Homework Assignment 2
1. Among 521 duodenal ulcer patients gathered by Clarke et al. (1959), the
following ABO bloodtypes were observed: A = 186, B = 38, AB = 13, and O =
284. Formulate a likelihood for estimating the three allele frequencies
underlying the ABO blood group. Use the EM-algorithm to find the
likelihood estimates. Give explicit description of the the E and M steps.
In the above formulation of the EM-algorithm you assumed HWE. Are the data
consistent with this assumption? To answer the question conduct a
significace test and make a decision based on a p-value.
2. In section 2.4.2, Shaw proposes an EM-algorithm to estimate the
(phenotypic) segregation ratio for a rare recessive trait based on
heterozygous matings (Dd X Dd). Formulate the likelihood based on the
observed data, and develop (in detail) an EM-algorithm that follows
equation 2.22. Confirm the EM results in Example 2.8.
Due: Feb 24.