On September 19, Martin Šefl will give a seminar presentation to undergraduate mathematics and statistics students from Whitman College in Walla Walla, Washington. His presentation, which is a part of the Mathematical Sciences Foundry Talks series, will describe how a principal component regression can be used to estimate the total amount of plutonium in the entire skeleton, based on the activity concentrations in a limited subset of bones. When a person wills their entire body to the USTUR, laboratory staff measure the amount of plutonium in each of the 90 bone samples that are removed from the right side of the body. It is a straightforward task to add up all of individual bone activities, and multiply by two, to estimate the amount of plutonium in the entire skeleton. However, the bulk of donations to the USTUR are partial body donations, where typically two to eight bones are donated to the USTUR for radiochemical analysis. The concentration of plutonium in these bones must be used to calculate the concentration in the entire skeleton, which can then be used, along with the skeletal weight, to calculate the total activity in the skeleton. There are several methods for estimating the skeletal concentration from a limited subset of bones, and each method has its limitations. Notably, a multiple regression is not an appropriate tool for calculating the concentration of plutonium in the skeleton, because bone concentrations are highly correlated with each other. A principal component regression addresses the multicollinearity among bones, making it a more appropriate tool for this application. A brief introduction to principal component regression will be provided, and its application for estimating the plutonium concentration in the skeleton will be discussed.

^{U.S. Transuranium and Uranium Registries}

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