Prb&Rand Proc EECS 501
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This 1 page Class Notes was uploaded by Ophelia Ritchie on Thursday October 29, 2015. The Class Notes belongs to EECS 501 at University of Michigan taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/231536/eecs-501-university-of-michigan in Engineering Computer Science at University of Michigan.
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Date Created: 10/29/15
EECS 501 ESTIMATION lVlLE7 MAP7 LS Fall 2001 Model Data Goal Example Model A known model of system or process with unknown parameter a An observation R of a random variable r whose pdf depends on a Model gt fT aRA If knew a A7 would know pdf of observation r Estimate a from R and conditional pdf fT aRA Compute ampR Flip coin 10 times Data heads in 10 independent ips Binomial pmf for r Unknown parameter aPrheads 1 Given Soln MLE NonBayesian a is an unknown constant do not know fa fT aRA from model observation data R of rv r nothing more Advantage Need very little no possibly wrong prior information Maximum Likelihood Estimator max likelihood of what happenedzrR aMLER M921 fT aRA Compute log fT aRA 0 BLUE Best minimum variance Linear Unbiased Estimator of constant a from y Ha v7Ev 0 is Y HH 1HY Proof p 290 Bayesian a is itself random with known a priori pdf faA fT aRA from model faAa priori info observation R of r Advantage Incorporate a priori in estimate7 but this better be right min Ece where e a amprerror and ccostllEP or LSE Mm Error Prob 06 i 0 if e lt 6 close only countsin horseshoes77 39 P 1 if e gt e amiss is as good asamile77 1 ff dR fig dA ham A 1 2e ff ham ampRdR This is minimized when fT7aR7 ampR maximized for each R MAP Compute Max A Posteriori aMApR My fT aRAfaA compare MLE log fT aRA log faA 0 MEP criterion gtMAP solution 2b LSE LSE Proof Least Squares Estimation criterion ce e2 Penalize big errors A i i fAfT aRlAfaAdA Denominatorjust frR aLSR P EMT R P ffriaRlA faAdA noeffect on argmaxofA Page 298 Moment of inertia minimized around center of mass Bias DEF Ema MSE Let a be an unknown constant Amt so that faA 6A Amt ampR is unbiased if Ear Amt lt gt Ee 0 How to compute f f ampRfrlaRA5A AmadeA f aRf aRIAactdR ampR unbiased gt Eamp r A 2 05m gtllSE variance of ampR act