A method is publishable when the equations are clear. A package is reliable when behavior is clear. Bridging that gap requires specification work that is both statistical and software-oriented.

Start With The Estimand

Before designing functions, define exactly what is being estimated. Write this as a machine-checkable statement where possible.

For example, if an estimator targets a parameter $\theta$ under assumptions $A$, the package contract should state:

$$ \hat{\theta} = f(X; \mathcal{H}, A) $$

where $\mathcal{H}$ is the algorithmic configuration and all defaults are explicit.

Convert Assumptions To Checks

Assumptions should map to runtime checks or warnings:

  1. Data domain constraints.
  2. Identification preconditions.
  3. Minimum sample requirements.
  4. Positivity or overlap diagnostics.

If an assumption cannot be verified, the package should state that clearly in output metadata.

Define Invariants

Invariants are properties that must always hold if the implementation is correct. Examples:

  1. Probabilities remain in $[0,1]$.
  2. Likelihood contributions are finite for valid inputs.
  3. Confidence intervals preserve ordering.

These become high-value tests because they catch broad classes of implementation errors.

Specify Edge Behavior

Most failures happen at boundaries, not in textbook scenarios. Document and test:

  1. Degenerate predictors.
  2. Near-singular matrices.
  3. Perfect separation cases.
  4. Very small and very large parameter scales.

Edge behavior should be part of public method semantics, not an incidental implementation detail.

Key Takeaway

Equations define intent. Interface contracts, invariants, and edge-case rules define reliable software behavior.