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Z[xaxa1 ?|y.nf^___PPT9@8 Any statistical relationship between two variables may be reversed by including additional factors in the analysis. Application: The adjustment problem Which factors should be included in the analysis.t" " d%" d" d2" :  2 %$       H  0޽h ? f̙fy___PPT10Y+D=' G = @B +o$0^N0 P%SXq(  X X s *lb PP @SIMPSON S PARADOX (1951  1994)!!(B X N D1?"e 0X He1?C"?O MM R R T 2 8 10 T 9 21 30 11 29 40dNd 1X Hm1?C"?O LM R R T 18 12 30 T 7 3 10 25 15 40dMd 2X H|u1?C"?z L R R T 20 20 40 T 16 24 40 36 44 80dMXB 3X 0DԔ?7XB 4X 0DԔ?IXB 5X 0DԔ? XB 6X 0DԔ?  XB 7X 0Do?M XB 8X 0Do? y XB 9X 0DԔ?IXB :X 0DԔ?CXB ;X 0DԔ?XB X 0Do?yXB ?X 0Do?b XB @X 0DԔ?nXB AX 0DԔ?nXB BX 0DԔ?XB CX 0DԔ?@@XB DX 0Do?xXB EX 0Do?$ GX H\1?C"?a 7+( HX H1?C"? 7=( IX HT1?  [ 0.6 < 0.76  JX H(1?   [ 0.2 < 0.36  KX H1?e [ 0.5 > 0.46   LX Hș1?4  T  Treated T  Not treated R  Recovered R  Dead M  Males M  FemalesM    XB MX 0Do? M XB NX 0Do? ` XB OX 0Do? n # QX <1?  ,$0 5Easy question (1950-1994) When / why the reversal?2 )^ RX N?" ,$0 LHarder questions (1994) Is the treatment useful? Which table to consult?65=P SX Z?"x,$0 N Why is Simpson s reversal a paradox?((H X 0޽h ? f̙f  ___PPT10 .+ScD ' G = @B D ' = @BA?%,( < +O%,( < +D ' =%(D' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*QX%(D' =-o6Bdissolve*<3<*QXD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*RX%(D' =-o6Bdissolve*<3<*RXD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*SX%(D' =-o6Bdissolve*<3<*SX++0+QX0 ++0+RX0 ++0+SX0 +0^N0 `S@q(   ( s *b &SIMPSON S REVERSAL,,,   B ) N D1?"?(? P Zxaxa1?ZJ  F|Pr(recovery | drug, male) < Pr(recovery | no-drug, male) Pr(recovery | drug, female) < Pr(recovery | no-drug, female) }8 Q  `xaxa1?Z EGroup behavior:  R  `xaxa1? ZX  GOverall behavior: 5 S  `xaxa1? Z" -Pr(recovery | drug) > Pr(recovery | no-drug)\.H  0޽h ? f̙fy___PPT10Y+D=' G = @B +0^N0 %ps P(      s *h | TO ADJUST OR NOT TO ADJUST?,! ,, !  B   N D1?"A(Aj2 [  BԔ?j2 \  BԔ?^ 9 j2 ]  BԔ?;XB ^  0>?^ XB _  0>?b XB ` @ 0>?  a   `dxaxa1?  ; ? Treatment   b   `xaxa1? BA  >Recovery   c   `xaxa1?@5  <Gender  d   `xaxa1?+ 7T  e   `$xaxa1?w]k 7F  f   `4xaxa1?Z  HMediating factor  g   `xaxa1?A  7F  h   `xaxa1?0  ? Treatment   i   `xaxa1?(( 7T  j   `xaxa1?o   7R  k   `xaxa1? 5A  >Recovery  d2 l  <Ԕ?4id2 m  <Ԕ?F Pz d2 n  <Ԕ?ZLRB o  s *>?`d0 RB p  s *>?bZP RB q  s *>?p5q r   `Hxaxa1?   7R ? s  Tt!?"'{ 3Solution: Adjust iff F blocks all back-door paths<4H   0޽h ? f̙fy___PPT10Y+D=' G = @B +0^N0 ; 3   (  H  <0)1?