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HQ?"UX^ Eg Why path-specific effects? What are the semantics of path-specific effects (in nonlinear and nonparametric models)? What are the policy implications of path-specific effects? When can path-specific effects be estimated consistently from experimental or nonexperimental data? Can these conditions be verified from accessible causal knowledge, i.e., graphs?4L5)45( ) =   PX @`H  0޽h ? f̙fy___PPT10Y+D=' = @B + P (    H8?"$ VNF___PPT9(  0Direct (or indirect) effect may be more transportable. Indirect effects may be prevented or controlled. Direct (or indirect) effect may be forbiddenbm0-1m- @`  H?" PWHY DECOMPOSE EFFECTS?,B  N D1?"p(p  T?"l :Pill  Tl?" s 5  @ Thrombosis    Tȿ?"\ | ? Pregnancy  2   Z o?"   2   Z o?"s 2   Z o?" 6B    ` D>?"/  B    ` D>?"I  B @  `m D>?"; F #  TĬ?"9  Y  9+  Tɬ?" k  L-.  TǬ?"9 > " Y  9+2  Z o?"Z  2  Z o?" s M 2  Z o?"w  B   ` D>?"  B   ` D>?" A wB @  `m D>?". ; F   T0Ҭ?"- M  >Gender  Tլ?"C  <Hiring  Tج?" /  C QualificationH  0޽h ? f̙fy___PPT10Y+D=' = @B + `0 `(    s *߬  {%EFFECT-DECOMPOSITION IN LINEAR MODELS&&,B  N D1?"  Z?"G"  ;X   Z?" X  ;Z   Z?"h 9   ;Y    Z?" n  ;c    ZL?"| ;a    Z?"W I  <b  B   Z D>?" B   Z D>?"8 hB @ Z D>?"8 h8 X 1  P )   c $A y??X  x wd  TH_?" 1  9a  T_?"n 1  Tbc  T_?"Q  C Definition:  8      s *A G?? x Gd  s *A B??"` X x Bd  s *A C??"`hR `x CdH  0޽h ? f̙fy___PPT10Y+D=' = @B +&  =5P  (    s *t#_R o!CAUSAL MODELS AND COUNTERFACTUALS""( "  B  N D1?"{h{V F p  u8  H+_?" ,$D 0 8pDefinition: A causal model is a 3-tuple M = V,U,F9 " @`  N8@_?",$D 0 (i) V = {V1& ,Vn} endogenous variables, (ii) U = {U1,& ,Um} background variables (unit)TV  NA_?"p$D 0LD___PPT9&  F = set of n functions, The sentence:  Y would be y (in unit u), had X been x, denoted Yx(u) = y, is the solution for Y in a mutilated model Mx, with the equations for X replaced by X = x. ( unit-based potential outcome ) 0       $,`3Q8Xx  c $A' ??"`d  x dpH  0޽h ? f̙f___PPT10i.|dž+D=' = @B +  p0L|7(  | | s *Ą_: s%COUNTERFACTUALS: STRUCTURAL SEMANTICS&&( &  w | 08_t Notation: Yx(u) = y Y has the value y in the solution to a mutilated system of equations, where the equation for X is replaced by a constant X=x.  Z&       B | N D1?"hhF  ) | Y   |  BaCDE@F >aM1"%< DOU)/?R _ tUU @     G ; V `Q   |# W W ,$ 0N E l | `Q  Z  | s *E  kN   h  |   lfB  | 6D>  hfB  | 6D>  hfB  | 6D>  hfB | 6D>  hN  l |  l`  l |C  lfB | 6D  h |  BCDE@F D7kxk](V@EX3q @      l |  BCVDEFV @` k |  BCXDE F*(8PXXX@`T  xB |B HZD>:W 1LrB | BD>K G xB | HZD>KM BErB | BD>KK  | <_f)  Wu&    | <_ Yx(u)=yF (     | < _k R WZ&    | <4_rd   WW&    | <_ 3 OX=x   Z | s *Ef2 | 6Ԕ  ;F o K  | Z xB !