0 Y i D 1 P X i 1 Y i D N D N DA N D P X i 1 Y i H N HA N H P X i 0 Y i H 1 P X

# 0 y i d 1 p x i 1 y i d n d n da n d p x i 1 y i h n

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= 0 | Y i = D ) = 1 - P ( X i = 1 | Y i = D ) = N D - N DA N D , P ( X i = 1 | Y i = H ) = N HA N H , P ( X i = 0 | Y i = H ) = 1 - P ( X i = 1 | Y i = H ) = N H - N HA N H . Estimate these probabilities from the data in trainPatient , and report their values. b) Test the Bayesian classifier based on feature A i using the data in testPatient . What is the accuracy (percentage of correctly classified patients) of this classifier on that data? c) Consider now the feature X i = E i , where E i = 1 if exercise causes patient i to experience chest pain, and E i = 0 if it does not. Estimate and report conditional probabilities for this new feature as in part (a). What is the accuracy of a Bayesian classifer based on feature E i on the data in testPatient ? d) Consider the pair of features X i = ( A i , E i ) . This pair of features can take on 4 values: (0 , 0) , (0 , 1) , (1 , 0) or (1 , 1) (we do not assume that A i and E i are independent). By counting as in part (a), compute and report the probabilities of these four events given Y i = D and given Y i = H . What is the accuracy of a Bayesian classifier based on feature X i on the data in testPatient ? Compare the accuracy of this classifier to those from parts (b) and (c), and give an intuitive explanation for what you observe. 3
• Fall '08
• Smyth,P
• Normal Distribution, Probability theory, probability density function, Yi, Cumulative distribution function

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