What is the Monte Carlo Method?

What is Monte Carlo Method

The Monte Carlo methodology is a data analytical technique utilised in cases wherein an intervention of a random variable is present. It was discovered during World War II to improvise the decision-making process under high uncertainty.

Are you wondering why is it called the Monte Carlo method? A Monte Carlo simulation method is named after the popular casino district of Monaco (sovereign city state within France) because the element of ‘chance’ or ‘luck’ is inherent to the modelling approach. This method uses multiple values for replacing uncertain variables instead of replacing them with just a simple average (a ‘soft’ method of analysis that does not yield accurate results).

Businesses quite often deal with variables of uncertainty that can influence significant outcomes. In this case, the Monte Carlo method if used can mitigate risks by predicting the probability of such outcomes.

Project management, artificial intelligence, pricing, stock prices, and sales forecasting are a few functions of Monte Carlo simulation. Moreover, it can also be utilised to execute sensitivity analysis and estimate the inputs’ correlation.

But Why You should learn about Monte Carlo Method? Let us Find Out!

Monte Carlo Simulations use Monte Carlo Sampling technology that is randomly sampling a probability distribution. Many study programs in Australian universities have incorporated this method in their coursework since the Monte Carlo method possesses a wide range of potential applications in business and finance.

Telecoms use the method for assessing network performance in distinct scenarios, assisting them in network optimization. Analysts use them for assessing the risk on which an entity will default, and for analysing derivatives like options. This method is also used by insurers and oil well drillers. Apart from these, Monte Carlo methods possess countless applications in other areas including meteorology, particle physics, and astronomy.

In machine learning, these methods provide the rationale for resampling technologies such as bootstrap method for the estimation of quantities, like model accuracy on a restricted dataset.

There are numerous questions around this topic, most of which are hell to the students in colleges or universities. Many students in Australia opt for essay writing service at Sample Assignment to get guidance with Monte Carlo methods from experts to circumvent time wastage doing something that may result in scoring poor grades in the end. Assignments or assessment tasks involving Monte Carlo methods are quite complicated. And that too with short deadlines. The experts at Sample Assignment are available 24*7 and 365 days a year to provide you the instant guidance and resolve all your queries at once.

How does the Monte Carlo Method Works?

How Monte Carlo method Works

Monte Carlo simulation methods come up with a range of varying outcomes in correlation with the estimated array of values, as opposed to employing fixed input values. Such outcomes are derived from the probability distributions depending upon one or more variables of uncertainty.

For running a Monte Carlo method of simulation, values are sampled randomly from the input probability distribution. Such samples are called iterations. After doing one iteration, it calculates the results for a distinct range of values again between the maximum and minimum values attained from the first iteration. This might be repeated numerous times to obtain a huge number of likely outcomes.

With the increase in the number of input variables, probable outcomes also increase. With this, you are able to make forecasts in time accurately. Hence, the Monte Carlo method is frequently exploited to make long-term predictions. Let us understand how Monte Carlo methods produce outcomes based on a few simple examples.

Enhance your Understanding with Monte Carlo Method Examples

Example 1: Assume that you are having a weighted dice. But, you are not aware which side is heavier. Manually, it is difficult to find out the odds of a particular number with the face side up. How to find out the correct answer? You must be wondering that it is close to impossible.

Here, the Monte Carlo method simulates rolling the dice a minimum of 10,000 times and uses the outcomes to make accurate predictions. Accuracy is directly proportional to the number of simulations.

Example 2: Let us assume that a deck of shuffled cards is present and we are required to find out the probability of getting two kings consecutively if the cards are laid down in the same order as they are placed.

By Analytical approach:

P (at-least two consecutive kings) = 1-P (none of consecutive king)

=1-(49! X 48!)/((49-4)! X52!) = 0.217376

By Monte Carlo Method:

Step-by-Step Solution

Repeatedly choose the points of random data. We will assume that the card shuffling is random.
Conducting deterministic computation. Number of such shuffling and determining the outcomes.
Combining the results: The results are explored and ended with the conclusion.

By following the Monte Carlo method, results are attained with a value near the analytical approach.

Did you get a clear idea of the Monte Carlo method? Or you are still confused and looking for someone whom you can ask ‘do my assignment’ based on Monte Carlo simulation methods? In that case, just approach the experts at Sample Assignment without having a second thought. Your queries will get resolved instantly.

Sample Assignment Done Under the Guidance of Our Experts

To have a clearer glimpse of the type of assessment tasks that our online tutors get to guide students with the solution, you can register on our website and view and download the assignment sample online. A snapshot of the assessment task solved under the expert’s guidance is depicted below for your reference:

Monte Carlo Method Example

Major Takeaways

So, you have it there! In this blog, we have covered the fundamentals of Monte Carlo simulation methods, their applications along with examples, and how these methods work. The major talking points are summarised below:

The Monte Carlo method is actually a data analytical method used for solving complex problems with one or more unknown variables.
It is referred to as an umbrella term dating back to World War II that is related to simulations for helping to frame-accurate predictions.
Sampling from probability distributions including Bernoulli, normal, uniform, or binomial distributions for finding out the likelihood of an event is generalised example of the Monte Carlo method.
With machine learning programs, users are allowed to run elaborate Monte Carlo simulation methods in the form of coded data-processing algorithms.
The library of pandas in Python can be utilised for making a simple, spreadsheet-like model. This is the most convenient method to run a machine learning-based Monte Carlo simulation method.

Sample Assignment offers trusted services with regard to assistance with related coursework, projects, assessment tasks, graphical tools, and exam preparation. Send your different writing tasks along with your urgency to the Sample Assignment team for instant guidance or speak to our experts and resolve all your doubts and queries. Our academicians can guide you in every possible way at pocket-friendly rates.

References

Arend, M. G., & Schäfer, T. (2019). Statistical power in two-level models: A tutorial based on Monte Carlo simulation. Psychological methods, 24(1), 1.

Zio, E. (2013). Monte Carlo simulation: The method. In The Monte Carlo simulation method for system reliability and risk analysis (pp. 19-58). Springer, London.

About Author

Nick

Nick is a multi-faceted individual with diverse interests. I love teaching young students through coaching or writing who always gathered praise for a sharp calculative mind. I own a positive outlook towards life and also give motivational speeches for young kids and college students.