|B HZD>  rB "| BD>  xB #| HZD>  rB $| BD>  %| <_8\  Wu&    &| <_K YY(    '| <_= o  WZ&    (| <4_D,   WW&    )| <_ + MX   Z *| s * ]xB +| HZD>+ "  ,| T0_?" H  WProbability of Counterfactuals:   -| T_?"   nFunctional Bayes Net  .| s *A ??dx d` /| c $A 7??, d  7 L| c $A! ??"` x dH | 0޽h ? f̙fy___PPT10Y+D=' = @B +K0  (    c $A 8??T x 8dAL  s *|_ 4< TTOTAL, DIRECT, AND INDIRECT EFFECTS HAVE CONTROLLED-BASED SEMANTICS IN LINEAR MODELSfU$$$ $9$B  N D1?"tt  T_?"wt 9X  T_?"  9Z  TDl?"5  9Y  Tl?"F  9c   Tl?"6W;} 9a   Th l?"n :b B   T D>?"Q B   T D>?"! B  @ T D>?"!    T l?"6 , b8z = bx + e1 y = ax + cz + e2,*  Tl?"   a + bcT  Z#l?"-0 t i bc(  Z(l?" 6  L 9aH  0޽h ? f̙fy___PPT10Y+D=' = @B + K0   y (    TP%l?" J <<z = f (x, e1) y = g (x, z, e2)  c $A 9??p $ x 9dA  T ;l?"wt 9X  T=l?"  9Z  T@l?"  9YB  T D>?"XQ XB  T D>?"!B  @ T D>?"! -   s *HGl LT kCONTROLLED-BASED SEMANTICS NONTRIVIAL IN NONLINEAR MODELS (even when the model is completely specified)0l>$. B   N D1?"   TRl?". g  ,   T0Ul?"  1a cDependent on z?8   T`Zl?"p G RVoid of operational meaning?H  0޽h ? f̙fy___PPT10Y+D=' = @B +{    2 (    N`l?"p  ``The central question in any employment-discrimination case is whether the employer would have taken the same action had the employee been of different race (age, sex, religion, national origin etc.) and everything else had been the same  [Carson versus Bethlehem Steel Corp. (70 FEP Cases 921, 7th Cir. (1996))] x = male, x = female y = hire, y = not hire z = applicant s qualificationsj 0!8      @`  s *yl M DLEGAL DEFINITIONS OF DIRECT EFFECT (FORMALIZING DISCRIMINATION),E'& B  N D1?""  T}l?"V t   HNO DIRECT EFFECT  0A ?Ԕ? 0 @(x dH  0޽h ? f̙fy___PPT10Y+D=' = @B +AK0 PH (  |  T,xl?"2 D z = f (x, u) y = g (x, z, u)  Tl?"wt  9X  Tdl?"  9Z  Tl?"%  9YB  T D>?"Q B  T D>?"! B @ T D>?"!     s *l  /NATURAL SEMANTICS OF AVERAGE DIRECT EFFECTS00$B   N D1?"44   H$l?"\  pAverage Direct Effect of X on Y: The expected change in Y, when we change X from x0 to x1 and, for each u, we keep Z constant at whatever value it attained before the change. In linear models, DE = Controlled Direct Effectt   <Z   S  :??pp  :Z   S  ;??pp  ;  c $A <??9Jx <d  c $A* ??"`h x x d   N|l?"Pp ~HRobins and Greenland (1992)   Pure %%H  0޽h ? f̙fy___PPT10Y+D=' = @B +]  ]U` (    Hl?"P k!POLICY IMPLICATIONS (Who cares?)."