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 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 outcome Counterfactual intervention sleep 7 hrs (vs 8 hrs) health e.g., what would have happen had the same person who sleeps 7 hrs slept 8 hrs instead?

Rubin’s potential outcome Counterfactual intervention cigarette (vs pipe) health e.g., what would have happen had the same person who smokes pipe 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 intervention Observational 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 Causal diagram Soil fumigant Oat crop yields Eelworm population Last year -- unobserved Before treatment After treatment End of season Birds -- unobserved

Soil fumigant Oat crop yields Eelworm population Farmers insist on they decide,which depends on How to define causal effect of on? Can it be obtained from passive observations?

Causal Model Soil fumigant Oat crop yields Eelworm population Causal diagram: more than conditional independence

Causal Model Causal diagram Structural equations ’s are independent

Rubin’s potential outcome Counterfactual intervention

Non-experimental observations Repeat 1 million times return End Get a new set of A million copies of known black

Causal effect: intervention Repeat 1 million times End Get a new set of A distribution of black

My code observing mode My code intervening mode You guess Let’s play a game

?

A million Not a million Causal effect may not be identifiable from observational study

But can we express without

= = = =

You guess

What is a causal model and what it can do for us? How to learn a causal model, structure and parameters?