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both factual outcomes -> both outcomes (#226)
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* both factual outcomes -> both outcomes

The factual outcome is what actually happened, not the counterfactual outcome.

* subtly -> subtlety
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djinnome authored Jul 31, 2023
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"So far we've seen how introducing intervention program transformations using ChiRho's `do` makes it straightforward to reason about the causal implications of (i) uncertainty over the strength of causal effects and (ii) uncertainty over causal structure. We can call this progress *causal modeling*. In practice however, we often don't want to just posit causal knowledge about the world, we also want to update that knowledge in light of observational and experimental data. We'll call this process of learning about cause and effect from data *causal inference*. The key insight underlying ChiRho is that once we have a Bayesian causal model representing our uncertainty about cause-effect relationships, causal inference simply reduces to probabilistic inference in what's known as a *multi-world* transformation of our original causal model. \n",
"\n",
"As we'll show in this section, to reduce causal inference to probabilistic inference using ChiRho we have to follow a few steps:\n",
"1. Transform our ChiRho program into a new Pyro program that represents a joint distribution over both factual outcomes, i.e. what actually happened, and counterfactual outcomes, i.e. what would have happened had we intervened. We'll call this a *twin world program*.\n",
"1. Transform our ChiRho program into a new Pyro program that represents a joint distribution over both outcomes, i.e. what actually happened, and counterfactual outcomes, i.e. what would have happened had we intervened. We'll call this a *twin world program*.\n",
"2. Condition the factual outcomes in our twin world program according to some observed data.\n",
"3. Run (approximate) posterior inference in the conditioned twin world program, resulting in an updated distribution over both parameters and counterfactual outcomes.\n",
"\n",
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"Using our conceptual diagrams from before, we can see how data informs our updated belief about causal models, which then propagate forward into counterfactual outcomes and causal conclusions. Even though we've only observed data in a world where people choose whether to smoke or not of their own free will, this observed data tells us something about which causal models are plausible. Importantly, this process of mapping data in one world to conclusions in another (e.g. a world in which people are randomly assigned smoking behavior), requires assumptions. When using ChiRho, the models we write encode those assumptions implicitly by how interventions transform them. In subsequent tutorials we'll discuss this subtly and consideration in more detail. For now, remember that this ability to reduce causal inference to probabilistic inference doesn't come out of thin air."
"Using our conceptual diagrams from before, we can see how data informs our updated belief about causal models, which then propagate forward into counterfactual outcomes and causal conclusions. Even though we've only observed data in a world where people choose whether to smoke or not of their own free will, this observed data tells us something about which causal models are plausible. Importantly, this process of mapping data in one world to conclusions in another (e.g. a world in which people are randomly assigned smoking behavior), requires assumptions. When using ChiRho, the models we write encode those assumptions implicitly by how interventions transform them. In subsequent tutorials we'll discuss this subtlety and consideration in more detail. For now, remember that this ability to reduce causal inference to probabilistic inference doesn't come out of thin air."
]
},
{
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