A General Example

• Two hypothesis: the patient has cancer, , the patient doesn't have cancer,
• Prior knowledge: over the entire population of people .008 have cancer
• The lab test returns a correct positive result in 98% of the cases in which cancer is actually present and a correct negative in 97% of the cases in which cancer is actually not present
• 
• So given a new patient with a positive lab test, should we diagnose the patient as having cancer or not??
• Which is the MAP hypothesis?
• Has cancer -
• Doesn't have cancer -
• 
• exact posterior probabilities -