Probit is an ideal case study for workflow discipline. The model is familiar, but implementation still involves optimization details, numerical stability, and inference choices.

Step 1: Planner Contract

The planner defines the target model:

$$ P(Y_i=1\mid X_i)=\Phi(X_i^\top\beta) $$

with explicit requirements for:

  1. Input preprocessing rules.
  2. Optimization tolerance and iteration limits.
  3. Standard error computation mode.
  4. Failure reporting for non-convergence.

Step 2: Builder Implementation

The builder implements estimation without access to simulation truth tables. Required outputs include:

  1. Coefficients and standard errors.
  2. Convergence diagnostics.
  3. Predicted probabilities.
  4. Structured warnings.

The builder should avoid embedding silent fallbacks that alter inference semantics.

Step 3: Simulator Design

The simulator independently creates synthetic datasets under known parameters with varied conditions:

  1. Balanced and imbalanced outcome prevalence.
  2. Collinearity stress scenarios.
  3. Weak-signal and strong-signal regimes.

Expected behavior is encoded as diagnostic targets, not by reading builder internals.

Step 4: Tester Gate

The tester validates against deterministic criteria:

  1. Parameter recovery within tolerance bands.
  2. Calibration and discrimination checks.
  3. Consistency of uncertainty estimates.

Release is blocked when criteria fail.

What This Demonstrates

The key point is not that probit is hard. The key point is that familiar methods still benefit from role separation and independent validation.

Key Takeaway

An end-to-end pipeline with independent simulation and testing can make routine estimators significantly more trustworthy.