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STAT 430 Homework 6
(due Sunday March 15, by 11:59PM)
This assignment will use the wbca data we have been using in class. Assume
throughout that the prior probability of sampling a malignant tumor is π0 =
1/3 and the prior probability for sampling a benign tumor is π1 = 2/3.
1. Using all 9 features to classify in the wbca data, find the confusion table
of the naive Bayes classifier using multinomial distributions for each variable
like we did in class, but doing LOOCV.
2. Once again use the naive Bayes classifier with multinomials, but use
whatever techniques you choose to see if you can find a good subset of the 9
features that classifies better than the full set. Again, use LOOCV.
3. Using the full set of features do LOOCV this time doing naive Bayes
classification assuming independent normal distributions for the 9 features.
4. Now assess the performance of the Bayes classifier assuming multivariate
normal distributions for the 9 variables, again using LOOCV.
5. Add all 9 features for each case, w =P9
j=1 xi
. Inspect histograms of w
for both cases and controls. Assess the performance of the Bayes classifier
assuming w has a normal distribution for both malignant and benign tumors.