$D0rj___PPT9LD .xTWO PROOFS: When two causal models generate the same statistical data and in one we decide to use the drug yet in the other not to use it, our decision must be driven by causal and not by statistical considerations. Thus, there is no statistical criterion to warn us against consulting the wrong table. Can Temporal information help? A. No!, see Figure (c). F = Car Type X' &X             @`  s *@J9 MTHE INEVITABLE CONCLUSION: THE PARADOX STEMS FROM CAUSAL INTERPRETATIONNN$B  N D1?"l  ,$D0R  TlC?"D<4___PPT9 lSurprise surfaces only when we speak about  efficacy, not about evidence for recovery.X*   @`  s *A ??"`v x dH  0޽h ? f̙f___PPT10+^[D' G = @B DX' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*2%(D' =-o6Bdissolve*<3<*2D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*3R%(D' =-o6Bdissolve*<3<*3RD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*Ry%(D' =-o6Bdissolve*<3<*Ry+'0^N0 &&<, %(   ) s *k9,$D 0 +WHY TEMPORAL INFORMATION DOES NOT HELP,,+   ,  B * N D1?"p,$D 0 q < 1?  :In (c), F may occur before or after T, and the correct answer is to consult the combined table. In (d), F may occur before or after T, and the correct answer is to consult the F-specific tables.F%**  @` r  `qxaxa1?|46 ? Treatment  s  `vxaxa1?T  >Recovery  t  `|zxaxa1?=e <Gender u  `~xaxa1?(P 7T v  `Qxaxa1? 7F w  `xaxa1?5]  7R x  `xxaxa1?|TV  ? Treatment  y  `4xaxa1?t2   >Recovery  z  `0xaxa1?= Z U DBlood Pressured2 { <|AԔ?  XB | 0|AԔ?~ 7 }  ` xaxa1?|  ? Treatment  ~  `xaxa1?k )  >Recovery    `pxaxa1?(%  P 7T   `Pxaxa1? 7F   `xaxa1?5 ]  7RdB @ <DԔ? @^B  6D1?p++pdB @ <DԔ? @dB @ <DԔ?@dB  <DԔ?@d2  <|AԔ?d2  <|Ao?3]d2  <|Ao?8c5d2  <|AԔ?     fxaxa1?(/P 7T   f\xaxa1?  7F   f4xaxa1?5]  7R^B @ 6Ԕ?hK V  ^B  6|AԔ?@ ^B @ 6Ԕ?# !j2  B|AԔ?d j2  B|AԔ? j2  B|AԔ?(XB @ 0Ԕ?h.9 XB  0|AԔ?k$XB @ 0Ԕ?!d2  <|AԔ?dd2  <|AԔ? d2  <|AԔ? v  NZGHIg1? $ ] Xvb  NG%iH4cIK1? F ] 0   `0xaxa1?(P 7T   `xaxa1? 7F   `xaxa1?5]  7RXB @ 0Ԕ?h8C XB  0|AԔ?t-d2  <|AԔ?dd2  <|AԔ? d2  <|AԔ?|b  TGHt1IԔ?\  H1?7 4W  7(a)  H1?7 C W  7(b)  H1?7 W  7(c)  HL1?7 +W  7(d) ,  `,xaxa1?s|0 9CarH  0޽h ??`qq f̙fy___PPT10Y+D=' G = @B +0^N0 >6 L 0  (  L  L s *ؗ^: HWHY  CAR TYPE SHOULD NOT MATTER,%$(( %  B L N D1?"H|H L ZF^xaxa1?M f,$D0 ?Listening to the Bell creates association between Treatment and Recovery though Treatment does not affect Recovery Treatment efficacy is distorted in the Bell-specific tables. Treatment efficacy is properly represented in the combined table. @`  L  `I^xaxa1?# K  ? Treatment   L  `V^xaxa1?# NK  >Recovery j2 L B|AԔ?,/l NLG L NLG,$D 0 L   `^xaxa1?N  <Coin-1 L   `4Sxaxa1? L <Coin-2rB L B BԔ?~Gr2 L  B|AԔ?) T rB L  BԔ? Gr2 L B B|AԔ?% P j2 L @ B|AԔ?Mx/>l H &  L H & ,$D 0  L   `^xaxa1?` [  :Belll2  L  <|AԔ?