Statistical Methodology — Hormuz Index

1.1 Sources and Reliability

Each source has a fixed reliability score (source_reliability, 0-1). The grading system is inspired by the NATO Admiralty Code (STANAG 2511 / AJP-2.1), which uses letters A-F for source reliability and numbers 1-6 for information credibility. The conversion to a 0-1 numerical scale is the authors' own adaptation, not a standard NATO procedure. The mapping is: A=0.95, B=0.85, C=0.75, D=0.65, E=0.50, F=not used.

Reference: NATO STANAG 2511 / AJP-2.1, "Evaluation of intelligence sources and information", Rating A-F for source reliability.

1.2 Deduplication

Articles are grouped by textual similarity using RapidFuzz (normalised Levenshtein algorithm) with a similarity threshold of 88%. This produces clusters of articles about the same event. Only the representative event of each cluster is ingested.

1.3 Event Classification

Each event is classified into one of 17 categories via regex pattern matching against the text (title + summary). The classification assigns:

• category: event type (e.g. military_strike, enrichment_signal)
• signal_keys: which indices it feeds (e.g. GAI, BSI)
• base_severity: baseline severity of the category (0-1)
• confidence: number of matched patterns / total patterns for the rule

The classification is rule-based (not LLM) for reproducibility and transparency. Each category has a geographic relevance filter: events unrelated to the Iran/Gulf/Middle East area are excluded for categories that require it.

5.1 Hard Rules (Threshold Effects)

The NOI includes non-linear rules to capture historically documented threshold effects:

5.2 Interpretive Thresholds

Aligned with IAEA Safeguards conclusion categories:

6.1 Baseline Scores (Literature-Informed Initial Values)

Each scenario starts from a baseline score informed by the literature. They are initial values of an additive linear model, calibrated on historical base rates to give the model a reasonable starting point.

References: International Crisis Group, CrisisWatch Database (2003-2024); Global Challenges Foundation (2020), "Global Catastrophic Risks 2020"; Metaculus, "At least 1 nuclear detonation in war by 2050" community forecast.

6.2 Weight Matrix

The weight matrix encodes the causal pathways from each index to each scenario. The design is inspired by the GCRI (Global Conflict Risk Index) framework of the European Commission's Joint Research Centre (2014), but with an important structural difference: the GCRI derives its weights empirically via logistic regression on historical conflict data, whereas our weights are assigned manually through causal reasoning and expert judgement. There is no sufficiently large historical dataset of "Iran-Gulf crises with known outcomes" to perform regression. The weights reflect the causal logic of the literature, not a statistical calibration.

Matrix design principles:

1. GAI and HDI are the primary drivers of conventional regional war (+0.30, +0.25).
2. NOI tracks the opacity of the Iranian programme. Since Iran does NOT possess nuclear weapons, NOI drives only "threshold" (approach to capability). NOI has ZERO weight on "actual use".
3. BSI tracks both the Iranian path towards a device AND nuclear posture signals from already-armed states (USA, Israel). BSI drives "threshold" (+0.30) and is the second driver of "actual use" (+0.08).
4. SRI captures escalatory rhetoric from states possessing nuclear weapons. It is the strongest driver of "actual use" (+0.10) because rhetoric precedes action.
5. DCI (diplomacy) is the sole restraining force. It is the only index with a positive weight on "contained" (+0.25) and a negative weight on all other scenarios.
6. Actual nuclear use can originate ONLY from the USA/Israel (which possess nuclear weapons) or from a Russia/China transfer to Iran (monitored but extremely unlikely).

Reference: EU Joint Research Centre (2014). "Global Conflict Risk Index (GCRI): A quantitative model — Concept and methodology." JRC Technical Reports. The GCRI uses logistic regression on historical data to derive weights empirically. Our weights are NOT derived in the same manner — they are assigned manually through causal analysis of the Iran-Gulf theatre. The GCRI is cited as conceptual inspiration for the index-to-scenario matrix approach, not as a replicated methodology.

6.3 Raw Score Computation

For each scenario s:

Where baseline_s is the baseline score of scenario s (Section 6.1), W_k,s is the weight of index k on scenario s (Section 6.2), and Index_k is the current index value (0-100). This is an additive linear aggregation, not a Bayesian update.

6.4 Trigger Rules (Non-Linear Effects)

The weight matrix is linear and does not capture the non-linear dynamics of escalation. Trigger rules add additive boosts or multiplicative factors when multiple indices simultaneously exceed critical thresholds.

6.5 Normalisation

Raw scores are clamped to ≥ 0 and normalised to sum to 100:

The resulting probabilities are relative plausibilities, not calibrated probabilities in the Brier score sense. They represent the distribution of plausibility across scenarios given the current state of the indices.

7.1 Monte Carlo for Scenarios

To quantify the uncertainty of scenario probabilities, the model runs a Monte Carlo simulation with N=500 iterations, following the global sensitivity analysis framework of Saltelli et al. (2004).

At each iteration:

1. Index perturbation: each index value is multiplied by a uniform random factor U(0.85, 1.15), i.e. ±15%, then clamped to [0, 100].
2. Weight perturbation: each weight in the matrix is multiplied by a normal random factor N(1.0, 0.20), clipped to [0.6, 1.4], i.e. ±20% with max ±40%.
3. Probabilities are recomputed with the perturbed values.

The seed is fixed (seed=42) for reproducibility within the same snapshot. The simultaneous perturbation of model inputs and parameters follows the principle of "global sensitivity analysis" — superior to one-at-a-time (OAT) perturbation because it captures parameter interactions.

Reference: Saltelli, A., Tarantola, S., Campolongo, F. & Ratto, M. (2004). Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. Wiley. Ch. 2: "Why should one perform sensitivity analysis?" and Ch. 5: "Global sensitivity analysis."

7.2 Bootstrap for Indices

Individual indices have uncertainty bands computed via non-parametric bootstrap (Efron & Tibshirani, 1993). Over N=200 iterations, events in the 24h window are resampled with replacement and the subindex is recomputed.

For indices with fewer than 5 events, the CI is analytically widened (±40% of the value or ±10 points, whichever is greater) to reflect the high uncertainty from a small sample.

Reference: Efron, B. & Tibshirani, R. (1993). An Introduction to the Bootstrap. Chapman & Hall/CRC. Ch. 13: "Bootstrap confidence intervals."