Transcription of Chapter 3: Basics from Probability Theory and Statistics
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Chapter 3: Basics from Probability Theory and Statistics
IRDM WS 2015 Chapter 3: Basics from Probability Theoryand Probability TheoryEvents, Probabilities, Bayes Theorem,Random Variables, Distributions, Moments, Tail Bounds, Central Limit Theorem, Entropy Statistical InferenceSampling, Parameter Estimation, Maximum Likelihood,Confidence Intervals, Hypothesis Testing, p-Values, Chi-Square Test, Linear and Logistic RegressionmostlyfollowingL. Wasserman Chapters6, 9, 10, 13 IRDM WS Statistical InferenceA statisticalmodelisa setofdistributions(orregressionfunctions ), , all unimodal, smooth parametricmodelisa setthatiscompletelydescribedbya finite numberofparameters,( , thefamilyofNormal distributions).Statistical inference: givena sample X1, .., Xnhowdo weinferthedistributionoritsparameterswit hina modelswithonespecific outcome(response) variable Y, thisiscalledpredictionorregression, fordiscreteoutcomevariable also (x) = E[Y | X=x] : biomedicalmarkers cancerornotExampleforregression: businessindicators stock priceIRDM WS 2015 Sampling Illustrated3-41 Distribution X(populationofinterest)Samples X1, X2.
Chapter 3: Basics from Probability Theory and Statistics 3-39 3.1 Probability Theory Events, Probabilities, Bayes‘ Theorem, ... For multivariate models with one specific ... the probability that the data of the sample are generated by
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