( CS sB L  NDԔ?"0@NNN?NH 4 NB L B NDԔ?"0@NNN?N: & NH L 0޽h ? f̙f1)___PPT10 +ySD' G = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*L %(D' =-o6Bwipe(up)*<3<*L D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*L %(D' =-o6Bwipe(up)*<3<*L D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*L s%(D' =-o6Bdissolve*<3<*L sD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*L s%(D' =-o6Bdissolve*<3<*L sD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*L %(D' =-o6Bdissolve*<3<*L +-0 () ) 48P ((  P  P H^?"8& d*THE SOLUTION OF THE ADJUSTMENT PROBLEM++$ P TdoD ?"h 'c P(y | do(x)) is estimable if there is a set Z of variables such that Z d-separates X from Y in Gx.d  B P N D1?"8h8L @0 0  P # 0 B P B  f DԔ?"@ B  P B  f DԔ?"@ ` B  P   f DԔ?"@0 B  P B  f DԔ?"`@0 B  P B  f DԔ?"@ 0 B  P   f DԔ?"0  B P   f DԔ?"  B P  f DԔ?"  B P B  f DԔ?"@0 P B P B  f DԔ?"   P  N Ԕ ?#" ` 0  P H^ ?" %D  HZ6*   P HD  ?" Ut  HZ3*   P H0D  ?"  HZ2*   P HTD  ?"   HZ5*   P HD  ?"a HZ1*   P HD  ?"    7X  P HlD  ?" uT  7Y  P HD  ?" Ut  HZ4*  B P @  f DԔ?"  B P @  f DԔ?"  B P  f DԔ?" p B P @  f DԔ?" p B P @  f DԔ?" p B  P  f DԔ?" p B !P  f DԔ?"  B "P @  f DԔ?" p B #P @  f DԔ?"N   $P N Ԕ ?#" `   %P HD  ?" e  HZ6*   &P H|D  ?"   HZ3*   'P H D  ?"  HZ2*   (P HD  ?"   HZ5*   )P H\D  ?" HZ1*   *P HE  ?" ` I  7X  +P BP E ?"   7Y  ,P HE  ?"8 X  HZ4*  2 -P N Ԕ?"8 @  .P HE  ?"8pOX  GZ*  B /P @ N DԔ?"(  z O  0P  O,$D0 1P  B%E  ?"O  H~Moreover, P(y | do(x)) = P(y | x,z) P(z) ( adjusting for Z) @    2P  <1E ?" y  7z  4P N;E ?" LGx. 5P Z o?"X 7P Z XE ?"} _ G @ 8P Z Ԕ?"XH P 0޽h ? f̙fE=___PPT10.6@ƾf+ D' G = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*0P %(D' =-o6Bdissolve*<3<*0P +z'0^N0 && <Recovery  T  `@cD xaxa1?=e <Gender T  `D0D xaxa1?(P 7T  T  `9D xaxa1? 7F  T  `D xaxa1?5]  7R  T  `D xaxa1?|TV  ? Treatment   T  `D xaxa1?t2   >Recovery   T  `L"C xaxa1?= Z U DBlood Pressured2 T <|AԔ?  XB T 0|AԔ?~ 7 T  `+C xaxa1?|  ? Treatment  T  `3C xaxa1?k )  >Recovery  T  `(=C xaxa1?(%  P 7T T  `0GC xaxa1? 7F T  `PC xaxa1?5 ]  7RdB T @ <DԔ? @^B T 6D1?p++pdB T @ <DԔ? @dB T @ <DԔ?@dB T <DԔ?@d2 T <|AԔ?d2 T <|Ao?3]d2 T <|Ao?8c5d2 T <|AԔ?   T  `]C xaxa1?(/P 7T T  `gC xaxa1?  7F  T  `pC xaxa1?5]  7RXB !T @ 0Ԕ?hK V  XB "T 0|AԔ?@ XB #T @ 0Ԕ?# !d2 $T <|AԔ?d d2 %T <|AԔ? d2 &T <|AԔ?(XB 'T @ 0Ԕ?h.9 XB (T 0|AԔ?k$XB )T @ 0Ԕ?!d2 *T <|AԔ?dd2 +T <|AԔ? d2 ,T <|AԔ? v -T NZGHIg1? $ ] Xvb .T NG%iH4cIK1? F ] 0 /T  `~C xaxa1?(P 7T 0T  `C xaxa1? 7F 1T  `C xaxa1?5]  7RXB 2T @ 0Ԕ?h8C XB 3T 0|AԔ?t-d2 4T <|AԔ?dd2 5T <|AԔ? d2 6T <|AԔ?|b 7T TGHt1IԔ?\ 8T HC 1?7 4W  7(a) 9T HC 1?7 C W  7(b) :T HdC 1?7 W  7(c) ;T HC 1?7 +W  7(d) 0s{>0s{ @`H  0޽h ? f̙fy___PPT10Y+D=' G = @B +y 0    (     s *,$D 0 $CAUSAL CALCULUS PROHIBITS REVERSAL,%$,, %  B  N D1?"p,$D 0LB  c $1?l l    `xaxa1?c . \ Pr(recovery | drug) < Pr(recovery | no-drug)~] $   `Hxaxa1? ;  %1Pr (male | do{drug}) = Pr (male | do{no-drug}) 2    `xaxa1?C"?K    Pr(recovery | drug, male) < Pr(recovery | no-drug, male) Pr(recovery | drug, female) < Pr(recovery | no-drug, female) $$   `"xaxa1?0j EGroup behavior:    `<'xaxa1? x  PEntailed overall behavior:    `h+xaxa1? C  A Assumption:  LB  c $Ԕ?lLB  c $Ԕ?