Monte Carlo Simulation

Monte Carlo simulation uses repeated random sampling to estimate the probability distributions of uncertain outcomes. Named after the famous casino, the method replaces analytical solutions with computational brute force: simulate a process thousands or millions of times with random inputs, then analyze the distribution of results. It is one of the most versatile and powerful tools in the forecaster's toolkit, applicable to finance, engineering, project management, physics, and any domain with quantifiable uncertainty.

## Key Points

1. Define a model of the system with uncertain inputs
2. Assign probability distributions to each uncertain input
3. Randomly sample from those distributions
4. Run the model with sampled inputs
5. Repeat thousands of times
6. Analyze the distribution of outputs
1. Monte Carlo simulation transforms uncertain inputs into probability distributions of outcomes
2. Choose distributions carefully: triangular for expert estimates, lognormal for positive skewed data, beta for proportions
3. Convergence analysis tells you when you have enough simulations; standard error should be less than 1% of the mean
4. Variance reduction techniques (antithetic variates, stratified sampling, Latin Hypercube) can cut required simulations by 50-90%
5. Sensitivity analysis (tornado diagrams) identifies which inputs matter most, focusing your uncertainty-reduction efforts
6. Always model correlations between inputs; independent sampling of correlated variables produces unrealistic scenarios