Transcription of Lecture 6. Bayesian estimation
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Lecture 6. Bayesian estimation
6. Bayesian estimationLecture 6. Bayesian estimation1 (1 72)6. Bayesian The parameter as a random variableThe parameter as a random variableSo far we have seen thefrequentistapproach to statistical inferential statements about are interpreted in terms of repeat contrast, the Bayesian approach treats as a random variabletakingvalues in .The investigator s information and beliefs about the possible values for ,before any observation of data, are summarised by aprior distribution ( ).When dataX=xare observed, the extra information about is combinedwith the prior to obtain theposterior distribution ( |x) for givenX= has been a long-running argument between proponents of thesedifferent approaches to statistical inferenceRecently things have settled down, and Bayesian methods are seen to beappropriate in huge numbers of applicati
In 1763, Reverend Thomas Bayes of Tunbridge Wells wrote In modern language, given r ˘Binomial( ;n), what is P( 1 < < 2jr;n)? Lecture 6. Bayesian estimation 6 (1{72) 6. Bayesian estimation 6.2. Prior and posterior distributions Example 6.1 Suppose we are interested in the true mortality risk in a hospital H which is
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