class_09_10 - Statistical Data Mining ORIE 474 Fall 2007...

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Statistical Data Mining ORIE 474 Fall 2007 Tatiyana V. Apanasovich 09/10/07 Data Analysis & Sampling Methods
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4.2 Uncertainty Frequentist view: Objective concept Probability of event = Limiting proportion of times that the event would occur in repetitions of essentially identical situations Relative restrictive concept, i.e. not applicable to one-time events Bayesian view: Subjective concept Explicit characterization of all forms of uncertainty in a data analysis, incl. uncertainty about parameters, model structures, forecasts etc. Very flexible concept The calculus is the same for both concepts but the underlying interpretation and the conclusions drawn differ
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4.3 Random Variables Random Variables X Mapping from a property of objects to a variable that can take on one of a set of possible values Mapping process appears to the observer to have some element of unpredictability to it Ex: coin toss Possible values for X: domain of X Review appendix of textbook for basic properties
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Multivariate Random Variables X=(X 1 ,…,X p ) set of random variables Joint density function: f(x)=f(X 1 =x 1 ,…,X p =x p )= f(x 1 ,…,x p ) Marginal density f(x 1 ) Conditional density f(x 1 |x 2 ) X and Y are independent iff f(x|y)=f(x) X is conditionally independent of Y given Z iff p(x,y|z) = p(x|z)p(y|z) First-order Markov property
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4.4. Samples & Statistical Inference Statistical Inference Probability Model Data
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Statistical Inference On the basis of a sample: Makes statements about the population structure Estimates the size of these structures Expresses our confidence in these estimates Must have some structure in mind
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A. Desirable Properties of Estimators
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This note was uploaded on 02/06/2011 for the course ORIE 474 taught by Professor Apanasovich during the Spring '07 term at Cornell University (Engineering School).

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class_09_10 - Statistical Data Mining ORIE 474 Fall 2007...

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