/NLB  c $Ԕ?)/LB  c $Ԕ?j |LB  c $Ԕ?XLB  c $Ԕ?p  Zp0?" `  do{drug}H ?  Z7?"   do{no-drug}f   ZH@?" do{drug}H =  ZF?"  do{no-drug}d   ZpH?"  do{drug}H J  ZV?"H   do{no-drug} p H  0޽h ? f̙f___PPT10i.p+D=' G = @B +0 0 4 @S(     s *L` wTHE SURE THING PRINCIPLE,,,   B  N D1?" 4 <i1?U}  JTheorem 6.1.1 An action A that increases the probability of an event E in each subpopulation must also increase the probability of E in the population as a whole, provided that the action does not change the distribution of the subpopulations.: ,&SH  0޽h ? f̙f___PPT10i.9+D=' G = @B +80 )7!7P Sb , 6(   2  Z Ԕ? #" ` p B  @ Z D>? "W0 B  Z D>? "Wp   Z Ԕ? #" `B  Z D)? "s 2  Z Ԕ? #" ` ]c L t   #   c 2   T Ԕ?#" `tt B  B T D>?"{  Z Ԕ? #" `{4L t   #  +}c 2   T Ԕ?#" `tt B  B T D>?"{B  Z D)? ", 2  Z Ԕ? #" ` c 2  Z Ԕ? #" `?  2  Z Ԕ? #" `? o( B  @ Z D>? "M fH6 B  Z D>? "M 6 2  Z Ԕ? #" `? L 2  Z Ԕ? #" `?  B ! @ Z D>? "M 6 B " Z D>? "M kM 6 2 % Z Ԕ? #" `? w / 2 & Z Ԕ? #" `?  B ' @ Z D>? "M 6 B ( Z D>? "M N16 2 + Z Ԕ? #" `?  2 , Z Ԕ? #" `? T B - @ Z D>? "M t6 B . Z D>? "M 6  0 T?"~ = T Female 0.5.  1 Tx?"2 = RMale 0.5.  2 T?"t ;T8  5 t 3  Th?" ;TB 4  N Do?"F  6  tvg 7  T?" ;TB 8  N Do?" 9 T̗?"tXI ;T : TX?">   OR 0.6. ; T?"> C  OR 0.2. < T?">   OR 0.7. = Tx?"> A  OR 0.3.F  >  >   ?  T?" ;RB @  N Do?"F {'  A  > /  B  T?"{'  OR 0.7.B C  N Do?"F  D  >   E  T`?" ;RB F  N Do?"F  G  >   H  T?" ;RB I  N Do?" J TĿ?" )> ?0.3  K T?" > =0.2 L Tt?" > @0.35  M TL?"  > >0.15 N T$?" g > ?0.1  O T?" => =0.4 P T?" Kt> @0.15  Q T?" Qz> >0.35 R T?"*X  j 0.3 < 0.35D $ S T?"* j 0.1 < 0.15D $ T  `xaxa1?l 5T U  `xaxa1?`S JF Gender&  V  `xxaxa1?y- 5RXB W @ 0Ԕ?FXB X 0|AԔ?bXB Y @ 0Ԕ?`Fnd2 Z <|AԔ?8bd2 [ <|AԔ?$CTd2 \ <|AԔ?uB ] N Do?"22< ^ Z?"+ 9(a)B _ N Do?"6,6 ` s *Huc DECISION TREE FOR F = GenderL $$$$   B a N D1?"J: b Ht ?"6@ NNN?N  GF H  0޽h ? f̙f___PPT10i.Q@g+D=' G = @B +=0 <<p ]q 0 <(   B  @ T D)?"] 0B  T D>?"Wp ;B  T D>?"s 2   T Ԕ?#" ` ]c L t    #  c 2    T Ԕ?#" `tt B   B T D>?"{L t   # +}c 2   T Ԕ?#" `tt B  B T D>?"{B  T D>?", 2  T Ԕ?#" ` c 2  T Ԕ?#" `?  2  T Ԕ?#" `? o( B  @ T D>?"M fH6 B  T D>?"M 6 2  T Ԕ?#" `? L 2  T Ԕ?#" `?  B  @ T D>?"M 6 B  T D>?"M kM 6 2  T Ԕ?#" `? w / 2  T Ԕ?#" `?  B  @ T D>?"M 6 B  T D>?"M N16 2  T Ԕ?#" `?  2   T Ԕ?#" `? T B ! @ T D>?"M t6 B " T D>?"M 6  % T?"X&  S -HBP 0.75.  - T?">   OR 0.6. . Td ?"> m  OR 0.7. / TD%?">   OR 0.2. 0 T)?"> M  OE 0.3.F {'  1  > A  2  T`/?"{'  OR 0.4.B 3  N Do?" 5 Z|3?"> Y  P-E 0.7.F {'  7  > g  8  T8?"{'  OR 0.3.B 9  N Do?"F {'  :  >   ;  T7?"{'  OR 0.8.B <  N Do?" = TB?" > >0.45 > TPG?" > =0.2 ? T,K?" > >0.05 @ TO?"  > =0.2 A TI?" > > ?0.175 B TM?" > ?0.075 C TQ?" x> ?0.225 D T`U?" > ?0.525 E T,Y?"; ?0.5  F T\?"3 ?0.4  G  ``xaxa1?l 5T H  `dxaxa1?