Causal Models and Interventions › Key Parameters

The key parameters for the confounded climate controller example are:

• CAUSAL_SLOPE: The true effect of cooling on temperature, $-1.5$ degrees per unit of effort. This is the mechanism quantity that the naive regression fails to recover. It is also the quantity that is invariant across all the questions in the example: the interventional fit recovers it, the counterfactual computation uses it, and the true expected-cost function is built from it.
• CONFOUNDING: The strength of the operators' reaction to the hidden heat load, $0.8$. It strengthens action-load coupling, but the slope bias is nonmonotonic: for these parameters it peaks at $0.5$ and then shrinks. At $\text{CONFOUNDING} = 0$, the backdoor closes and the observational regression is unbiased.
• SIGMA_A: The standard deviation of the noise in operator behavior, $0.5$. It controls how much cooling variation comes from the confounder rather than from deliberate variation of the action. The ratio $\text{CONFOUNDING}^2 / (\text{CONFOUNDING}^2 + \text{SIGMA}_A^2) \approx 0.72$ is the fraction of action variance driven by the hidden heat load, but the slope bias itself is $\text{CONFOUNDING} \cdot \text{U\_VAR} / (\text{CONFOUNDING}^2 \cdot \text{U\_VAR} + \text{SIGMA}\_A^2) \approx 0.90$; the bias peaks at intermediate reaction strengths and shrinks for very strong reactions rather than scaling monotonically with that fraction.
• SIGMA_Y: The standard deviation of the temperature noise, $1.0$. It contributes to outcome variance and expected cost but not to omitted-variable bias. The two designs can still have different finite-sample slope precision because their action distributions differ.
• BASELINE: The baseline temperature deviation from comfort, $2.0$ degrees, which sets the cooling level both planners must apply. Without it, the optimal action would be zero and the planning contrast would vanish, so this parameter is what gives the planning comparison its teeth.
• U_VAR: The prior variance of the hidden heat load, $1.0$, used by the abduction step and by the true expected-cost computation. In the abduction it acts as a regularizer, pulling the inferred load toward zero when the evidence is weak; in the cost function it appears as irreducible variance that no plan can remove.
• n_obs, n_int: The observational and randomized samples each contain $4000$ points. Equal nominal counts sharpen the population-bias comparison, although action support and independent noise realizations still differ across the designs.