Date of Defense
Daniel Mihalko, Mathematics and Statistics
Michael Stoline, Mathematics and Statistics
Brian Smith, First of America Bank Corporation
This paper considers the problem of estimating the parameters of a population of measures which is a mixture of two normal sub-populations using data containing incomplete information. Specifically, complete data for an observation from the mixture consists of a measurement and a label. The label indicates to which normal sub-population the measurement belongs. Incomplete information consists of only the measurement with the correct sub-population label unknown. Incomplete observations occur in the sample due to some non-random process. A medical example of such an instance may consist of a test of whether or not a patient has heart disease. Before a patient is subjected to an invasive test for heart disease, such as catheterization, the patient is given a non-invasive screening test. The invasive test is then performed on those patients whose screening test indicates a high enough risk of heart disease. This invasive test then definitively categorizes each patient as either having heart disease or not. In this example, the measurement is the information from the non-invasive screening test, while the label is the membership in the sub-population of individuals with or without heart disease.
Cleveland, Christopher J., "The Gibbs Sampler" (1996). Honors Theses. 263.
Honors Thesis-Campus Only