Monte Carlo Simulation

Overview

This stage is stochastic — it samples from bounds many times. Contrast with run-scenarios, which evaluates the model deterministically at three points only.

The simulation itself is performed by a Python script (experiments/napkin_math/run_monte_carlo.py), not by the LLM. The script imports calculations.py, draws samples with a seeded NumPy RNG, runs the loop, and writes montecarlo.json. The script is authoritative; this skill is a thin wrapper that locates inputs, builds an optional settings file, and invokes the runner.

Stage 7 of the pipeline described in planexe_simulator/README.md.

When to Use

• User asks to "run Monte Carlo", "sample the bounds", "compute distributions", "estimate gate-pass probability", or "find which inputs drive uncertainty"
• User wants percentile bands (p05/p50/p95) or threshold pass rates (e.g. P(avoided_events ≥ 10))
• Final stage in the pipeline; only run after run-scenarios already shows a sane deterministic model

Not for: regenerating any prior artifact, replacing the deterministic scenario table (use run-scenarios), or claiming causality from sensitivity correlations.

Workflow

1. Get the inputs. Three required, one optional:

• parameters JSON (e.g. output/v12/parameters.json)
• bounds JSON (e.g. output/v12/bounds.json)
• calculations Python module (e.g. output/v12/calculations.py)
• settings JSON (optional — n_runs, seed, distribution_default, outputs_of_interest, thresholds, gate_probabilities, correlation_groups)

If any required input is missing, ask. If the user wants thresholds or non-default settings, write them to a small JSON file and pass --settings.

1. Invoke the runner. Requires Python 3.11+ with NumPy:

   /opt/homebrew/bin/python3.11 experiments/napkin_math/run_monte_carlo.py \
     --parameters   <path>/parameters.json \
     --bounds       <path>/bounds.json \
     --calculations <path>/calculations.py \
     [--settings   <path>/settings.json] \
     [--output     <path>/montecarlo.json]

Default output path is <dir-of-parameters>/montecarlo.json. The script prints a one-line summary (n_runs, output count, threshold count, warning count) on stdout.

1. Report back. Tell the user the output path and the one-line summary. If the user asks for interpretation, read the JSON, then explain — but never replace running the script with hand-computed numbers.

What the runner does (so the LLM can describe results accurately)

The runner does no lexical pattern-matching on id strings, unit strings, or rationale text. Every semantic classification it needs is read verbatim from upstream-declared fields. If a required field is missing, the runner exits with SCHEMA ERROR and names which upstream stage to re-run.

• Distributions per bounded variable — driven by the bound's sampling_discipline field (required, declared by generate-bounds):
• "fixed" — always returns the single pinned value
• "bernoulli_gate" — Bernoulli draw with probability from settings.gate_probabilities[id] if set, else the bound's default_pass_probability (required, in [0, 1]). Returns high on pass, low on fail. Works for any unit — currency tranches, permit toggles, regulatory pass/fail.
• "integer" — sample triangular/uniform, round to nearest integer, re-clamp to [low, high]
• "fraction" — sample triangular/uniform, clamp to [0, 1]
• "continuous" — sample triangular/uniform with no extra rounding or clamping beyond [low, high]
• Default base distribution: triangular (low, mode=base, high). distribution_default: "uniform" switches to uniform.
• The bound's non_negative: bool (required) drives whether draws are clamped to >= 0.

• Output names and units: the runner uses entry.output_name and entry.output_unit from each recommended_first_calculations / derived_questions entry, declared by extract-parameters-from-full. The runner does not parse formula_hint to recover the name, and does not infer units from id tokens. The LLM is the single authority for both.

• Calculation execution: uses inspect.signature on each generated function to pull args from the run's input pool. Order: recommended_first_calculations first, then derived_questions. Outputs are added to the pool so later functions can depend on them. Missing dependencies / non-finite results / exceptions skip the run for that output (one aggregated warning, not per-run noise).

• Sensitivity: Pearson correlation between each sampled input and each summarized output, top 5 by |correlation|. Only inputs that vary AND are used directly or indirectly by the output AND have ≥20 finite paired samples are considered. NaN correlations become null + warning.

• Thresholds: operators > >= < <= == != only. Probability = success_count / valid_count. valid_count == 0 → probability null.

• By default variables are independent. correlation_groups is currently parsed but not yet implemented in the runner; if the user passes them, the script will accept the setting and ignore correlation enforcement. Update the runner if correlation is actually needed.

Required upstream schema

For the runner to accept the artifacts, the upstream LLM stages must have emitted:

• Each `bounds.json` entry — sampling_discipline (string, one of fixed | bernoulli_gate | integer | fraction | continuous), non_negative (bool), default_pass_probability (number in [0, 1] when sampling_discipline == "bernoulli_gate", otherwise null).
• Each `recommended_first_calculations` and `derived_questions` entry with non-null `formula_hint` — output_name (snake_case id of the computed value) and output_unit (unit string).

If any required field is missing, the runner exits with SCHEMA ERROR: <message>. Re-run <stage>. and exit code 2. Fix the upstream artifact and re-run; the runner has no fallback path that re-guesses any of these.

Output Shape

{
  "valid": true,
  "plan_summary": { "plan_name": "...", "plan_type": "..." },
  "settings": { "n_runs": 10000, "seed": 12345, "distribution_default": "triangular" },
  "outputs": {
    "<output_id>": {
      "unit": "...",
      "count": ..., "missing_count": ...,
      "mean": ..., "std": ...,
      "min": ..., "p05": ..., "p25": ..., "p50": ..., "p75": ..., "p95": ..., "max": ...
    }
  },
  "thresholds": {
    "<output_id>": { "operator": ">=", "value": ..., "success_count": ..., "valid_count": ..., "probability": ... }
  },
  "sensitivity": {
    "<output_id>": { "top_inputs": [ { "id": "...", "correlation": ... } ] }
  },
  "warnings": [
    { "stage": "monte_carlo", "run": null, "calculation": null, "message": "...", "severity": "WARN" }
  ]
}

JSON forbids NaN/Infinity — the runner writes null and adds a warning. Identical inputs + identical seed produce a byte-identical output file.

Common Mistakes

Reference

• Runner (authoritative implementation): experiments/napkin_math/run_monte_carlo.py
• Pipeline overview: ../../README.md, Stage 7
• Companion skills: ../extract-parameters-from-full/SKILL.md, ../validate-parameters/SKILL.md, ../generate-bounds/SKILL.md, ../generate-calculations/SKILL.md, ../run-scenarios/SKILL.md
• Synthetic fixture exercising every sampling_discipline (used as the runner smoke test):
• experiments/napkin_math/tests/fixtures/smoke/parameters.json
• experiments/napkin_math/tests/fixtures/smoke/bounds.json
• experiments/napkin_math/tests/fixtures/smoke/calculations.py