Monte Carlo Simulation: How to Learn the Technique?

Monte Carlo Simulation

To get a specific numerical conclusion, experts rely on the Monte Carlo simulation method. It belongs to the category of Computational based algorithm. It solely depends on the system of random – sampling. Monte Carlo is a technique to solve uncertainty in terms of prediction. Also, it uses forecast models to comprehend the effect of risk.

You can also call the Monte Carlo as the multiple – prospect simulation. It uses the randomness to resolve any deterministic problem. They are the best in the field of mathematical and science-related studies. It is because they turn out positive where other types of approaches fail to give the result. Thus, today let’ s pick some ideas on the Monte Carlo simulation method, advantages, and areas of application.

Insight on the Monte Carlo simulation method

Monte Carlo Simulation uses models to analyze the risk. Mostly rely on methods like the probability distribution or substituting the value ranges. They use the said methods to understand any factor that comes with uncertainty. It follows repeated calculation. And every time, the method uses different groups of random- values from the probability.

Monte Carlo can use thousands or more thousand recalculation method depending on the uncertainty number. It also distributes the possible value of the result. Using the probability distribution method, variables can show diverse probability value for a different result. Note, that the probability distribution method follows a more realistic and definite approach. Indeed,  it is the best way to talk about the uncertainty related to variables in the field of risk evaluation.

The probability distribution method includes:

Normal method:

The normal method or you can say it as the bell curve is the process of defining the expected or the mean value. In addition, users pay attention to the standard deviation value to define the mean- variation. Note that the values in proximity to the mean and in the middle have a greater chance to occur.

The method is symmetric. Also, it can highlight the natural occurrences like the height of the people. Examples of the normal distribution of variables method are the prices of energy and the inflation – prices.

Lognormal method:

Here the values are asymmetric. It defines the values that are above zero. Additionally, values should have infinite positive potentiality. Examples of this method are like the prices of oil resources, stock market, real estate values.

Uniform method:

Here every value has the chance to occur in equal format. The user proceeds with the method by simply underlining the maximum and the minimum value. Examples of the values that follow equal distribution are the manufacturing price or the future revenue from the sales of any brand new item.

Triangulation method:

Here the user mainly focuses on the minimum value. At most explains the maximum value as well. Remember that values that are most likely have more chances to occur. The triangulation method defines the variables that include the level of inventory, history of sales based on each time.

PERT method:

It is almost similar to that of the triangulation method. It is because here also the user defines the most- likely values including the maximum and the minimum values. Now the values labeled as most likely have occurrences that are more predictable. In the PERT method, those values, which belong to the most- likely categories and to the extreme, have more chances to repeat. Here the user does not lay that much importance on the extreme values. An example is the time duration of the task in regards to the project – management.

Discrete method:

With this method, the user has the chance to define particular values. Those values may take place and have likelihood. For example like the outcome of the law verdict having 20% chances to get a negative verdict while 10% chance of having positive comments. Also with a 30% chance of settling, the issue, and 5% scope of the mistrial.

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Points to remember:

The Monte Carlo simulation method uses the random sample values obtained from the probability input distribution. Users can call each group of samples as the iteration. And they record the result from each of them. The best about the method is that they do repeat the sampling process hundreds of times. That is why you can expect a definite result from the method. Obviously, the Monte Carlo simulation method is comprehensive. It tells the user the possibility of the occurrence. But, also tells how likely it may occur.

Is the Monte Carlo simulation method accurate?

You have to understand that the accuracy of the Monte Carlo simulation depends on the realization numbers. Precisely, you can compute the confidence- bound of the result based on the number realization.

History of the Monte Carlo Simulation method

The Monte Carlo simulation dates back to the City of Monaco. It was famous then for casino games especially the Roulette. As the game of chance, roulette involved the repetition of events that define probabilities. Before 1940, the application of the Monte Carlo simulation method was not common. After that, the application of the method became common in areas of atomic – nuclear bombs. Also, hats off to Stanislaw Ulam, a mathematician, who discovered the outstanding privilege of applying the method in the field of computer science. Its application solved many of the complex computer problems.

Advantages of the Monte Carlo simulation

You can get ample of advantages from the Monte Carlo simulation method. So go through the following to understand each one of them.

  • Result on based probability: This result not only put up what can happen but also shows how likely the result is.
  • Draw graphs easily: With the help of the Monte Carlo simulation you can easily derive the result based on graphs. Precisely, it also shows how to prepare the graphs based on different results. Also, understand how many times it can occur. The graph-based results turn out helpful for the stakeholders.
  • Sensitivity evaluation: You will not be able to see which variable gives the most impactful result with the deterministic method. In comparison to that, you can find that out easily with the help of the Monte Carlo Simulation method. It is because Monte Carlo gives a deep-rooted impact.
  • Evaluation of the scenario: Deterministic methods or models are not appropriate and easy to understand. You won’t find it easy to use diverse combination values for various inputs in order to see the impact of truly diverse scenarios.

