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Unformatted text preview: we have . is more than probability of being De finition:
The set is called the decision boundary. Remark:
1)Bayes classification rule is optimal. Proof:[1] (http://www.ee.columbia.edu/~vittorio/BayesProof.pdf)
2)We still need any other method, since we cannot define prior probability in realistic.
Example :
We’re going to predict if a particular student will pass STAT441/841. We have data on past student performance. For each student we know: If student’s GPA > 3.0 (G) If
student had a strong math background (M) If student is a hard worker (H) If student passed or failed course wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 5/74 10/09/2013 Stat841  Wiki Cour se Notes , where 1 refers to pass and 0 refers to f ail. Assume that
For a new student comes along with values
, we calculate as Thus, we classify the new student into class 0, namely, we predict him to fail in this course. Not ice: Although the Bayes rule is optimal, we still need other methods, since it is generally impossible for us to know the prior
density
and ultimately calculate the value of
, which makes Bayes rule inconvenient in practice. , and class conditional Currently, there are four primary classifier based on Bayes Classifier: Naive Bayes classifier[2] (http://en.wikipedia.org/wiki/Naive_Bayes_classifier) , tree augmented naive
Bayes (TAN), Bayesian network augmented naive Bayes (BAN) and general Bayesian network (GBN).
usef ul link :Decision Theory, Bayes Classifier (http://moodle.cs.ualberta.ca/file.php/127/SDTheory.ppt#256,1,Statistical) Bayes ian vs . Frequentis t
Intuitively, to solve a two class problem, we may have the following two approaches:
1) If , then , otherwise . 2) If , then , otherwise . One obvious difference between these two methods is that the first one considers probability as changing based on observation while the second one considers probablity as
having objective existence. Actually, they represent two different schools in statistics.
During the history of statistics, there are two major classif...
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 Winter '13

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