ADR 0007: Unbiased estimators as the default, thesis estimator as baseline

• Status: Accepted (2026-11-10)
• Date: 2026-11-10
• Deciders: Vincent Mader
• Related: Findings F1 to F4; RQ1 to RQ3; E5 to E8

Context

The thesis estimator samples without replacement and does not reweight, so it underestimates every rate by its inclusion probability (F1). The runs also used a proposal different from the documented one (F2). Dullemond’s notes and prototype use an unbiased importance-sampling form.

Decision

An Estimator trait returns a SampledKernel that implements Rhs. Implementations: Full (exact), Thesis (faithful baseline, without replacement, no weights, configurable weights including the scalar bug), ImportanceSampling (with replacement, weights 1/(S p)), HorvitzThompson (without replacement, weights 1/π), Hybrid (exact dominant set plus sampled tail). Proposals are a separate trait (uniform, ρ_iρ_j, factorized F_iF_j with weight W, ΔM^net N_iN_j, optimal ‖T‖ with cost awareness). Sampling uses the alias method. Default for new studies: Hybrid or ImportanceSampling with the optimal proposal, decided after E7 and E12.

Alternatives considered

• Keep only the thesis estimator and tune ρ_sample: cannot remove the bias.
• Only factorized index sampling (Dullemond’s sample2d): cheaper proposals, but cannot express pair-level relevance such as Δv-dependent rates; kept as a proposal option.

Consequences

• Statistical tests (bias, variance) become part of CI.
• The thesis results are reproducible as a baseline and the bias can be quantified (E6).