The data is split into two matrices trainPatient and testPatient Each row of

The data is split into two matrices trainpatient and

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completely random sample of the population) who may or may not have heart disease. The data is split into two matrices, trainPatient and testPatient . Each row of these three-column matrices represents a patient. The first column contains the age of the patient in years. The second indicates whether exercise causes them to experience chest pain, with “1” indicating yes and “0” no. The third column is the ground truth of whether they have heart disease, again with “1” indicating yes and “0” no. trainPatient will be used to “train” your classifier by estimating various probabilities. testPatient will be used to evaluate classifier performance, but not to estimate probabilities. To define a probabilistic model of this data, we let Y i = D if patient i has heart disease, and Y i = H if patient i does not. To construct a simple Bayesian classifier, we will compute the posterior probability P ( Y i | X i ) of the class label given some feature X i . If P ( Y i = D | X i ) > P ( Y i = H | X i ), we classify patient i as probably having heart disease. Otherwise, we classify them as probably not having heart disease. By Bayes’ rule, the posterior probability P ( Y i | X i ) = P ( X i | Y i ) P ( Y i ) P ( X i ) . Consider the feature X i = A i , where A i = 1 if patient i has age > 55, and A i = 0 if patient i has age 55. a) We estimate probabilities by counting event frequencies in the training data. Let N be the total number of patients, N D the number of patients with heart disease, N DA the number of patients with heart disease over age 55, N H the number of patients without heart disease, and N HA the number of patients without heart disease over age 55. We set P ( Y i = D ) = N D N , P ( Y i = H ) = N H N , P ( X i = 1 | Y i = D ) = N DA N D , P ( X i
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  • Fall '08
  • Smyth,P
  • Normal Distribution, Probability theory, probability density function, Yi, Cumulative distribution function

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