Monte Carlo Engine Skill

Monte Carlo Engine

Overview

The Monte Carlo Engine skill provides comprehensive probabilistic simulation capabilities for quantifying uncertainty, assessing risk, and propagating variability through complex models. It supports multiple sampling strategies, correlation handling, and statistical analysis of simulation outputs for data-driven decision support.

Capabilities

Random variate generation (normal, triangular, PERT, uniform, lognormal, beta, etc.)
Latin Hypercube Sampling (LHS)
Correlation structure handling (Cholesky decomposition, copulas)
Convergence monitoring and adaptive iteration
Statistical output analysis (mean, variance, percentiles)
Tornado diagram generation
Value at Risk (VaR) and CVaR calculation
Parallel simulation execution

Used By Processes

Monte Carlo Simulation for Decision Support
Strategic Scenario Development
What-If Analysis Framework
Predictive Analytics Implementation

Usage

Distribution Specification

# Define input distributions
input_variables = {
    "revenue": {
        "distribution": "triangular",
        "parameters": {"min": 800000, "mode": 1000000, "max": 1500000}
    },
    "cost": {
        "distribution": "normal",
        "parameters": {"mean": 600000, "std": 50000}
    },
    "market_share": {
        "distribution": "PERT",
        "parameters": {"min": 0.05, "mode": 0.10, "max": 0.20}
    },
    "unit_price": {
        "distribution": "uniform",
        "parameters": {"min": 45, "max": 55}
    }
}

Correlation Matrix

# Define correlations between variables
correlations = {
    "variables": ["revenue", "cost", "market_share"],
    "matrix": [
        [1.0, 0.6, 0.3],   # revenue correlations
        [0.6, 1.0, 0.2],   # cost correlations
        [0.3, 0.2, 1.0]    # market_share correlations
    ]
}

Model Function

# Define the model to simulate
def profit_model(inputs):
    revenue = inputs["revenue"]
    cost = inputs["cost"]
    profit = revenue - cost
    return {"profit": profit, "margin": profit / revenue}

Sampling Strategies

Simple Random Sampling: Standard Monte Carlo
Latin Hypercube Sampling: Better coverage with fewer samples
Quasi-Monte Carlo: Low-discrepancy sequences (Sobol, Halton)
Importance Sampling: Focus on tail events

Convergence Monitoring

The skill monitors:

Running mean and standard deviation
Coefficient of variation convergence
Percentile stability
Adaptive stopping criteria

Input Schema

{
  "input_variables": {
    "variable_name": {
      "distribution": "string",
      "parameters": "object"
    }
  },
  "correlations": {
    "variables": ["string"],
    "matrix": "2D array"
  },
  "model": "function or expression",
  "simulation_options": {
    "iterations": "number",
    "sampling_method": "random|lhs|quasi_mc",
    "random_seed": "number",
    "parallel": "boolean",
    "convergence_threshold": "number"
  },
  "output_options": {
    "percentiles": ["number"],
    "risk_metrics": ["VaR", "CVaR"],
    "confidence_level": "number"
  }
}

Output Schema

{
  "summary_statistics": {
    "output_variable": {
      "mean": "number",
      "std": "number",
      "median": "number",
      "min": "number",
      "max": "number",
      "percentiles": "object"
    }
  },
  "risk_metrics": {
    "VaR": "number",
    "CVaR": "number",
    "probability_of_loss": "number"
  },
  "convergence_info": {
    "iterations_run": "number",
    "converged": "boolean",
    "stability_scores": "object"
  },
  "raw_results": "array (optional)",
  "tornado_data": "object",
  "visualization_paths": ["string"]
}

Best Practices

Use at least 10,000 iterations for stable percentile estimates
Apply Latin Hypercube Sampling for efficiency
Validate input distributions with subject matter experts
Include correlations for realistic results
Monitor convergence before accepting results
Perform sensitivity analysis to identify key drivers
Document all distribution assumptions

Integration Points

Receives distributions from Risk Distribution Fitter
Feeds into Sensitivity Analyzer for importance analysis
Supports Value at Risk Calculator for risk metrics
Connects with Decision Tree Builder for decision node valuation
Integrates with Real Options Analyzer for option valuation

Agent Skills: Monte Carlo Engine

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Skill Files