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Statistics Colloquium

November 16 (Fri) 11 a.m.

Alavi Commons Room, 6625 Everett Tower

Casey Jelsema

Department of Statistics

Western Michigan University

Coal is an important natural resource throughout the world and the United States. It is classified into four main categories based on geochemical properties; the percentage of moisture, volatile material, carbon content, and ash. Samples are taken only at point locations, but we would like to develop a model able to characterize these geochemical components over a region. But this type of data, known as compositional data (CoDa) require special care due to the constant sum (e.g. 100% or 1). Failure to consider this will result in a negative bias in the covariances when modeling. Therefore, compositional data is typically analyzed via some form of a log-ratio transformation. For instance, the centered log-ratio takes the log of each component after dividing by the product of all components; the log-ratio may then be analyzed with standard methods. Instead of treating these log-ratios as Gaussian, we consider the ratios of components as log-normal. We develop multivariate log-normal kriging and block kriging equations to predict the geochemical properties at point locations and over a region of finite area, together with measures of precision.

When spatial datasets become large computation becomes difficult or impossible to handle efficiently. Fixed Rank Kriging (FRK) is a powerful tool which overcomes this problem through rank reduction. We show how to implement our log-normal kriging and block kriging equations through FRK. To illustrate our methods we analyze the geochemical components of coal samples taken throughout the state of Illinois, obtained through the Illinois State Geological Survey.

All statistics students are expected to attend.

Past colloquiums