Transcription of Lecture 20 | Bayesian analysis
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Lecture 20 | Bayesian analysis
STATS 200: Introduction to Statistical InferenceAutumn 2016 Lecture 20 Bayesian analysisOur treatment of parameter estimation thus far has assumed that is an unknown butnon-random quantity it is some fixed parameter describing the true distribution of data,and our goal was to determine this parameter. This is the called thefrequentistparadigmof statistical inference. In this and the next Lecture , we will describe an alternativeBayesianparadigm, in which itself is modeled as a random variable. The Bayesian paradigm natu-rally incorporates our prior belief about the unknown parameter , and updates this beliefbased on observed Prior and posterior distributionsRecall that ifX,Yare two random variables having joint PDF or PMFfX,Y(x,y), then themarginal distributionofXis given by the PDFfX(x) = fX,Y(x,y)dyin the continuous cas
de nes a parametric model with parameter , as in our previous lectures.1 The joint distri-bution of and Xis then the product f X; (x; ) = f Xj (xj )f ( ); 1For notational simplicity, we are considering here a single data value X, but this extends naturally to the case where X = (X 1;:::;X n) is a data vector and f Xj (xj ) is the joint ...
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