A common misconception about Monte Carlo simulation is that the computational effort is combinatorial exponential in the number of uncertain inputs - making it impractical for large models. This is true for simple discrete probability tree or decision tree methods. But, in fact, the great advantage of Monte Carlo is that the computation is linear in the number of uncertain inputs - it is proportional to the number of input distributions to be sampled.
The sample size you need is controlled by the degree of precision that you want in the output distributions you care about. Suppose you are interested in estimating percentiles of a cumulative distribution, there's no need to increase the sample size just because you have more uncertain inputs.
For most models, a few hundred up to a thousand runs are sufficient. You only need a larger sample if you want high precision in your resulting distributions, and a smooth-looking density function. Given the inherent uncertainty in the inputs, higher precision is usually an aesthetic preference rather than a functional need. Sometimes you can fit a distribution to historical data based on the quantity. But often you are trying to forecast using quantities for which you have little or no historical data - or data on related quantities only.
However it is often more convenient and faster to use a quantitative modeling environment, like Analytica, which integrates Monte Carlo simulation into its original design. This approach offers major advantages in terms of ease of use and speed of computation.
Using Analytica, you can define any variable, or any cell in an array, as a discrete or continuous distribution. You can view the probability distribution for any resulting variable as a set of probability bands selected percentiles , as a probability density function, cumulative distribution function or even view the underlying random sample.
This makes it vastly easier to define and analyze multivariate variables with serial correlation such as sales or interest rates over time, and cross-dependency across multiple regions and products. Contact us today to learn more about the platform, or to schedule a product demo. Automated page speed optimizations for fast site performance.
Skip to content. Monte Carlo simulation and risk analysis: What you can learn and how you can benefit Ready for some Monte Carlo? Monte Carlo simulation: A definition. A quick history. How a Monte Carlo simulation works. What are the advantages of Monte Carlo simulations? Performing a Monte Carlo simulation offers a number of advantages over deterministic calculations across an array of decision-making applications.
The topline advantage of a Monte Carlo simulation is to faithfully address uncertainty in a quantitative model. This does not, however, guarantee that you will get the most likely or average value in the model results. This deficiency can be seen in the Flaw of Averages — pardon us, the Law of Averages. However, consider a drunk trying to walk down the middle of a busy two-lane highway.
In reality, he staggers left and right. The state of the drunk in his average position is alive but his average state is dead. On the night of August 18, the roulette ball fell on black 26 straight times. The ball would eventually touch red again, but it was too late for many.
Monte Carlo simulation can provide a reliable inoculation against the natural biases, confusion, and, most importantly, wishful thinking that we often bring to dealing with uncertainty.
Comparing Monte Carlo analysis to other methods. While machine learning can be used to run data simulations, Monte Carlo simulations differ from usual machine learning programs. An average machine learning algorithm is data-centric and focusses more on exploration for example, finding patterns in consumer purchases.
On the other hand, Monte Carlo simulations are process-centric and focus entirely on making predictions for example, finding out how a particular marketing decision might affect a demographic.
As a rule of thumb, it would be a good idea to use simulations instead of machine learning algorithms if:. Finally, consider defining a Bernoulli distribution for flipping a coin. Now, if you sample your calculations from this distribution, you are essentially performing a Monte Carlo simulation! Using pandas to construct a Python model that simulates a spreadsheet is one of the easiest and most efficient ways of running Monte Carlo simulations in Python.
A table has been created, which represents the sales targets given to sales reps this year, their actual sales for the year and the commission rate they charge. This information will be used to predict the sales commission these reps are expected to make next year.
This step involves declaring the predefined variables and assigning them appropriate values. This is the sample set created by executing the previous step. This step involves manually feeding some values for the independent predefined variable in order to achieve a normal distribution. A pandas DataFrame is the Excel sheet or table that will store the result values. In this step, we are using the commission rate values obtained from the previous step to calculate the commission amount.
You can repeat this multiple times to get more accurate predictions. So, there you have it! Here were the main talking points:. Interested in other aspects of the data analytics process? To learn more about data analytics, check out this free, 5-day data analytics short course , or read the following posts for more introductory topics:. In all, the article will cover: What is the Monte Carlo method? How does the Monte Carlo method work? What is the Monte Carlo method?
The software then randomly samples from the probabilities for each input variable of interest. Three common distributions that are used include triangular, normal, and uniform. For a Monte Carlo analysis, one must select the number of iterations that the simulation will run.
0コメント