ps2 (1)

ps2 (1) - Problem Set 2 MAS 622J/1.126J: Pattern...

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Problem Set 2 MAS 622J/1.126J: Pattern Recognition and Analysis Due Monday, 2 October 2006 [Note: All instructions to plot data or write a program should be carried out using either Python accompanied by the matplotlib package or Matlab. Feel free to use either or both, but in order to maintain a reasonable level of con- sistency and simplicity we ask that you do not use other software tools. Please provide a printed copy of any code used for this problem set.] Problem 1: In a particular binary hypothesis testing application, the conditional density for a scalar feature y given class w 1 is p y | w 1 ( y | w 1 ) = k 1 ( exp ( y 2 / 10)) Given class w 2 the conditional density is p y | w 2 ( y | w 2 ) = k 2 ( exp ( ( y 2) 2 / 2)) a. Find k 1 and k 2 , and plot the two densities on a single graph using Mat± lab/Python. b. Assume that the prior probabilities of the two classes are equal, and that the cost for choosing correctly is zero. If the costs for choosing incorrectly are C 12 = 1 and C 21 = 5, what is the expression for the Bayes risk? c. Find the decision regions which minimize the Bayes risk, and indicate them on the plot you made in part (a) d. For the decision regions in part (c), what is the numerical value of the Bayes risk? 1

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Problem 2: [Note: Use Matlab or Python for the computations, but make sure to explicitly construct every transformation required, that is either type it or write it. Do not
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This note was uploaded on 12/04/2011 for the course ESD 1.124 taught by Professor Kevinamaratunga during the Fall '00 term at MIT.

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ps2 (1) - Problem Set 2 MAS 622J/1.126J: Pattern...

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