docs: improve narrative flow, standardize math notation, and fill gaps

- Causal Inference: Clarify bare demonstrative pronouns, standardize formal
  definitions to use \eqdef, add toy numerical examples for potential outcomes
  and population estimands, detail step-by-step derivations for RCT exchangeability
  and G-computation linear model equivalence, update slidebreaks, and wrap IPW table in div.
- Predictor Selection: Fix div heading levels from ### to #### to prevent section
  numbering conflicts, resolve bare demonstratives, define VIF with \eqdef, and add
  numerical VIF example.
- Probability: Standardize theorem/definition div headings to level 4 (####), replace
  bare --- slidebreaks before theorem divs with {{< slidebreak >}}, and add step-by-step
  parenthetical justifications in proof aligned blocks.

Co-authored-by: dem-extra1 <112029334+dem-extra1@users.noreply.github.com>

Author: google-labs-jules[bot]

_subfiles/causal-inference/_sec_causal_estimands.qmd

@@ -68,7 +68,10 @@ We calculate the population-level estimands across all three units:
 2. **ATT**: Average over treated units ($i = 1, 3$): $\frac{\tau_1 + \tau_3}{2} = \frac{10 + 2}{2} = +6.0$.
 3. **ATU**: Average over untreated units ($i = 2$): $\frac{\tau_2}{1} = +6.0$.
 
-In this toy population, treatment effect heterogeneity exists ($\tau_i$ varies across units), but because average gains happen to balance across treatment groups, ATE = ATT = ATU. In general observational datasets with selection bias, ATT and ATU often differ markedly from ATE.
+In this toy population, treatment effect heterogeneity exists ($\tau_i$ varies across units),
+but because average gains happen to balance across treatment groups, ATE = ATT = ATU.
+In general observational datasets with selection bias,
+ATT and ATU often differ markedly from ATE.
 :::
 
 ::: notes

chapters/probability.qmd

@@ -1039,7 +1039,7 @@ under the conditional distribution given $Z=z$:
 $$
 \ba
 \E{\E{Y \mid X,Z} \mid Z=z}
-&= \sum_{x \in \rangef{X}} \E{Y \mid X=x,Z=z} \cd \P(X=x \mid Z=z) && \text{(expectation under conditional dist. given } Z=z \text{)}
+&= \sum_{x \in \rangef{X}} \E{Y \mid X=x,Z=z} \cd \P(X=x \mid Z=z) && \text{(expectation under conditional distribution given } Z=z \text{)}
 \\&= \E{Y \mid Z=z} && \text{(law of total probability given } Z=z \text{)}
 \ea
 $$