GE 331-Lecture 22 - Parameter Estimation An unknown...

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IE 300/GE 331 Lecture 22 Negar Kiyavash, UIUC 1 Parameter Estimation • An unknown parameter denoted by random variable Θ • Initially we have a prior p Θ (This is a Bayesian framework) • After making an observation X, we have a model p x| Θ • We want to estimate Θ • What about the classical case (non- Bayesian)?
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IE 300/GE 331 Lecture 22 Negar Kiyavash, UIUC 2 BHT and Parameter Estimation • Recall that in the Bayesian framework the hypothesis are random variables. • Let us denote the random variable corresponding to the hypothesis by Θ . Θ takes the values θ 0 or θ 1 corresponding to hypothesis H 0 and H 1 , respectively Θ is a discrete r.v. with PMF {p( θ 0 ), p( θ 1 )} • BHT is a special form of parameter estimation • Parameters are the two hypotheses
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IE 300/GE 331 Lecture 22 Negar Kiyavash, UIUC 3 Parameter Estimation • In general Θ is not binary • It can be finite or infinite • Finite: Want to estimate a bit {0,1} sent over a channel, number of people voting for a candidate • Infinite: Estimate the wait time of customers at a service center, average of students height in this class • Any ideas for estimators?
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This note was uploaded on 09/08/2009 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

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GE 331-Lecture 22 - Parameter Estimation An unknown...

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