are evaluated on synthetic examples. Also a closed-skew T-distribution is presented to include heavy tails in the pdf and the model is presented with some examples. In the last part the simulation algorithm, the different prior models and parameter estimators are demonstrated on real data from a well in the Sleipner Øst field. The full-likelihood estimator seems to be the best estimator for data with exponential dependence structure