( (  Zlo?"; o m  M f ( Ez B! c  ! Bc,$D 0  Tl?"B! A  NGENDER,   Tl?"Z ! A  S QUALIFICATION*    Tl?" C c <HIRINGB   T D>?" } B   T D>?" _ % B   T D>?"w . . V B @ T D>?" % B  N D1?"\  Hs?"G $What is the direct effect of X on Y?%   @`f  Zl?"},$ 0 @Is employer guilty of sex-discrimination given data on (X,Y,Z)?>A9  T s?"! A  ;X  T s?"! j S A  IZ,  TD s?"C c GY*B @ N DԔ?"8    T8s?" xK  QCAN WE IGNORE THIS LINK?  c $A" ??ix dH  0޽h ? f̙f___PPT10.|P/<+kVD' = @B D' = @BA?%,( < +O%,( < +D' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+l + K0   B (  j  TI?" DN z = f (x, u) y = g (x, z, u)  TL?"wt 9X  T?s?"  9Z  THDs?"  9YB  T D>?"XQ XB  T D>?"!B @ T D>?"!    s *As  ~(NATURAL SEMANTICS OF INDIRECT EFFECTS))$B   N D1?"44   HlUs?"\  YIndirect Effect of X on Y: The expected change in Y when we keep X constant, say at x0, and let Z change to whatever value it would have attained had X changed to x1. In linear models, IE = TE - DE t  5   `   c $A =?? |  =   c $A >??yFx >d  c $A) ??"`i b y x dAH  0޽h ? f̙fy___PPT10Y+D=' = @B +_K0 WO(    H`qs?"P k!POLICY IMPLICATIONS (Who cares?)."( (  Z vso?"; o m  M f ( Ez B! c  ! Bc,$D 0  T@{s?"B! A  NGENDER,  Ts?"Z ! A  S QUALIFICATION*   Ts?" C c <HIRINGB  T D>?" } B   T D>?" _ % B   T D>?"w . . V B  @ T D>?" % B   N D1?"^   Hs?"G &What is the indirect effect of X on Y?'   @`G  Zs?"},$ 0 {CThe effect of Gender on Hiring if sex discrimination is eliminated.DD  TXs?"! A  ;X  Tԟs?"! j S A  IZ,  Ts?"C c GY*B @ N DԔ?"8    T s?" _  <IGNOREH  0޽h ? f̙f___PPT10p+D' = @B D' = @BA?%,( < +O%,( < +D' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+s +     p  8 (    0ts(b p6SEMANTICS AND IDENTIFICATION OF NESTED COUNTERFACTUALS7 7(B  N D1?"hh   0  Consider the quantity Given M, P(u), Q is well defined Given u, Zx*(u) is the solution for Z in Mx*, call it z is the solution for Y in Mxz Can Q be estimated from data? Experimental: nest-free expression Nonexperimental: subscript-free expressionB $$ 4$$:  @`  c $A# ?? x d   c $A$ ??( V x d   c $A% ?? !Q9 x dH  0޽h ? f̙f___PPT10i.|\@+D=' = @B +    @X (  XK X Hp?"1  Corollary 3: The average direct effect in Markovian models is identifiable from nonexperimental data, and it is given by where S stands for any sufficient set of covariates.    T  @` X Hq?" \"IDENTIFICATION IN MARKOVIAN MODELS##,B X N D1?"2 X N o ?"?  N c 2 X N o ?" 2 X N o ?"  J B X T D>?"Z = B X T D>?"R = *  X Tw?" L@  9X X T${?" 1 4  9ZB X@ T D>?" - * X T9s?"X   Example: S = `  X T7s?" w  9Y X c $A ??4x d X c $A !??8x !dH X 0޽h ? f̙fy___PPT10Y+D=' = @B +% *+T+(  T2 T N Ԕ ?"