19estim - EECS 501 ESTIMATION: MLE, MAP, LS Fall 2001...

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EECS 501 ESTIMATION: MLE, MAP, LS Fall 2001 Model: A known model of system or process with unknown parameter a . Data: An observation R of a random variable r whose pdf depends on a . Model f r | a ( R | A ): If knew a = A , would know pdf of observation r . Goal: Estimate a from R and conditional pdf f r | a ( R | A ): Compute ˆ a ( R ). Example: Flip coin 10 times. Data: #heads in 10 independent flips. Model: Binomial pmf for r . Unknown parameter: a=Pr[heads]. 1. Non-Bayesian: a is an unknown constant (do not know f a ( A )). Given: f r | a ( R | A ) from model; observation (data) R of rv r ; nothing more. Advantage: Need very little; no (possibly wrong) prior information. Soln: Maximum Likelihood Estimator: max likelihood of what happened:r=R. MLE: ˆ a MLE ( R ) = argmax A [ f r | a ( R | A )]. Compute: ∂A [log f r | a ( R | A )] = 0. BLUE: Best (minimum variance) Linear Unbiased Estimator of constant x from y = Hx + v,E [ v ] = 0 is ˆ x ( Y ) = ( H 0 H ) - 1 H 0 Y . Proof: p. 290. 2.
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This note was uploaded on 07/22/2011 for the course EECS 370 taught by Professor Lehman during the Spring '10 term at University of Florida.

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19estim - EECS 501 ESTIMATION: MLE, MAP, LS Fall 2001...

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