Week 12: Bayesian Decision Theory
DSAN 5650: Causal Inference for Computational Social Science
Summer 2026, Georgetown University
Schedule
Today’s Planned Schedule:
| Start | End | Topic | |
|---|---|---|---|
| Lecture | 6:30pm | 7:00pm | Why Should We Use Bayes’ Rule? → |
| 6:45pm | 7:10pm | Why Should We Think Causally About Decisions? → | |
| 7:10pm | 8:00pm | Heterogeneous Treatment Effects → | |
| Break! | 8:00pm | 8:10pm | |
| 8:10pm | 9:00pm | Causal Forests → |
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Why Should We Use Bayes’ Rule At All?
Assume Big Dave has the following beliefs about the likelihood of events \(P\) and \(Q\):
| \(p\) | \(q\) | \(\Pr(P = p, Q = q)\) |
|---|---|---|
| 0 | 0 | 1/4 |
| 0 | 1 | 1/4 |
| 1 | 0 | 1/4 |
| 1 | 1 | 1/4 |
But decides not to use Bayes’ Rule to update after learning \(Q = 1\): he just decides… he likes 0.6, so \(\Pr(P = p \mid Q = 1) = 0.6\)…
The Dutch Ticket
- If Q is true, this ticket entitles the bearer to $1 if P is true and nothing otherwise.
- If Q is false, this ticket may be returned to the seller for a full refund of its purchase price.
Why Should We Focus On Causality When Making Our Decisions?
- Savage’s Rule
- \(\leadsto\) Jeffrey’s Rule (no relation)
- \(\leadsto\) Causal Decision Theory!