Variations in MIK Class Means Jeremy Vincent Outline

Variations in MIK Class Means Jeremy Vincent

Outline • Overview of MIK Estimator • Review of initial results of indicator class-mean investigation • Cross validation study results • Problem statement driving future work 2

Review of MIK Estimator • The MIK estimator assumes a constant class mean, : • MIK generates a distribution of uncertainty at the estimated location, but it does not rely on a mathematical model. Motivating question: How does a constant class mean impact MIK estimation? 3

Class Mean Bias in Upper Tail Class Means of Gaussian Data Upper Tail Class Mean Log-Normal Data 4 Spatial Distribution of Estimation Error: Constant Class Mean vs. Correct Class Mean

Impact on Contained Metal • Preliminary results suggested the upper tail class mean was resulting in a bias in the contained metal 5

Cross Validation Study Conclusions • Cross validation confirms no global bias in the MIK estimator (expected). • Indicator probability weighting of the class mean shows it is unbiased with respect to the global class mean. 6

Future Work Problem statement: Given that MG Kriging will always outperform MIK with multivariate-Gaussian data, how non-Gaussian must the data be before MIK outperforms MG Kriging? 7

Future Work Gaussian Data • The exact indicator variograms are known for a bivariate Gaussian distribution: Indicator Class • Quantify difference between Gaussian and non-Gaussian data for corresponding indicator variograms. Non-Gaussian Data • Compare MG and MIK estimates and determine at which point MIK outperforms MG. 8 Indicator Class

Thank you! Questions? 9