A GUIDE TO MONTE-CARLO SIMULATION:
WORKING WITH UNCERTAINTY
or
"PREDICTING THE FUTURE IS RISKY"
WHAT IS MONTE-CARLO SIMULATION?
Monte Carlo simulation is a mathematical technique for numerically solving mathematical equations.
Input parameters are expressed as probability distributions, and results are given as a probability distribution in the form of a histogram.
Input values are determined by "tossing a coin". The number of simulations can be anything from a minimum of 3000 to an optimum of 10,000 or more:
The computer randomly chooses a number that is used together with an input probability distribution to generate an input value. This is repeated for each input parameter, using a new random number, until all input parameters are determined. The values are then used in the equation to obtain one "simulation" or "scenario". This is repeated again and again until the required number of simulations has been obtained.
WHEN IS MONTE-CARLO SIMULATION USED?
Monte Carlo simulation can be used when it is difficult or impossible to determine exact numbers for parameters to enter into an equation. As long as the result can be expressed as a mathematical relationship all that is needed is to determine a distribution of values for each input parameter. The result is not a single value but a range of values with their probabilities.
A SIMPLE EXAMPLE OF MONTE-CARLO SIMULATION
Let's estimate the volume of a box if we don't know its exact size.
The volume of a box is its Height times Width times Length, i.e V = H * W * L
1) We decide on triangular distributions, and estimate minimum, most likely and maximum values for each of the three dimensions.
2) We use a random number to decide on the height, another random number to decide the width and a third to decide the length.
3) The three values are multiplied together to give a volume.
4) This process is repeated 10,000 time to give 10,000 values of the volume.
5) These results are used to draw a histogram that shows the most likely volume.
6) We can also make statements like "There is only a 1% chance that the volume is greater than 100 litres." or "there is 95% confidence that the volume is between 20 and 30 litres."