This section explains some of the basic ideas underpinn= ing Monte Carlo (MC) simulation. The goal here is to give you a pretty simp= le introduction into what MC Simulation is and how powerful it can be for y= ou, what its advantages and disadvantages are, when it can and can't be use= d and how to perform MC simulation with different simulation software packa= ges.

**What is Monte Carlo Simulation?**

Monte Carlo (MC) simulation is a quantitative risk anal= ysis technique in which uncertain inputs in a model (for example an Excel s= preadsheet) are represented by probability distributions (instead of by one= value such as the most likely value). By letting your computer recalculate= your model over and over again (for example 10,000 times) and each time us= ing different randomly selected= sets of values from the (input) probability distributions, the compute= r is using all valid combinations of possible input to simulate all possibl= e outcomes. The results of a MC simulation are distributions of possible ou= tcomes (rather than the one predicted outcome you get from a deterministic = model); that is, the range of possible outcomes that could occur and the li= kelihood of any outcome occurring. This is like running hundreds or thousan= ds of "What-if" analyzes on your model, all in one go, but with the added a= dvantage that the "what-if" scenarios are generated with a frequency propor= tional to the probability we think they have of occurring.

**Why Monte Carlo Simulation**

The most important advantage= s of Monte Carlo include:

The probability distributions within the model can be ea= sily and flexibly used, without the need to approximate them;

Correlations and other relations and dependencies (such = as "if" statements) can be modeled without difficulty;

The level of mathematics required is quite basic;

Simulation software packages can automate the tasks= involved in simulation;

The behavior of and changes to the model can be investig= ated with great ease and speed.

An often claimed disadvantag= e of MC Simulation is that it is an approximate technique. However, = any degree of precision can be achieved (at least in theory) by simply incr= easing the number of iterations, so the real limitations of MC simulation a= re:

The number of random numbers that can be produced from a= random number generating algorithm and;

The time a computer needs to generate the iterations (an= d the time the risk analyst has).

However, for most problems you will face these limitations are totally i= rrelevant or can be avoided by splitting up a model as described in Vose, 2000 (page 209-212).

**When to use Monte Carlo Simulation (and when not to)**

"Calculate when you can, simulate when you can't!" Monte Ca= rlo simulation can be used for most of the risk analysis models you will en= counter. However, in situations where exact calculation is possible, this i= s always preferred. An example is the determination of the probability that= the sum of 3 dice is 3. Although with an MC simulation with many iteration= s we can indeed get very close to the real probability (1/(6*6*6) =E2=89=88= 0.4630%, the calculation is much quicker and exact. A calculation model ca= n also be instantaneously updated if any of the parameter values need chang= ing.

**How to do Monte Carlo Simulations in Simulation Software Package=
s**

Simulation software packages provide an easy, efficient and flexible too= l to perform Monte Carlo Simulations. You can find the steps to create thes= e simulations in the following software specific models:

The links to the Performing Monte Carlo Simulations software specif= ic models are provided here:

The simulation software package ususally offers two methods of generatin= g samples from probability distributions: Monte Car= lo sampling, and Latin Hypercube sampling. The latter is the one we recommend you use for normal models. Mon= te Carlo sampling is mostly used when we are trying to replicate the patter= n of randomly observed data. There are also a number of other sampling methods available in simulation you may wish to i= nvestigate. All the methods for generating random samples rely on a Seed value, and it is sometimes useful to control th= at value to check the quality of your results.

If your simulation software doesn't have a distribution you would like t= o use, visit this section for meth= ods to generate your own distributions. In ModelAssist we introduce a numbe= r of such distributions, which of course we need to somehow generate values= for.

ModelAssist provides you with topics on how to determine how many iterations to run a Monte Carlo model for. It's= a good question, which is frequently asked in courses we give.