><2 T N Ԕ ?"x m B T@ T DԔ?"W B T T D?"2 T N Ԕ ?"J2 T N Ԕ ?"}nB T T D?"Y YB  T@ T D?"f l  T T̈?"b  7Y  T T8s?"4 7Z  T T4?"<kT\ 7X  T Tp-?" 4 7W2 T N Ԕ?"3B T@ T DԔ?" )2 T N Ԕ?"c/z . J T J. ,$D  0B T N D?"A  T T?". J=p Hx** ~z Y T Y,$D  0B T N D?"Y` T T?"  z* = Zx* (u)|     T Hp?" ^$GENERAL PATH-SPECIFIC EFFECTS (Def.)%%$B T N D1?"(( T c $A ?? x x d  T c $A ??x d2 T N Ԕ ?">A2 T N Ԕ ?"x,$D 0B T@ T DԔ?" ,$D 0B T T D?"22,$D  02  T N Ԕ ?"O,$D 02 !T N Ԕ ?"}sB "T T DԔ?">@,$D 0B #T T D?"  ,$D  0B $T@ T D?",$D 0 %T TL?"3  7Y &T T?"j 4 7Z 'T Td?"<\ 7X (T T?"4 7W2 )T Tк?" nU0  6Form a new model, , specific to active subgraph g,75, *T c $A ?? D T x d +T T\?" n  Definition: g-specific effectL H T 0޽h ? f̙f___PPT10+AcD' = @B DC' = @BA?%,( < +O%,( < +Dz' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-o6Bwipe(up)*<3<*TD' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-s6Bwipe(down)*<3<*T+' <  11j(  ~  s *@    F     `B B 0DԔY+32  N??"6?@`NNN?N@g`B B 0DԔ88'`B  0DԔ+@`B  0DԔ38 `B  B 0DԔ `B   0DԔP RB   s *D>b b vz      ,$D 0N      `B B 0DԔY+32  N??"6?@`NNN?N@g`B B 0DԔ88'`B  0DԔ+@`B  0DԔ38 `B B 0DԔ `B  0DԔP ZB  s *D> B  0Do33,$D 0B  0Do&N&,$@ 0z  +6   + 6 ,$@ 0N  +N    +6 2  N??"6?@`NNN?N^ `B  0DԔ 2  N??"6?@`NNN?N_+  s BCDEFԔN wI@  \N B s BCDEFԔN wI@   \jfB  6DԔ\ZB  B s *D>P6NZB ! s *D>NNZB " s *D>  NZB # s *D>  Tz >,  $ ,> ,$D 0N  +N  % >, 2 & N??"6?@`NNN?N^ `B ' 0DԔ 2 ( N??"6?@`NNN?N_+ ) s BCDEFԔN wI@  \N *B s BCDEFԔN wI@   \jfB + 6DԔ\ZB ,B s *D>MZB - s *D>MSMZB . s *D>>M / 0 *  @Rule 1 2  0 0 * P,$ 0 @Rule 2 2 B 1 N D1?"((H  0޽h ? 3ff~O G ___PPT10' .K{O++D ' = @B D~ ' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(+8+0+0  +  =   ' (  ~  s *      s *ԭ v    (n'o(  0    aR - Recanting witness00   00 j  ?Z"0   6l ^ ~ ?Y"0 2  < "`N _  8$0 2  < "`_  8$0 2   < "`n _  8$0 dB   <DԔ n     BCDEFԔH8pHx@  "` _ D    BCDEFԔH8pHx@  "` v DXB   0D># ' B  N D1?"((H  0޽h ? 3ff~___PPT10i.^{+D=' = @B + >   j(  ~  s * p     6 '  G  =X 0   <D I1 i =Y 0   6l  1  =Z 0   6$  {k  =W 0 2   Z ?Ԕ?"6?@`NNN?NO 0  6"0 2   Z) ?Ԕ?"6?@`NNN?N/   6"0 2   Z1 ?Ԕ?"6?@`NNN?N0 o 6"0 B  @ Z?DԔ?"0?@NNN?N 0 / B   Z?DԔ?"0?@NNN?N 0 B @ Z?DԔ?"0?@NNN?N_  ` 2  ZD ?Ԕ?"6?@`NNN?N/ @  6"0 B  Z?DԔ?"0?@NNN?N / B @ Z?DԔ?"0?@NNN?N B  Z?DԔ?"0?@NNN?N ` a 2  <LN "`/ @  6"0 2  <X "`/  6"0   6X   @Z  0   6k  Z  @Z  0 B  Z?DԔ?"0?@NNN?N @/ B  Z?DԔ?"0?@NNN?N / B @ Z?DԔ?"0?@NNN?N B @ Z?DԔ?"0?@NNN?N ?XB  0D>   BTt  ud   B  N D1?"((H  0޽h ? 3ff~___PPT10i._{Y+D=' = @B +j ? `'X' 5@&(    6  m IAZT EXAMPLE REVISITEDXB @ 0D33ԔMB @ T?D33Ԕ?"0?