However, in that case, the Monte Carlo simulation method is useful. It is because it lets you understand precisely which values belong to which inputs when a particular result took place. No doubt, this is vital for further examination.

  • Input Correlation analysis: This one helps to find out the input – variables dependent on each other. Definitely, it turned out significant because one can understand that this process is accurate. Also, helps to evaluate the factors rising up and down in terms of reality.

Areas of applying the Monte Carlo simulation method:


You can see the use of the Monte Carlo simulation in various branches of Physics. Like, you can find their usability in physical chemistry, computation, quantum- chromodynamics etc. Even you have to acknowledge the contribution in designing the heat armors. In addition to that, its usability in the field of aerodynamics is equally remarkable.

Even Statistical physics uses the Monte Carlo simulation for calculating the simple polymer and particle systems. In quantum, the quantum Monte Carlo turns every useful in resolving the several body problem.

The Monte Carlo simulation approach is the key to understand the implantation of ions in the binary collision in regards to the radiative material scientific study. Also, the Method proved purposeful in the field of particle physics as well. One can use the method to design the detectors and comprehend their behaviors.

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In addition to that, Astronomical physics also resorts to the Monte Carlo simulation technique. There it talks about the evolution of the galaxy. On top of that, it highlights the transmission of microwave radiation through an even planetary ground.

In engineering

The Monte Carlo simulation technique is common in the field of engineering. One can use both the probabilistic and sensitive evaluation methods in the process of designing the study. You need to do so in relation to the non-linear, co-linear and interactive behavior of the particular simulation process. Example of such follows below:

  • Monte Carlo method used in microelectronic engineering for analyzing the uncorrelated and correlated variations. The methods are applicable both for the digital and analog integrated circuits.
  • In the domain of geo-metallurgy and geostatistics, one can rely on the method for understanding the mineral processing design and comprehend the risk.

Climatic study

The weather department solely believes in the Monte Carlo simulation technique. The processionals use the method in evaluating the radiative force and the probability- density process.

Computer graphics domain

Computer graphics designer really acknowledges the benefit of using the Monte Carlo simulation.  Designers often use the process called path tracing which is the other name of the Monte Carlo ray – tracing. With the help of this, one can get three-dimensional scenes that randomly trace samples of the probable paths of the light.

The sampling of the repeated pixel will finally let the sample averages to meet rightly on the equation. Thus, the designers will come across the most precise and physically correct Three-dimensional graphics.

Applied statistics field

Sawilosky defined the applicability of the Monte Carlo uses in the field of applied statistics. One can use it to understand four important processes.

  • It helps to compare the statistics obtained from smaller samplings based on the real condition of the data. Example of such is Cauchy condition and the normal- curves.
  • The Monte Carlo simulation is good for conducting the test based on a hypothesis. Note that you can call such types of tests as the permutation test as well. This format is more precise.
  • It also helps to get a random sampling from the posterior- distribution in the Bayesian interference study.
  • The method is also a privilege to understand the estimates of the random sampling in the Hessian matrix study as well.

Computational- biology arena:

Today various domains of computational biology are relying on the Monte Carlo simulation technique. Note that experts use it to study the systems of biology like the membranes, proteins, or genomes. One can study the method of understanding the ab initio or rough-grained framework. It depends on the expected accuracy.

It also assists the professionals to understand the local ambiance of the specific module. Also, helps to understand the reaction between chemicals as well. In addition to that, you can use the same to carry out physical experiments. Examples of physical experiments include breaking the bonds, initiating the impurities at the particular sites,

Business and finance

The business – risk analyst experts also use the Monte Carlo simulation method to understand the outcome impact in regards to the various decisions. It also makes one understand the detailed impact of the uncertainty in terms of variables such as the prices of labor, sales, commodity and volume. Additionally, it also makes you comprehend the rate of exchange as well as interest. Also, analyze the impact of diverse risky events like the change in the law or cancellation of the agreement.

Field of law

Monte Carlo simulation is a fruitful process to help the female petitioners in regards to Wisconsin. Law experts do use the study to understand the rate of success in the context of domestic violence reasoning- orders as well as for harassing women.

The method came into light with a mission to help the women so that can win in their appealed petitions. Thus, it also ensures to reduce the rate of physical abuse and rape as well.

 Final thoughts

There is always a risk factor related to every decision. Everyone has to face ambiguity, uncertainty, and variability. As no one has the right information, therefore it is difficult to make the exact prediction of the future. However, The Monte Carlo simulation comes into the forefront as the savior. It is because it lets you understand the probable result of the decision. Also, help you analyze the risk effect. Thus, help you make the proper decision.

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