Stat841f09 - Wiki Course Notes

# During the history of statistics there are two major

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Unformatted text preview: ication methods : Bayesian and frequentist. The two methods represent two different ways of thoughts and hold different view to define probability. The followings are the main differences between Bayes and Frequentist. Fre que ntis t 1. 2. 3. 4. Probability is objective. Data is a repeatable random sample(there is a frequency). Parameters are fixed and unknown constant. Not applicable to single event. For example, a frequentist cannot predict the weather of tomorrow because tomorrow is only one unique event, and cannot be referred to a frequency in a lot of samples. Baye s ian 1. 2. 3. 4. Probability is subjective. Data are fixed. Parameters are unknown and random variables that have a given distribution and other probability statements can be made about them. Can be applied to single events based on degree of confidence or beliefs. For example, Bayesian can predict tomorrow's weather, such as having the probability of of rain. Example Suppose there is a man named Jack. In Bayesian method, at first, one can see this man (object), and then judge whether his name is Jack (label). On the other hand, in Frequentist method, one doesn’t see the man (object), but can see the photos (label) of this man to judge whether he is Jack. Linear and Quadratic Discriminant Analysis - October 2,2009 Introduction Notation Let us first introduce some new notation for the following sections. M ulti-clas s Clas s ification: Y takes on more than two values. Recall that in the discussion of the Bayes Classifier, we introduced Bayes Formula: We will use new labels for the following equivalent formula: wikicour senote.com/w/index.php?title= Stat841&amp;pr intable= yes 6/74 10/09/2013 Stat841 - Wiki Cour se Notes is called the clas s conditional de ns ity; also referred to previously as the likelihood function (http://en.wikipedia.org/wiki/Likelihood_function) . Essentially, this is the function that allows us to reason about a parameter given a certain outcome. is called the prior probability (http://en.wikipedia.org/wiki/Pri...
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