@NNN?N5XB  0DԔ x B @ T?D33Ԕ?"0?@NNN?N w B  T?D33Ԕ?"0?@NNN?NTwB  T?D33Ԕ?"0?@NNN?N?| B  @ T?D33Ԕ?"0?@NNN?N? B   T?D33Ԕ?"0?@NNN?NZ    0T H/ 9AZT 2   0Ġ n U ? Pneumonia 2    0 d *G K  A Antibiotics 2   0 n`U A Headaches ( 2   0X ` G  C Painkillers ( 2   0  d  >Survival 2 2  N??"6?@`NNN?NtI2  N??"6?@`NNN?N  2  N??"6?@`NNN?Nf  `2  s *"`a2  N??"6?@`NNN?NI2  N??"6?@`NNN?N1 RB @ s *D> OZ   0h   v>Painkiller contribution to the total effect of AZT on survival? 2?  00 ` G ,$ 0 A Antibiotics 2 B @ T?D33Ԕ?"0?@NNN?NIV ,$@  0B @ T?D33Ԕ?"0?@NNN?N1O ,$@  0B  T?D33Ԕ?"0?@NNN?N O  ,$@  0B @ T?DԔ?"0?@NNN?N R ,$@  0B  T?D33Ԕ?"0?@NNN?NP;,$@  0B  T?D33Ԕ?"0?@NNN?N;.,$@ 0B  @ T?D33Ԕ?"0?@NNN?N;@ ,$@ 0B ! T?D33Ԕ?"0?@NNN?NV ,$@ 0 " 0< D\+,$ 0 9AZT 2 # 0 j%Q,$ 0 ? Pneumonia 2  $ 0 j %Q,$ 0 A Headaches ( 2  % 0$  [ $ eB ,$ 0 C Painkillers ( 2  & 0t   ,$ 0 >Survival 2 2 ' N??"6?@`NNN?N8E,$@ 02 ( N??"6?@`NNN?N G ,$@ 02 ) N??"6?@`NNN?N* ,$@ 02 * s *"` G],$@ 02 + N??"6?@`NNN?NUE,$@ 02 , N??"6?@`NNN?N c - ,$@ 0B - s *D> g` ,$@ 0B . c $D2 2 H,$@ 0  / 0  ),$ 0 w?Antibiotics contribution to the total effect of AZT on survival@ 2@B 0 s *D>HB,$@ 0B 1 s *D>W,$@ 0B 2@ s *D>wT5,$@! 0 9 H ?#" `!a,$D#  0 < C 8A  Export Wizard-2 ,$D  0B @ N D1?"((H  0޽h ? 3ff~BB___PPT10B.W{PS+B0DA' = @B D@' = @BA?%,( < +O%,( < +D#' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D]' =4@BBBB%(D' =,54*3>#Bstroke.color=@BPB<*D' =1:B true*a3>Bstroke.on<*D#' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*0%(D]' =4@BBBB%(D' =,54*3>#Bstroke.color=@BPB<*D' =1:B true*a3>Bstroke.on<*Dn' =%(D' =%(D' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?`CB4*#ppt_wBCB#ppt_wB*Y3>B ppt_w<*<D' =+4 8?`CB4*#ppt_hBCB#ppt_hB*Y3>B ppt_h<*<D$' =%(D?$' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*.%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*-%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D#' =%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*-%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*2%(D]' =4@BBBB%(D' =,54*3>#Bstroke.color=@BPB<*D' =1:B true*a3>Bstroke.on<*Dn' =%(D' =%(D' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*9%(D' =+4 8?`CB4*#ppt_wBCB#ppt_wB*Y3>B ppt_w<*9D' =+4 8?`CB4*#ppt_hBCB#ppt_hB*Y3>B ppt_h<*9++0+  ++0+"  ++0+#  ++0+$  ++0+%  ++0+&  ++0+/  +' @ e] $)(  ^F ;P   GX B  T?D33Ԕ?"0?@NNN?N;PB  T?DԔ?"0?@NNN?N.;B B T?D33Ԕ?"0?@NNN?N@; 2  N??"6?@`NNN?N8E~  s *lj       0o ` N Z  A Antibiotics 2 B  @ T?D33Ԕ?"0?@NNN?NIoB  @ T?D33Ԕ?"0?@NNN?N1 }B   T?D33Ԕ?"0?