# Monte Carlo methods for risk analysis Stochastic simulation and numerical experiments

## Overview Some problems in risk analysis cannot be expressed in an analytical form. Others are difficult to define in a deterministic manner. Monte Carlo methods (also known as stochastic simulation techniques) consist of running “numerical experiments” to observe what happens over a large number of runs of a stochastic model. They consist of using repeated random sampling from input probability distributions, execution of the model with these stochastic inputs, then aggregation of the large number of executions to obtain an estimate of the quantity of interest. These methods rely on the ability of computers to generate pseudo-random numbers from various relevant probability distributions.

Monte Carlo methods are widely used in risk analysis, for instance for:

• propagating uncertainty through a numerical model to obtain confidence intervals on your model outputs

• estimating quantile measures for performance measures

• simulating evacuation from a building during the design phase

• predicting failure, cost overruns and schedule overruns in project management

This submodule is a part of the risk analysis module.

## Course material Monte Carlo methods in risk analysis Lecture slides (PDF) View on Slideshare Estimating pi using a Monte Carlo simulation View Python notebook online Download Python notebook Launch interactive notebook  Project risk analysis with Monte Carlo simulation View Python notebook online Download Python notebook Launch interactive notebook  Monte Carlo simulation of failure probability in mechanical design View Python notebook online Download Python notebook Launch interactive notebook  Monte Carlo simulation of landslide risk View Python notebook online Download Python notebook Launch interactive notebook  Numerical integration using Monte Carlo methods View Python notebook online Download Python notebook Launch interactive notebook  Monte Carlo sampling methods View Python notebook online Download Python notebook Launch interactive notebook  Limits of stochastic simulation methods: the Saint Petersburg problem View Python notebook online Download Python notebook Launch interactive notebook  Various poker odds: working with discrete probability distributions View Python notebook online Download Python notebook Launch interactive notebook In these course materials, applications are presented using the NumPy, SciPy and SymPy libraries for the Python programming language.

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