` TF Blood Pressure( I  `qxaxa1?y- 5RXB J @ 0Ԕ?FXB K 0|AԔ?bXB L @ 0Ԕ?`Fnd2 M <|AԔ?8bd2 N <|AԔ?$CTd2 O <|AԔ?uB P N Do?"22< Q Zw?" 9(b)B R N Do?"6,6 S T|?"  ;TF  T    U  T?" ;TB V  N Do?" W T Ԕ?#" ` n d X T?"% &  RHBP 0.25.  Y T?" ]&  S -HBP 0.25.  Z T?"&  RHBP 0.75. 8 * b @ * a *B [  N Do?"B \ T Do?"*B ] T Do?"*B ^ N Do?"eeF * c   N * d  *B e  N Do?"B f N Do?"*B g N Do?"*B h N Do?"ee k Z?"ZH d  ;>$2 l T Ԕ?#" `'v/2 m T Ԕ?#" `' n s *̣uc 'DECISION TREE FOR F = Blood PressureL($$$$ (  B o N D1?"J: p H  ?"6@ NNN?NNK  GF  q Hp ?"6@ NNN?N  GF H  0޽h ? f̙f___PPT10i.V]W+D=' G = @B +0  +c 7(   B  @ T D)?" v B  T D>?"p { B  T D>?" s 2  T Ԕ?#" ` ] L t    #   2    T Ԕ?#" `tt B   B T D>?"{L t    #  +} 2   T Ԕ?#" `tt B  B T D>?"{B  T D>?" , 2  T Ԕ?#" `   # Tz?"0   QR 0.50 $ Td?"0 ^   QR 0.40F {'  .  0   /  T?"{'  OR 0.5.B 0  N Do?" ;  `xaxa1?l 5T <  ` xaxa1?` TF Blood Pressure( =  `xaxa1?y- 5RXB > @ 0Ԕ?FXB ? 0|AԔ?bXB @ @ 0Ԕ?`Fnd2 A <|AԔ?8bd2 B <|AԔ?$CTd2 C <|AԔ?uB D N Do?"22< E Z?" 9(b)B F N Do?"6,6 G T?" = ;TF  H   = I  T?" ;TB J  N Do?" K T Ԕ?#" ` n 2 \ T Ԕ?#" `g v/- 2 ] T Ԕ?#" `g - F {'  ^  0 `  _  T?"{'  OR 0.6.B `  N Do?" a Tp?", t  k 0.5 > 0.4D $ b s *Duc )COMPRESSED TREE FOR F = Blood PressureL*$$$$ *  B c N D1?"J:H  0޽h ? f̙f___PPT10i.X0i+D=' G = @B +0   ?(     s *$u 6WHAT DECISION TREE SHOULD WE BUILD FOR F = Car ?\7-$$$$$ 7  B  N D1?"d2  <|AԔ? XB  0|AԔ?n'`     `xaxa1? ? Treatment     `xaxa1?\ C  >Recovery     `xaxa1? 7T    `4xaxa1? 7F    `Txaxa1?   7RdB  @ <DԔ? 0 ^B  6D1?> > dB  @ <DԔ?0dB  @ <DԔ?0dB  <DԔ?0 d2  <|AԔ?d2  <|Ao?#Md2  <|Ao? (S d2  <|AԔ?     `0xaxa1?2IZ  9Car   `!xaxa1?. UV 9(c)  TP ?"D 9???]  T 0?"|b G  AShould F = Car be handled like F = Gender or F = Blood Pressure nB   Z1?"6 DV 9???H  0޽h ? f̙f___PPT10i.Y+D=' G = @B +L0 DD k| YD(    k T7?" )> ?0.3   m NP> ?"6@ NNN?NK   Q0.6 @`2  T Ԕ?#" ` p B  @ T D>?"W0 B  T D>?"Wp   T Ԕ?#" `B  T D)?"s 2   T Ԕ?#" ` ]c L t    #  c 2    T Ԕ?#" `tt B   B T D>?"{   T Ԕ?#" `{4L t   # +}c 2   T Ԕ?#" `tt B  B T D>?"{B  T D)?", 2  T Ԕ?#" ` c 2  T Ԕ?#" `?  2  T Ԕ?#" `? o( B  @ T D>?"M fH6 B  T D>?"M 6 2  T Ԕ?#" `? L 2  T Ԕ?#" `?  B  @ T D>?"M 6 B  T D>?"M kM 6 2  T Ԕ?#" `? w / 2  T Ԕ?#" `?  B  @ T D>?"M 6 B  T D>?"M N16 2  T Ԕ?#" `?  2   T Ԕ?#" `? T B ! @ T D>?"M t6 B " T D>?"M 6  # TO?" = S Cheap 0.5.  $ TQ?"E = W Expensive 0.5.  % T Z?"t ;TF  &  t '  Tp^?" ;TB (  N Do?"F  )  tvg *  TW?" ;TB +  N Do?" , Tf?"tXI ;T . T ]?"> I  OR 0.2. / Tn?">   OR 0.7. 0 Ts?"> ;  OR 0.3.F  1  >   2  Tdy?" ;RB 3  N Do?"F {'  4  > Y  5  T}?"{'  OR 0.7.B 6  N Do?"F  7  >   8  T?" ;RB 9  N Do?"F  :  >   ;  T`?" ;RB <  N Do?" > T8?" > =0.2 ? T|?" > @0.35  @ TT?"  > >0.15 A T̗?" g > ?0.1  B T?" => =0.4 C T@?" Kt> @0.15  D TԢ?" Qz> >0.35 E Th?"IO  j 0.3 < 0.35D   F T$?"I j 0.1 < 0.15D  B P N Do?"28B R N Do?", S s *Tuc zTEMPORAL ORDER IS DECEPTIVE,$$   B T N D1?"J: U Z?"