BAYES CLASSIFIER; STATISTICS; BIOLOGY There are two well-known marker genes for

Question

BAYES CLASSIFIER; STATISTICS; BIOLOGY

There are two well-known marker genes for breast cancer: BRCA2, ERBB2. Canadian Disease Control Center carried out a clinical trial to check the gene expression levels for these two genes in the subjects diagnosed with breast cancer: one group of 50 randomly recruited subjects has no metastasis; and the other group of 50 subjects has metastasis. After normalization. BRCA2 expression levels follow a normal distribution N(0, 1) for non-metastatic subjects while N(1, 1) for metastatic subjects. For ERBB2, the corresponding expression levels in non-metastatic subjects and metastic subjects follow normal distributions N(0,1) and N(-1, 1), respectively. Taking naive Bayes classifier, if we know BRCA2=2, ERBB2 = 1, what will be the naive Bayes score of the patient being metastatic?

Explanation / Answer

The basic assumption of the naive bayes classifier is the independence of the predictor variables. The independence assumption is not a suitable one for realistic models. Because in real life the predictor variables may be correlated (in fact that is the case most of the time),then the assumption of independence fails.

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