The Monte Carlo Simulation Method has been the most studied and the most dreaded part of all data-analysis courses. In statistical terms, the method is an evaluation process of Mathematical functions and risk analysis with the help of random samples. The method has its own historical significance in being used extensively for atom bomb designing during the Second World War. Even though the Monte Carlo method in Statistics may seem like a big terror and is often looked upon as a subject incomprehensible to the average person, it is actually a much simpler process.
How did the name originate?
The name of the method comes from the city in Monaco – the place famous for its casinos and the gambling games of luck and chance in them. The term stands for the random behavior depicted in gambling games like dice and roulette.
What does the method say?
A Monte Carlo simulation allows users to know how uncertainty of a certain task may propagate or how random differences and variations may influence the performance and reliability of that task.
How is the process carried out?
The very first step of this method in Statistics is to pick out a random value for each given task. The statistician, then, calculates a spreadsheet model based on this value. After recording the result, he, then, repeats the process with different randomly picked values of tasks. The resulting large number of outcomes indicates the chances of reaching up to the various results in the model.
How about an example for the same?
Let us assume that we are throwing a pair of dice, each having a value of one through six. If we are to calculate summation of two throws, there shall be thirty-six combinations of the dice rolls. Here, we can manually estimate the chances of a certain result. For instance, there will be six different ways in which the dice rolls can sum up to eight. The probability shall thus be thirty-six divided by six, i.e., 0.167. But, this is just a manual estimation. Instead, we can use the Monte Carlo method to calculate probability. For example, we can throw the dice a hundred times and keep a tract of the result each time. If the total dice rolls summing to eight occur fifteen times, we can estimate that the probability is 15%. But, manually carrying out such an experiment is impractical. So, using a computer, we can simulate the dice rolls to ten thousand times or even more, leading to more accurate results.
Why should Monte Carlo simulation be used?
If a person is about to make a certain estimation that indulges a lot of major uncertainties, the best option is to use the Monte Carlo method of simulation. In case this method is not used, the estimates may go haywire, leading to fallacious decisions.
How much is its accuracy?
The Monte Carlo method in Statistics works much like a forecasting process. But, the outcome will depend totally on the way a person performs it. It is advisable to remember that what the result of the method represents are just probabilities, not sureties.