~ 9(c)d2 V <|AԔ?ZHsXB W 0|AԔ?6 X  `Hxaxa1?g ? Treatment  Y  `$xaxa1?Y >Recovery  Z  `|xaxa1?}^ 7T [  `Խxaxa1?C/ 7F \  `xaxa1?  7RdB ] @ <DԔ?x^B ^ 6D1?dB _ @ <DԔ?mxdB ` @ <DԔ?hdB a <DԔ?hd2 b <|AԔ?Yd2 c <|Ao?ad2 d <|Ao?d2 e <|AԔ?u( f  `Hxaxa1?2# 9Car g T?"  9F  | N ?"6@ NNN?NC he  OR @`l N`b y N`b,$@ 0@ Ni> q Ni> @ Ni  n Ni  -  Tt?">   Q 0.60@ Ni  j Ni B h  T D>?"0 z  i  Z<o?"Ni2  =WrongB o  BD>?"0@NNN?N~< 8d p  T?") > ?0.3 @ 6 b u 6 bB s  <DԔ?"0@NNN?N6 bB t <DԔ?"0@NNN?N6 bN 6 b v  `bB w  <DԔ?"0@NNN?N6 bB x <DԔ?"0@NNN?N6 bH  0޽h ? f̙f___PPT10v.ZX+݄7D' G = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*y %(D' =-o6Bwipe(up)*<3<*y D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*m %(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*k %(+8+0+k 0 +!0   5A [ (   B  @ T D)?" v B  T D>?"p { B  T D>?" s 2  T Ԕ?#" ` ] L t   #   2   T Ԕ?#" `tt B  B T D>?"{L t   #  +} 2   T Ԕ?#" `tt B  B T D>?"{B  T D>?" , 2  T Ԕ?#" `    T?"0   QR 0.50  T?"0 ^   QR 0.40F {'    0     T$?"{'  OR 0.5.B   N Do?"B  N Do?"22  Z ?" 9(c)B  N Do?", ! T?" = ;TF  "   = #  T?" ;TB $  N Do?" % T Ԕ?#" ` n 2 & T Ԕ?#" `g v/- 2 ' T Ԕ?#" `g - F {'  (  0 `  )  T?"{'  OR 0.6.B *  N Do?" + T@?"o )  k 0.5 > 0.4D  d2 , <|AԔ?ZHsXB - 0|AԔ?6 .  `"xaxa1?g ? Treatment  /  `&xaxa1? >Recovery  0  `*xaxa1?}^ 7T 1  `P.xaxa1?C/ 7F 2  `1xaxa1?  7RdB 3 @ <DԔ?x^B 4 6D1?dB 5 @ <DԔ?mxdB 6 @ <DԔ?hdB 7 <DԔ?hd2 8 <|AԔ?Yd2 9 <|Ao?ad2 : <|Ao?d2 ; <|AԔ?u( =  `8xaxa1?2# 9Car > s *4?uc rCORRECT DECISION TREE,$$   B ? N D1?"J: @  c $A ??"` < x d A  c $A  ??"` x  dH  0޽h ? f̙f___PPT10i.[`T+D=' G = @B +G0 AA coD 2A(  D  D TtD?" )> ?0.3   D NHF ?"6@ NNN?NK   Q0.6 @`2 D T Ԕ?#" ` p B  D @ T D>?"W0 B  D T D>?"Wp   D T Ԕ?#" `B  D T D)?"s 2  D T Ԕ?#" ` ]c L t  D #  c 2 D  T Ԕ?#" `tt B D B T D>?"{ D T Ԕ?#" `{4L t  D # +}c 2 D  T Ԕ?#" `tt B D B T D>?"{B D T D)?", 2 D T Ԕ?#" ` c 2 D T Ԕ?#" `?  2 D T Ԕ?#" `? o( B D @ T D>?"M fH6 B D T D>?"M 6 2 D T Ԕ?#" `? L 2 D T Ԕ?#" `?  B D @ T D>?"M 6 B D T D>?"M kM 6 2 D T Ԕ?#" `? w / 2  D T Ԕ?#" `?  B !D @ T D>?"M 6 B "D T D>?"M N16 2 #D T Ԕ?#" `?  2 $D T Ԕ?#" `? T B %D @ T D>?"M t6 B &D T D>?"M 6  'D TL\?" = S Cheap 0.5.  (D Txa?"E = W Expensive 0.5.  )D Te?"t ;TF  *D  t +D  Tpd?" ;TB ,D  N Do?"F  -D  tvg .D  Tm?" ;TB /D  N Do?" 0D Tq?"tXI ;T 1D T8u?"> I  OR 0.2. 2D Ttz?">   OR 0.7. 3D Td0?"> ;  OR 0.3.F  4D  >   5D  T?" ;RB 6D  N Do?"F {'  7D  > Y  8D  Tp?"{'  OR 0.7.B 9D  N Do?"F  :D  >   ;D  T ?" ;RB    >D  T?" ;RB ?D  N Do?" @D T ?" > =0.2 AD T?" > @0.35  BD T?"  > >0.15 CD T?" g > ?0.1  DD T?" => =0.4 ED T<?" Kt> @0.15  FD TЪ?" Qz> >0.35X GD T?"uV D0.6 = P(R | T,F) P(R | do(T), F)D# B ID N Do?"28B JD N Do?", KD s *8uNHc !WHAT WENT WRONG WITH F = Car ?