Homework 3.  Statistics 771, Spring 09
Posted online Monday Feb 23/09
Due in class Monday March 9/09.


1. The following data on blood types were obtained in a sample of n=30
   subjects

    type            A      B      AB     O
    frequency      12      8      6      4

   Using the simple genotype->phenotype model discussed in class, 
   compute the maximum likelihood estimate of the allele frequencies
   theta = (p,q,r).  Do so using your own implementations of the 
   Nelder-Mead algorithm and the EM algorithm.


2. Reconsider the mutation-frequency example discussed in class.  Data
   are structured { (y_i, x_i), i=1,2,...n } where y_i is an indicator
   that well i is  fertile (i.e. exhibits growth after cells exposed
   to 6TG) and x_i contains covariate information.  In the specific case
   reported in the file `MF1.txt', x_i is a binary indicator of where
   the T cells were harvested (1=in normal tissue, 0=at tumor site).  
   Additionally, we know m_i = number of cells deposited initially into well 
   i (dilution).  We want to estimate the mutation frequency for cells at the 
   tumor site and otherwise.   Find the maximum likelihood estimate for these 
   two parameters.  Do so using your own implementations of IRLS and EM.
  
3. In Givens and Hoeting do problems 4.2a,b and 4.3a,b.