Monte carlo simulation

Assessing risks is an important aspect of any business's ability to make the right decisions, and the Monte Carlo simulation (MCS), a commonly used mathematical technique, provides a way to inform decision-making by estimating potential outcomes of a particular event.

Learn more about Monte Carlo simulation uses with Micron.

What is the Monte Carlo simulation?

Monte Carlo simulation definition: A Monte Carlo simulation is a model used to predict the possibility of various outcomes when multiple variables are present. It provides a probability distribution of all outcomes rather than just identifying the most likely one.

Unlike other artificial intelligence (AI) models, the Monte Carlo method is nondeterministic . It incorporates external factors that can influence outcomes, resulting in different predictions each time the simulation is run. This variability accounts for mitigating circumstances that can affect the results.

The Monte Carlo simulation is a robust mathematical technique, and its integration with artificial intelligence enhances the model’s capabilities and efficiency. When combined with deep learning models, the model can efficiently categorize large datasets, further improving the accuracy and usefulness of the results.

How does the Monte Carlo simulation work?

The Monte Carlo simulation builds a model of all the possible results and outcomes of an event using a probability distribution. Once the initial results are collated, the simulation is rerun and recalculated several times. Each iteration uses different values within the specified range to generate a variety of outcomes.

This approach provides a large dataset of results, with the averages of each outcome also being produced, to help identify the most and least likely outcomes.

The use of AI has significantly accelerated this process, and improved computational power and efficiency have been a major contributor. This additional power allows for more MCS predictions in less time.

What is the history of the Monte Carlo simulation?

This mathematical technique dates to the 1940s, when mathematicians John Von Neumann and Stanislaw Ulam took inspiration for the name from the area of Monaco known for its gambling. This relation to gambling is due to the shared characteristics with the game of roulette, which is random.

The two mathematicians put their invented Monte Carlo method to the test when they worked together on the Manhattan Project to develop nuclear weapons. The two collaborated to fine-tune the MCS.

What are key types of Monte Carlo simulation?

The Monte Carlo simulation has several types.

• The standard Monte Carlo simulation is the simplest form. In this simulation, random samples are taken from the range of data being analyzed. An average is then calculated to reach an approximate value.
• Importance sampling focuses on the most relevant areas within the dataset. Instead of randomly sampling the data to get an approximate value, the most important and relevant data is prioritized.
• Stratified sampling breaks the data into smaller groups, known as strata. From each stratum, random samples are taken to get a randomized but also categorized sample of data.
• Markov Chain Monte Carlo (MCMC) is more complex, with the contents of the next sample relying on the previous sample. This method incorporates more statistical elements to create a more complex process and more accurate output.
• Sequential Monte Carlo watches changing data over time, so it responds dynamically to new data, new observations and new learnings.

What are key steps in a Monte Carlo simulation?

The Monte Carlo simulation has three main steps, regardless of the specific application or the desired outcome:

1. Identify the independent and dependent variables within the dataset and set up the predictive model.
2. Assign likely values to the independent variables by applying probability weights to the data, ensuring more accurate predictions will be applied when running the MCS.
3. Run the simulation repeatedly until the size of the sample generated from the simulation is correct. The size of the sample and the accuracy of the predictions can vary depending on the number of possible combinations that can be projected from the variables and dataset.

How is the Monte Carlo simulation used?

With its simplicity and ease of use when coupled with AI-powered tools, Monte Carlo analysis can be used across a wide range of fields and industries.

• Business decision-making: Companies of various sizes and ventures use the MCS for budget increases. By considering multiple factors, the Monte Carlo simulation projects the pros and cons of various decisions, aiding in more informed decision-making.
• Financial analysis: Financial analysts use the MCS to provide accurate projections. The Monte Carlo simulation is a useful forecasting tool for share prices as the simulation can account for mitigating circumstances such as the current shape of the financial market.
• Sports betting: The ever-growing popularity of sports betting globally has increased use of the Monte Carlo simulation, often coupled with deep learning models. These simulations produce real-time odds at a remarkable speed.