@NNN?N O B  @ T?DԔ?"0?@NNN?N N B   T?D33Ԕ?"0?@NNN?NV~~   0z ! 9AZT 2  0 jd ? Pneumonia 2   0@ j |d A Headaches ( 2   0     C Painkillers ( 2   0ܠ  k;  >Survival 2 ^F ;P   GX B  T?D33Ԕ?"0?@NNN?N;PB  T?DԔ?"0?@NNN?N.;B B T?D33Ԕ?"0?@NNN?N@; 2  N??"6?@`NNN?N8E2  N??"6?@`NNN?N Z 2  N??"6?@`NNN?N= `2  s *"` Z]2  N??"6?@`NNN?NiE2  N??"6?@`NNN?Nw -   0   w?Antibiotics contribution to the total effect of AZT on survival@ 2@RB @ s *D>w5 $ <, & ,$ 0 HR-Recanting Witness  % 0 P  J ,$ 0 RR behaves as I( 2 & 0   p ,$ 0 SR behaves as II( 2^ ' 0 pex,$ 0 ,P(RX,RX*) is not experimentally identifiable- 2MM% ( H ?#" `ZB ) N D1?"((H  0޽h ? 3ff~___PPT10 .|`=R+D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D/' =4@BB#BB%()?)?D' =.K7 BBBBB]M -4.72222E-6 -4.95829E-6 L -0.54878 0.06048 *3>*B ppt_xB ppt_y=@0BBAApBBB;<<*D0' =4@BBBB%(D' =0l9 CCBB*<3<*DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(Ds' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(++0+$  ++0+%  ++0+&  ++0+'  + *"(    Z  Ԕ? `SUMMARY OF RESULTS(   B  N D1?"hh  H?"UD<4___PPT9 2\Formal semantics of path-specific effects, based on signal blocking, instead of value fixing. Path-analytic techniques extended to nonlinear and nonparametric models. Meaningful (graphical) conditions for estimating effects from experimental and nonexperimental data. Graphical techniques of inferring effects of policies involving signal blocking.]54d0b"X @`H  0޽h ? f̙fy___PPT10Y+D=' = @B +C 0 (  ^ S 0P    3 r" Kp   ; The subject of my lecture this evening is CAUSALITY. It is not an easy topic to speak about, but it is a fun topic to speak about. It is not easy because, like religion, sex and intelligence, causality was meant to be practiced, not analyzed. And it is fun, because, like religion, sex and intelligence, emotions run high, examples are plenty, there are plenty of interesting people to talk to, and above all, an exhilarating experience of watching our private thoughts magnified under the microscope of formal analysis.   H  0xl>L ? ̙33 0 B: (  d  c $D5E   .  s * D w   Here we discuss the two graph transformations which we use in our proof. These rules do not change the path-specific effect. Dashed arrows represent directed _paths_.H  0xl>L ? 3380___PPT10.g{> 0  "(  d  c $D5E   ~  s *( D w   H  0xl>L ? 3380___PPT10.g{ U^ 0  n(  d  c $D5E     s *4} D w   XDHere we can say that identifiable path-specific effects are related to natural direct and indirect effects. 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