Causal Model Ying Nian Wu UCLA Department of Statistics July 13, 2007 IPAM Summer School
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Causal Model Ying Nian Wu UCLA Department of Statistics July 13, 2007 IPAM Summer School
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Causal Model Ying Nian Wu UCLA Department of Statistics July 13, 2007 IPAM Summer School. Observational study --- observed relationship may not be cause-effect Example: people who sleep 7 hours report better health. sleep 7 hrs (vs 8 hrs). health. health. sleep 7 hrs (vs 8 hrs). - PowerPoint PPT Presentation
Transcript of Causal Model Ying Nian Wu UCLA Department of Statistics July 13, 2007 IPAM Summer School
Causal Model
Ying Nian Wu
UCLA Department of Statistics
July 13, 2007IPAM Summer School
Observational study --- observed relationship may not be cause-effect
Example: people who sleep 7 hours report better health
sleep 7 hrs (vs 8 hrs)
health
health
sleep 7 hrs (vs 8 hrs)
Example: people who smoke cigarette have better health than people who smoke pipe
cigarette (vs pipe)
health
cigarette (vs pipe)
health
age
cigarette (vs pipe) health
Confounding variable
Donald B. Rubin EM algorithm – Dempster, Laird, Rubin Missing data: ignorability multiple imputation Little & Rubin book Bayesian statistics: foundations and applications Gelman et al. book Causality: Rubin causal model Neyman-Rubin model
Rubin’s potential outcomeCounterfactual intervention
sleep 7 hrs (vs 8 hrs)
health
e.g., what would have happen had the same person who sleeps7 hrs slept 8 hrs instead?
Rubin’s potential outcomeCounterfactual intervention
cigarette (vs pipe)
health
e.g., what would have happen had the same person who smokespipe smoked cigarette instead?
Rubin’s advice
Define estimand before trying to estimate it from data.
Counterfactual intervention:
why counterfactual? we cannot jump into the same river twice fundamentally missing data problem
define estimand in terms of complete data try to estimate it in the presence of missing data
Experiment: randomized assignment or interventionObservational study: actual intervention not ethical
Today’s reference is Judea Pearl, Causality
What is a causal model and what it can do for us?How to learn a causal model, structure and parameters?
Cochran example
0Z
B
X
Y
1Z
2Z 3Z
X
Y
0Z
1Z
2Z
3Z
BCausal diagram
Soil fumigant
Oat crop yieldsEelworm populationZ
Last year -- unobserved
Before treatment
After treatment
End of season
Birds -- unobserved
0Z
B
X
Y
1Z
2Z 3Z
X
Y
Soil fumigant
Oat crop yieldsEelworm populationZ
Farmers insist on they decide X ,which depends on 0ZHow to define causal effect of X on Y ?
Can it be obtained from passive observations?
Causal Model
0Z
B
X
Y
1Z
2Z 3Z
X
Y
Soil fumigant
Oat crop yieldsEelworm populationZ
Causal diagram: more than conditional independence
0Z
B
X
Y
1Z
2Z 3Z
Causal Model
Causal diagram
)( 000 fZ
),( 1011 ZfZ
),,( 2122 ZXfZ
),,( 3233 ZBfZ
),( 0 BB ZfB
),( 0 XX ZfX
),,,( 32 YY ZZXfY
Structural equations
’s are independent
0Z
B
X
Y
1Z
2Z 3Z
Rubin’s potential outcome
),,( 2122 ZXfZ
Counterfactual intervention
equationsor ablesother vari of regardless
),,,( bemust then
, set to were and , set to were If
2122
11
zxfZ
zZxX
Non-experimental observationsRepeat 1 million times
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),,( 2122 ZXfZ
),,( 3233 ZBfZ
),( 0 BB ZfB
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),,,( 32 YY ZZXfY return ),,,,( 321 YZZZX
End
Get a new set of 0Z
B
X
Y
1Z
2Z 3Z
A million copies of
),,,,( 321 YZZZX
knownblack
Causal effect: intervention
Repeat 1 million times
)( 000 fZ
),( 1011 ZfZ
),,( 2122 ZXfZ
),,( 3233 ZBfZ
),( 0 BB ZfB
),( 0 XX ZfX
),,,( 32 YY ZZXfY End
Get a new set of 0Z
B
X
Y
1Z
2Z 3Z
A distribution of
black
Y
xX
)at set |Pr( xXyY
black
My codeobservingmode
My codeinterveningmode
You guess
Let’s play a game
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at thoselook about what
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more!any )(not is Z
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Not a million ),,,,,,( 3210 YZZZXZB
Causal effect may not be identifiable from observational study
But can we express )|Pr( xXyY without ?,0 bz
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What is a causal model and what it can do for us?How to learn a causal model, structure and parameters?
