BSJ2012 Tutorial final web - ar.sanken.osaka-u.ac.jp

1 : 40 2012 9 13 , ~ : : 2 (= ) 4 1: ( ) + : vs : + 2: ( ) + : 5 ?

2 : + + 6 X x4x21x3x57x83x15 Contents 1 : 2 : ( ) 7 : David Hume (1766) (Neyman, 1923; Rubin, 1974; cf. Hernan, 2004) ( 1 ) 3 10 (Holland, 1986) : ? 3 11 (Neyman, 1923; Rubin, 1974) (.)

3 ( )3 ? : (Bollen, 1989; Pearl, 2000) =f( , ) = , : : y (x ): ),(yyxexfyex x ( )y( ) 14xeye ( ) ( ) ( ) ),(yyxexfyex x ( )y( ) x ( )y( )z( )15xe ye yexe( ) (Pearl, 2000): f p(u) p(v) v o p(o) :)(,:},,{:],,[:],,[111uuvfuvpfvffuuvviip qp -- ( ) 16 2u1uo= [ ] (Pearl, 2000).

4 ( = ) do( = ) or do(x=1) x x=1 ( ) ),(yyxexfyex x ( )y( ) ( )),(1yyexfyx x ( )y( )1 )18 (Pearl, 2000) y := y x c d x y ypxdoypxM1:1| dxdoypcxdoyp ||),(1yyexfyx x ( )y( )1 ( )19 : dopdop|| dopdop||20 : (Rubin, 1974; Pearl, 2000) x c d y do(x=c) c d : cxdoyEdxdoyE ||:)( 21 cxdoyVardxdoyVar || x c d y =E( y | x d )-E( y | x c )=== yyxyyxecbEedbE cdbyx cxdoyEdxdoyE ||yyxxexbyex 1:xyexeyyyxexbydx 1 :xydey22 y c d x =E( x | y d )-E( x| y c )=== xxeEeE 0 cydoxEdydoxE ||yyxxexbyex 1:xyexeydyexx 1 :xyexd23 : (x ) (Pearl, 2000) do(x=d) y do(x=c) y cdbecbedbyyyxyyxyyxcxdx yyxxexbyex 1:xyexeyyyxexbydx 1 do(x=d).

5 Xydeyye ye24 yyyyecfedf,, = ( ) (Pearl, 2000)x( ) y( )z ( )26xeyeze x z( ) ))(|())(|( xdozExdozEx( )y( )z( ) x= x( )y( )z( ) x= )()( xxzEzE :27yezezeyevs. : x( )y( )z ( )28yezeye (Robins & Greenland, 1992; Pearl, 2001) x z( ) )()(, xyyxzEzExx( )y( )z( ) x= , x( )y( )z( ) x= xyy 29zezeyevs. (Pearl, 2001) x( )y( )z ( )30yezexe (Pearl, 2001) x z( ) )()(, xyyxzEzExx( )y( )z( ) x( )y( )z( ) x= x= , xyy31zezeyevs.

6 X (0) (1) z =a+bc =a =bc( ) x( ) y( )z ( )zyxecaebe abc32xeyeze ( ) ( ) 34 do ? (Pearl, 1995) : yyexfydx, 1 do(x=d):xyd dxyEdxdoyE |)(| yyedfEdxdoyE,| yyxexfyex, 1:xy35yeyexe yyyyyyedfEdxedfEdxexfEdxyE,|,|,| do ? x ( (Pearl, 1995)): Shpitser and Pearl (2006,2008) ( ) xxyEExdoyEx,|)|( yxzwuvq cdxcxdoyEdxdoyE ||36 1: = 2( ): ( )x ( )y ( ) x ( )y( ) xyExdoyE|| 37yexeyexe = 38 : : : E( | = ) : : E[ | do( = ) ] E[ | do( = ) ].

7 E[ | do( = ) ] E( | = )39 : - - ? ( ) ( ) ( ) X x3x21x3x57x83x15 41 ( ) 42 (Sachs et al. Science, 2005; Smith NeuroImage, 2012;Maathuis et al. Nature Methods, 2010; Peer et al. Cell, 2011) (MEG, fMRI) / : / / and/or , non- 44 (Ramsey et al.)

8 , 2009) (Sachs et al., 2005) Ferkingsta et Economics. 2011 Moneta et al. Oxford Bulletin of Economics and Statistics,2012 Ozaki et al. Behavior Genetics, 2009, 2010 Takahashi et al., Japanese Psychological Research, 2012 von Eye et al., Int. Journal of Behavioral Development, 2012 D. Niyogi et al. Water Resources Research , 2012 (t) 45 (t) (t)R&D(t) (t+1) (t+1)R&D(t+1) (t+1) (t+2) (t+2)R&D(t+2) (t+2)(Moneta et al., 2012) : + + : (Peer et al., 2011, Cell) 47x3x1e3e1x2e2 (1/2) X ( : ) X X 1 2 or2121211exbxex 2212121exexbx 1: 2:x1x2e1e2x1x2e1e2 0,1221 bb48 (2/2) (Shimizu et al.

9 , 2005; 2006) (Hoyer et al., 2009; Zhang & Hyvarinen, 2009; Peters et al., 2011)or 212211exfxex 22121exexfx 3: 4 (1/2) : x3x1e3e1x2e2x3x1e3e1x2e2 : :ix( )51 (2/2) : : ( ). eBxx iikjkjijiexbx )()(orix52 3 : B / : or ijijxxb 0 ijijxxb 053 B (Bollen, 1989). Be2ix B00).(,,.3)2(,2)1(,1)3(213 xxxkkk :54 (Spirtes et al.

10 1993) 2 ( ) : x1x2fe1 e2 x1x2e1e255 X : Goal: X B ! B / (3/3): + + eBxx x1x2e1e221b56 c d : : : B 57 1 BIA : B B p(x) B B / = ( ) : B p(e) p(x) B p(x) (or p(x) ) , B eBxx x1x2e1e221b 59 Causal Markov condition Causal Markov condition : (Pearl & Verma, 1991) : piiixxpp1| xx3x1e3e1x2e260p(x).