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# 263 Class Note for ECE 51100 with Professor Tan at Purdue

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COURSE
PROF.
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TYPE
Class Notes
PAGES
11
WORDS
KARMA
25 ?

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This 11 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 23 views.

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Date Created: 02/06/15
Estimation of Gd Hong Z Tan amp Zygmunt Pizlo The Problem I 6d can not be estimated directly from 11 or 21 experiments I We can always nd a cumulative Gaussian curve that goes through 2 points EXACTLY PR2S1 or 2 2F AH zscore Hong Z Tan amp Zygmunt Pizlo I We can always nd a straight line that goes through 1 point EXACTLY zH Id I Therefore we can NOT measure the goodness of t in either case with rms error Hong Z Tan amp Zygmunt Pizlo Two Ways to Estimate ad I 1 When you only collect one pair of H F ONeed assumptions to estimate 6d I 2 When you measure multiple pairs of H F OUse the rms error of ROC curve tting OThere are two ways to estimate ROC Run multiple experiments Ask subjects to use different k in different sessions 01 Rating paradigm Ask subjects to maintain multiple k in the same session Hong Z Tan amp Zygmunt Pizlo The Main Idea I Given that d39ZH ZF I We have 00139 022w 0220 I Therefol e w estimate 6d we need to estimate O39ZH and cm rst Hong Z Tan amp Zygmunt Pizlo Method 1 Estimate ad with One Pair of H F Values I Assumptions OThe only source of variability in d39 is sampling error therefore we are getting a lowerbound estimate OBinomial distribution approximates Gaussian with suf cient number of trials This is true if e p probability of responding yes is not extreme or N number of trials is large when p is extreme Hong Z Tan amp Zygmunt Pizlo I It then follows that the variability of H and F are 0F F1 F N1 0H Ha H N2 Where N1 0139 N2 is the number of times stimulus S1 or S2 has been presented respectively I All we need to do now is to estimate GZH and cm Hong Z Tan amp Zygmunt Pizlo PR2S1 or 82 rm 1 x2dx 00 427 NF 62F FGF from Igt F iiiiii lt F0quotZFB assumptions 0t3 constants gt 039 a oz ZF zscore F F NZF9 o2zF based on local linear approximation Hong Z Tan amp Zygmunt Pizlo Summary of Method 1 1 1 zFgt2 zltFF UZltFgt0F27rez fwez N1 1 f zltHgt2 02w 2 27rH1 H 62 N2 FinellJ 001 0220 022F It should be clear that Cd is inversely proportional to N1 and N2 Hong Z Tan amp Zygmunt Pizlo Method 2 Estimate 6d with ROC I No explicit I I I I 0 LAD v PGG evo assumptlons are 6400 Trials 5134 Trials 6592 Tn als needed I Estimate 62H and cm as the rms error of straight 39 line Best linear ms LSE LAD Zd 064 Z1 134 dev006 PGG 2d 092 21 141 dev012 GYO 26 101 z39 149 dev0i04 l I I l I Then compute 39 1 1 2 2 B 05139 02H 02F Hong Z Tan amp Zygmunt Pizlo 11 Two Ways of Obtaining ROC I Multiple sessions with different k values Osee Pang et al 1991 I Same session with multiple k values 9 Rating Experiment Hong Z Tan amp Zygmunt Pizlo

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