Difference between revisions of "MonteCarloMethod"
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Principles of Monte Carlo Simulations the way we know it today were developed at the beginning of the 18th century. The history of Monte Carlo started with the work of a French scientist Georges Louis LeClerc, Comte de Buffon (1707-1788), who created “Buffon’s Needle.” <ref> Buffon's needle. Wikipedia.org [online]. Available at: https://en.wikipedia.org/wiki/Buffon%27s_needle</ref> In his work he used a method of dropping random needles on a lined background to estimate π. He proved that for a needle the same length as the distance between the lines the probability that each time a needle would intersect a line was 2/ π. He tested his theory by throwing baguettes over his shoulder on to a tile floor. | Principles of Monte Carlo Simulations the way we know it today were developed at the beginning of the 18th century. The history of Monte Carlo started with the work of a French scientist Georges Louis LeClerc, Comte de Buffon (1707-1788), who created “Buffon’s Needle.” <ref> Buffon's needle. Wikipedia.org [online]. Available at: https://en.wikipedia.org/wiki/Buffon%27s_needle</ref> In his work he used a method of dropping random needles on a lined background to estimate π. He proved that for a needle the same length as the distance between the lines the probability that each time a needle would intersect a line was 2/ π. He tested his theory by throwing baguettes over his shoulder on to a tile floor. | ||
| − | His formula was: | + | His formula was: π = 2N/X |
Where N is the number of tosses and X is the number of times a needle intersected a line. | Where N is the number of tosses and X is the number of times a needle intersected a line. | ||
Revision as of 10:15, 22 January 2018
- The Essay topic: Monte Carlo Method in Simulations
- Class:4IT496 Simulation of Systems (WS 2017/2018)
- Author: Bc. Yauheniya Andreyuk
1. Introduction
Monte Carlo method is an algorithm that rely on repeated random sampling to obtain numerical results. Essential idea of Monte Carlo is using randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. [1] Monte Carlo simulation is a technique that allows to see all the possible outcomes of the decisions and assess the impact of risk, allowing better decision making under uncertainty. The technique is used by professionals in such fields as finance, project management, energy, manufacturing, engineering, research and development, insurance, oil & gas, transportation, and the environment. The simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action. It shows the extreme possibilities — the outcomes of going for broke and for the most conservative decision — along with all possible consequences for middle-of-the-road decisions. [2]
2. History
Principles of Monte Carlo Simulations the way we know it today were developed at the beginning of the 18th century. The history of Monte Carlo started with the work of a French scientist Georges Louis LeClerc, Comte de Buffon (1707-1788), who created “Buffon’s Needle.” [3] In his work he used a method of dropping random needles on a lined background to estimate π. He proved that for a needle the same length as the distance between the lines the probability that each time a needle would intersect a line was 2/ π. He tested his theory by throwing baguettes over his shoulder on to a tile floor.
His formula was: π = 2N/X
Where N is the number of tosses and X is the number of times a needle intersected a line.
References
- ↑ Monte Carlo method. Wikipedia.org [online]. Available at: https://en.wikipedia.org/wiki/Monte_Carlo_method
- ↑ Monte Carlo Simulation. Palisade.com [online]. Available at: http://www.palisade.com/risk/monte_carlo_simulation.asp
- ↑ Buffon's needle. Wikipedia.org [online]. Available at: https://en.wikipedia.org/wiki/Buffon%27s_needle
- ↑ Introduction To Monte Carlo Simulation. NCBI [online]. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2924739/