\"$$$$$ "  B LD N D1?"J: MD Z?"~ 9(c)d2 ND <|AԔ?ZHsXB OD 0|AԔ?6 PD  `xaxa1?g ? Treatment  QD  `pxaxa1?Y >Recovery  RD  `xaxa1?}^ 7T SD  `xaxa1?C/ 7F TD  `\xaxa1?  7RdB UD @ <DԔ?x^B VD 6D1?dB WD @ <DԔ?mxdB XD @ <DԔ?hdB YD <DԔ?hd2 ZD <|AԔ?Yd2 [D <|Ao?ad2 \D <|Ao?d2 ]D <|AԔ?u( ^D  `xaxa1?2# 9Car _D T?"  9F  `D N ?"6@ NNN?NC he  OR @`L Ni> bD # Ni>&N Ni  cD  Ni  dD  T\?">   Q 0.60N Ni  eD  Ni B fD  T D>?"0 z  gD  Z o?"Ni2  =WrongB hD  BD>?"0@NNN?N~< 8d iD  TD:?") > ?0.3 H D 0޽h ? f̙f{___PPT10[.'B+D' G = @B D' = @BA?%,( < +O%,( < +D' =%(%(Dq' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*D %(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*D %(+8+0+D 0 +<0 ;; ZeH a;(  H L N> VH # N>&N N  WH  N  XH  T :?">   Q 0.60N N  YH  N B ZH  T D>?"0 z  [H  Z:o?"N2  =RightB \H  BD>?"0@NNN?N~< 8d ]H  T:?") > ?0.3  =H Th:?" X> =  2 H T Ԕ?#" ` p B H @ T D>?"W0 B H T D>?"Wp  H T Ԕ?#" `B H T D)?"s 2  H T Ԕ?#" ` ]c L t   H #  c 2  H  T Ԕ?#" `tt B  H B T D>?"{  H T Ԕ?#" `{4L t  H # +}c 2 H  T Ԕ?#" `tt B H B T D>?"{B H T D)?", 2 H T Ԕ?#" ` c 2 H T Ԕ?#" `?  2 H T Ԕ?#" `? o( B H @ T D>?"M fH6 B H T D>?"M 6 2 H T Ԕ?#" `? L 2 H T Ԕ?#" `?  B H @ T D>?"M 6 B H T D>?"M kM 6 2 H T Ԕ?#" `? w / 2 H T Ԕ?#" `?  B H @ T D>?"M 6 B H T D>?"M N16 2 H T Ԕ?#" `?  2  H T Ԕ?#" `? T B !H @ T D>?"M t6 B "H T D>?"M 6  #H T :?"~ = T Female 0.5.  $H Tx":?"2 = RMale 0.5.  %H T*:?"t ;TF  &H  t 'H  Th/:?" ;TB (H  N Do?"F  )H  tvg *H  T3:?" ;TB +H  N Do?" ,H T7:?"tXI ;T -H TX;:?"> he  MR . .H T@:?"> C  OR 0.2. /H TD:?">   OR 0.7. 0H TxI:?"> A  OR 0.3.F  1H  >   2H  T9:?" ;RB 3H  N Do?"F {'  4H  > /  5H  TQ:?"{'  OR 0.7.B 6H  N Do?"F  7H  >   8H  T`W:?" ;RB 9H  N Do?"F  :H  >   ;H  T[:?" ;RB H T_:?" > =0.2 ?H Tc:?" > @0.35  @H Ttg:?"  > >0.15 AH TLk:?" g > ?0.1  BH T$o:?" => =0.4 CH Tr:?" Kt> @0.15  DH Tv:?" Qz> >0.35 GH  `z:xaxa1?l 5T HH  `p:xaxa1?`S JF Gender&  IH  `:xaxa1?y- 5RXB JH @ 0Ԕ?FXB KH 0|AԔ?bXB LH @ 0Ԕ?`Fnd2 MH <|AԔ?8bd2 NH <|AԔ?$CTd2 OH <|AԔ?uB PH N Do?"22< QH Z:?"+ 9(a)B RH N Do?"6,6  SH s *:uc $WHAT WENT RIGHT WITH F = Gender ?\%$$ $$$ %  B TH N D1?"J:6 dH Tx:?"ub "0.6 = P(R | T,F) = P(R | do(T), F)D#   eH H̩: ?"6@ NNN?N  GF H H 0޽h ? f̙f___PPT10i.'`O+D=' G = @B +0  *4$ `,(  $ B $ N D1?"j2 $ B|AԔ? ^B $ 6|AԔ? n't  $  f:xaxa1? ? Treatment   $  f|:xaxa1?p C  >Recovery   $  fH:xaxa1?  7T  $  fh:xaxa1?  7F  $  fL:xaxa1?   7RjB  $ @ BDԔ? 0 dB $ <D1?R R jB $ @ BDԔ?0jB $ @ BDԔ?0 jB $ BDԔ? 0 j2 $ B|AԔ?  j2 $ B|Ao?#Mj2 $ B|Ao? (S j2 $ B|AԔ?   $  f(:xaxa1?F In  9Car $  fl:xaxa1?wF 9(c) $  f :xaxa1?_ E Compelled Actj2 $ B|AԔ?2]^B $ 6|AԔ? yt  $  f:xaxa1?  ? Treatment  $  f:xaxa1?p   >Recovery  $  fL:xaxa1?I*  7T $  f(:xaxa1?-  7F $  f:xaxa1?    7RjB  $ @ BDԔ?  dB !$ <D1?R mmR jB #$ @ BDԔ? jB $$ BDԔ?  j2 %$ B|AԔ?  j2 &$ B|Ao?uj2 '$ B|Ao? z j2 ($ B|AԔ?   )$  fx:xaxa1?F On  9Car *$  f:xaxa1?m 9(c) +$  f:xaxa1? 5 @Free Act  .$ Td:?"Y YTHE PERCEPTION OF FREE WILL  ( /$  `Lxaxa1? G 4 J(Explained reaction) 0$  `Lxaxa1?  4 @ (Decision) H $ 0޽h ? f̙f___PPT10i.[+D=' G = @B +0 @ 0 v(  0 B 0 N D1?" 0 T L?"&Y b(DISAMBIGUATING THE TWO ROLES OF ACT ))( 0 TL?"   $Whatever evidence an act might provide On motives that cause such acts, Should never be used to help one decide On whether to choose that same act. (p. 109):7H 0 0޽h ? f̙f___PPT10i.)0P? +D=' G = @B +Y%0 ` 0H4 @z(  4 B 4 N D1?"j2 4 B|AԔ? ^B 4 6|AԔ? n't   4  f$Lxaxa1? ? Treatment   4  fLxaxa1?p C  >Recovery   4  fH Lxaxa1?  7T  4  f$Lxaxa1?  7F  4  fd(Lxaxa1?   7RjB 4 @ BDԔ? 0 dB 4 <D1?R R jB 4 @ BDԔ?0jB 4 @ BDԔ?0 jB 4 BDԔ? 0 j2 4 B|AԔ?  j2 4 B|Ao?#Mj2 4 B|Ao? (S j2 4 B|AԔ?   4  f4/Lxaxa1?F In  9Car 4  f 3Lxaxa1?wF 9(c) 4  `6Lxaxa1?_ E Compelled Actj2 4 B|AԔ?2]^B 4 6|AԔ? yt  4  f@;Lxaxa1?  ? Treatment  4  f?Lxaxa1?p   >Recovery   4  fLCLxaxa1?I*  7T !4  fGLxaxa1?-  7F "4  fhKLxaxa1?    7RjB #4 @ BDԔ?  dB $4 <D1?R mmR jB %4 @ BDԔ? jB &4 BDԔ?  j2 '4 B|AԔ?  j2 (4 B|Ao?uj2 )4 B|Ao? z j2 *4 B|AԔ?   +4  fPLxaxa1?F On  9Car ,4  fTLxaxa1?m 9(c) -4  `lXLxaxa1? 5 @Free Act  .4 T \L?"Y UTHE PARADOX OF FREE WILL( /4  `(ZLxaxa1? G 4 J(Explained reaction) 04  `dLxaxa1?  4 @ (Decision) 8 _ E4 _ C4  ZxcL?"_>  9God D4  ZkL?" 9GodLz _ F4  _,$D0 G4  ZoL?"_i  =Physics H4  ZsL?" =PhysicsH 4 0޽h ? f̙f___PPT10.)G++D' G = @B Df' = @BA?%,( < +O%,( < +D' =%(DE' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*E4 %(Dc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*F4 %(D' =-o6Bdissolve*<3<*F4 +g0 ~v @ (  @  @ BzL ?"6@ NNN?N(PH@___PPT9" rFree will is an illusion that demands a computational model, to explain: What mental activity generates the illusion of acting freely? Why/how is such illusion generated from the activity above? How can we survive the distortion generated by the illusion? Is the distortion harmless? Is the illusion dispensable? What is the computational usefulness of the illusion?<K(K( @`& @ s *L,$D 0 :COMPUTATIONAL RESOLUTION OF THE PARADOX OF FREE WILL.;:$$ ;  B @ N D1?"9d9,$D 0H @ 0޽h ? f̙f___PPT10i.$?a+D=' G = @B +X0 ogp < (  <  < s *pL,$D 0 i CONCLUSIONS.  ,,   B < N D1?"9d9,$D 0 < HL?"\O D<4___PPT9 6Simpson's Paradox is resolved through the calculus of causation. People think causally, not probabilistically Decision trees cannot replace causal models Free-will is a software illusion to be explained in computational terms.  @`H < 0޽h ? f̙f___PPT10i.#d+D=' G = @B +0 ( P(  ( d ( c $D>    ( s *ϗD C   : H ( 0jB ? ̙33xXOA3[.`"X1r(&&Ѥ(m."iaƃ'cЃ1z㠉c ȁѨh뼙ew& 53o>}f!Al >bP r99+ɚ0h없CCq²Re30B  ]NTzdLe**P{a 5 fO -ھ- YSJhC F|dϡt*Jhodg8߬W/n?rq{?r/5.?ASpq9y@ XUP€&Ԉ_#O|Cn@Gx^e>.jo! 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