16.422 Information Signal Detection Theory Prof, r, john hansman Acknowledgements to Profs tom Sheridan and Jim Kuchar whose notes are the core of this lecture
System Supervisory Control Computer Interface Display Control Sensors Direct Observation 16.422 Information & Signal Detection Theory Prof. R. John Hansman Acknowledgements to Profs Tom Sheridan and Jim Kuchar whose notes are the core of this lecture
Outline Information Theory Signal Detection Theory Alerting Introduction
System Supervisory Control Computer Interface Display Control Sensors Direct Observation Outline y Information Theory y Signal Detection Theory y Alerting Introduction
口中 Information Theory What is information? Control theoretic view a Lines in Control Block Diagram nDirect observatio DIsplay Supervisory ontrol System Control Computer Interface Sensors Bayesian view a Information is something which reduces uncertainty in a world model
System Supervisory Control Computer Interface Display Control Sensors Direct Observation Information Theory y What is information? y Control Theoretic View Lines in Control Block Diagram y Bayesian View Information is something which reduces uncertainty in a world model System Supervisory Control Computer Interface Display Control Sensors Direct Observation
Bayes Theory h= Hypothesis, D=Data P(H D=PO HP(p(D) With new data p(H D1, D2)=p(2 H) [p(D1 H)p(Hp(DI)/p(D2) With 2 hypotheses p(HI D1, D2)=p(D2 H1 p(D1 HD) p(H1) p(H2D1,D2)p(D2|H2)p(D1|H2)p(H2) Posterier odds ratio prior odds ratio
System Supervisory Control Computer Interface Display Control Sensors Direct Observation Bayes Theory H = Hypothesis, D = Data p(H | D) = p(D | H) p(H)/p(D) With new data p(H | D1,D2) = p(D2 | H) [p(D1 | H) p(H)/p(D1) /p(D2) With 2 hypotheses p(H1 | D1,D2) = p(D2 | H1) p(D1 | H1) p(H1) p(H2 | D1,D2) p(D2 | H2) p(D1 | H2) p(H2) Posterier odds ratio prior odds ratio
I NfORMADOA MEASURGM L:∠ StANDN INFoRMANDN MDDE Ball Sys*a Tackmieal Journo Mn? ww book Shannon Information Theory sebe→oe→小→航→ 口 Bell labs 日 Telephony 圈35 STA→5sa→bah→eecn→ 2aNMET MESSAGE SET Tom Sheridan notes FROND RuLeS. K小NAPR1R siMuLus(MeSSAGrE )CHose AT RAwDon Plx[)CousTaNT (Courtesy of Thomas Sheridan. Used with permission
System Supervisory Control Computer Interface Display Control Sensors Direct Observation y Shannon Information Theory Bell Labs Telephony y Tom Sheridan Notes (Courtesy of Thomas Sheridan. Used with permission.)
S IOTUITIVE CONCEPT DF INFoRNAnDA Itow MANY BINAY DIS CRIMINADONS To ReDUcE I NITAL UN CETHNTY To 3eD Bit view of information a of bits to disambiguate a Bit= binary discrimination Xx×XxX★x 01o a Drive uncertainty to zero ∈ ALY PRS6A6LE CHE VIRaNMEUT APoRMATON IN MeSSAGE SeT H n2p(x)=3 2 :)y 2p(x)ln, bOx 15X BT NT IF ONCQIPRBA6LE I wHrf67mens?。rt()=,1 ADDM-STLL NEED 3 MINADONSSamenmes REDVcE oNe最 TAINT to 2e (Courtesy of Thomas Sheridan. Used with permission
System Supervisory Control Computer Interface Display Control Sensors Direct Observation y Bit view of Information # of bits to disambiguate Bit = binary discrimination Drive uncertainty to zero (Courtesy of Thomas Sheridan. Used with permission.)
Info transmission H= information D= Data 丹。 TD MGKSULE INA. TNSMITTeD 5 M PLesT毛 xAmpLes P(rs) X1→从 D→Y p(x T IS xi 5 KpbwN APRIDRI b(Hi) IMPRNNED P(X, I COADTONAL p(×)(X|) (x)=21)n Pli CATGRIA FOR A 600b MEASURE 5(-、2)+5( w+[p),(x!1) H(Y)=SAME 2)INFo. GNED &Y KDWIAG Y,MDDs To →个:l(xx)-1p(x INAo, GNPD BY KNOWIAG Y,ETC. ()-h2(5)=1 x→Y个 =7L(x) P(xxL YkY +,5 PERFECT INFo. TNSMI3SIDN b/, (Courtesy of Thomas Sheridan. Used with permission
System Supervisory Control Computer Interface Display Control Sensors Direct Observation Info Transmission H = information, D = Data (Courtesy of Thomas Sheridan. Used with permission.)
P() p(, NOLnPLTAUASAMoK Mb DENOHIAATOL p(Y).THeN SAME H(Ay P(x,Y) b(x:I) 乏p(x 个=|-1 THNSnr!X, =1-1 22x)p()w X,→个 个-| +H(r)-(x) T:INP + WTPT -Jo N。1P。. TANNSMITTG GEN Tho H(x)=( IF X Nb T VNCORRE LATEP, FRan GeNL. CQN. p(xry)=r(x)→个=° A CDtAL TRAN SMITTeS INPD (x+)=22(x)P I r) F X Ab Y PeRfecn-y cheLated h(x,) p(x)=P(x)=(y) 个(x=()=H() (Courtesy of Thomas Sheridan. Used with permission
System Supervisory Control Computer Interface Display Control Sensors Direct Observation (Courtesy of Thomas Sheridan. Used with permission.)
口凸 CA NSD REwITE GeNL. eaA. MOINE IN DIAGRAM =22P(xx()m /H(xIt) EourvlecAned(LesT po) H(XIY Mlx HCY 2 p(x)looP(xa) s网rH(x INPVT 个(x ONTPUT HCrIx) Norst(G/wFO Mp H(*)-H(* INPUT- ERUNOCATON INFo Is UNCERTA/NTY cHA。良 GWRITE GeL.∈s心 (no 8 ReDueD MULT NOM.·b6M.BY p(PixY INPVT /NFD 个)22(y)9次上 小2 22x)1)“2 2P(x:)ley p(x, Ir) EOUIVDCAToN 9:=2kc NoIse 22 b(x) 对 L) HCrI H(r)-H(r(*) (Courtesy of Thomas Sheridan. Used with permission
System Supervisory Control Computer Interface Display Control Sensors Direct Observation (Courtesy of Thomas Sheridan. Used with permission.)
A(x1r) EourvecAnos(LosT INFo) () H(T) I NPVT 个(x:r △uTvT TRANSMITTED (rix)NoIsE(GAMPO ay) EMGM6eY-INFo I5 UN(GRTA/NTY H(*xJ.2P: l> NPVT I同 H(5b( OUTPUT INFD -&5P(* Y)loy PixI 5) EOUINDCATIoN ( Courtesy of Thomas Sheridan. Used with permission
System Supervisory Control Computer Interface Display Control Sensors Direct Observation (Courtesy of Thomas Sheridan. Used with permission.)
