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
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