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Unformatted text preview: ic framework for binary hypothesis testing is illustrated in Figure 2.11. It is assumed that H1 system X decision rule H1 or H0 H0 Figure 2.11: The framework for binary hypothesis testing.
either hypothesis H1 is true or hypothesis H0 is true, as indicated by the position of the switch at
the left end of the ﬁgure. Based on which hypothesis is true, a system generates an observation
X. The observation is fed into a decision rule, which then declares either H1 or H0 . The system is
assumed to be random, so the decision rule can sometimes declare the true hypothesis, or it can
make an error and declare the other hypothesis. For example, the data could be from a computer
aided tomography (CAT) scan system, and the hypotheses could be H1 : a tumor is present; H0 : no
tumor is present. Here we model the observed data by a discretetype random variable X. Suppose
if hypothesis H1 is true, then X has pmf p1 and if hypothesis H0 is true then X has pmf p0 . The
likelihood matrix is an array with one row for each of the two hypotheses, and one column for each
possible value of X . The entries in the row for hypothesis Hi are values of the corresponding pmf,
pi . For example, the likelihood ma...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

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