Lect2_Bayes_decision_theory

Lect2_Bayes_decision_theory - Lecture 2: Bayesian Decision...

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1 Lecture 2: Bayesian Decision Theory I Outline: 1. Diagram and formulation 2. Bayes rule for inference 3. Bayesian decision 4. Discriminant functions and space partition 5. Advanced issues Reading material: Duda/Hart/Stork: Sections 2.1-2.6 Lecture note Stat 231-CS276A, © S.C. Zhu Diagram of pattern classification Procedure of pattern recognition and decision making Subjects Selected Features Observables Action Inner belief W x X α p(w|x) X --- all the observables using existing sensors and instruments x --- is a set of features selected from components of X or linear/non-linear functions of X. p(w| x ) --- is our belief/perception about the subject class with uncertainty represented by probability. α --- is the action that we take for x. We denote the three spaces by Lecture note Stat 231-CS276A, © S.C. Zhu } ,..., , { , classes of index the is w vector a is ) ,..., , ( x α , w , x k 2 1 C d 2 1 α C d w w w x x x = Ω = Ω Ω Ω
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Examples Ex 1: Fish classification Ex 2: Medical diagnosis X= I is the image of fish, x =(brightness, length, #fin, ….) w is our belief what the fish type is Ω c ={“sea bass”, “salmon”, “trout”, …} α is a decision for the fish type, X= all the available medical tests, imaging scans (ultra sound, CT, blood test) that a doctor can order for a patient x =(blood pressure, glucose level, …, shape) w is an illness type Ω c ={“cold”, “TB”, “pneumonia”, “lung cancer”,…} in this case Ω c = Ω α Ω α ={“sea bass”, “salmon”, “trout”, …} α is a decision for treatment, Ω α ={“Tylenol”, “Hospitalize”, …} Lecture note Stat 231-CS276A, © S.C. Zhu Tasks Subjects W Features x Observables X Decision α Inner belief p(w|x) control sensors selecting Informative features statistical inference risk/cost minimization In Bayesian decision theory, we are concerned with the last three steps in the big ellipse assuming that the observables are given and features are selected . Lecture note
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This note was uploaded on 11/24/2010 for the course STAT 201a taught by Professor Wu during the Spring '10 term at Pasadena City College.

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Lect2_Bayes_decision_theory - Lecture 2: Bayesian Decision...

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