# Explained: Monte Carlo simulations

##### May 17, 2010 by Peter Dizikes

Speak to enough scientists, and you hear the words 'Monte Carlo' a lot. "We ran the Monte Carlos," a researcher will say. What does that mean?

The scientists are referring to Monte Carlo simulations, a used to model probabilistic (or “stochastic”) systems and establish the odds for a variety of outcomes. The concept was first popularized right after World War II, to study ; mathematician Stanislaw Ulam coined the term in reference to an uncle who loved playing the odds at the Monte Carlo casino (then a world symbol of gambling, like Las Vegas today). Today there are multiple types of Monte Carlo simulations, used in fields from to engineering, finance and more.

To get a handle on a Monte Carlo , first consider a scenario where we do not need one: to predict events in a simple, linear system. If you know the precise direction and velocity at which a shot put leaves an Olympic athlete’s hand, you can use a linear equation to accurately forecast how far it will fly. This case is a deterministic one, in which identical initial conditions will always lead to the same outcome.

The world, however, is full of more complicated systems than a shot-put toss. In these cases, the complex interaction of many variables — or the inherently probabilistic nature of certain phenomena — rules out a definitive prediction. So a Monte Carlo simulation uses essentially random inputs (within realistic limits) to model the system and produce probable outcomes.

In the 1990s, for instance, the Environmental Protection Agency started using Monte Carlo simulations in its risk assessments. Suppose you want to analyze the overall health risks of smog in a city, but you know that smog levels vary among neighborhoods, and that people spend varying amounts of time outdoors. Given a range of values for each variable, a will randomly select a number within each range, and see how they combine — and repeat the process tens of thousands or even millions of times. No two iterations of the simulation might be identical, but collectively they build up a realistic picture of the population’s smog exposure.

“In a deterministic simulation, you should get the same result every time you run it,” explains MIT computer science professor John Guttag in his OpenCourseWare lecture on Monte Carlo simulations. However, Guttag adds, in “stochastic simulations, the answer will differ from run to run, because there’s an element of randomness in it.”

The aggregation of data makes it possible to identify, say, a median level of smog exposure. To be sure, Monte Carlo simulations are as good as their inputs; accurate empirical data would be necessary to produce realistic simulation results.

Explore further: Magic and symmetry in mathematics

## Related Stories

#### A new calculation code opens new possibilities in nuclear reactor modelling

Jun 28, 2007

Research Scientist Jaakko Leppänen from VTT Technical Research Centre of Finland has developed a new calculation code in his doctoral thesis, for the modelling of neutron physics in nuclear reactors. The so-called Monte ...

#### New computer simulation helps explain folding in important cellular protein

Jul 29, 2009

(PhysOrg.com) -- Most parts of living organisms come packaged with ribbons. The ribbons are proteins—chains of amino acids that must fold into three-dimensional structures to work properly. But when for any reason the ribbons ...

#### Spurious Phase in a Model for Traffic on a Bridge

Nov 14, 2005

Researchers at Virginia Tech are providing further insight into the physics of systems far from equilibrium by studying traffic patterns across a narrow bridge.

#### Quantum mechanics reveals new details of deep earth

May 10, 2010

(PhysOrg.com) -- Scientists have used quantum mechanics to reveal that the most common mineral on Earth is relatively uncommon deep within the planet.

#### When molecules leave tire tracks: A new approach to optimizing molecular self-organization

Feb 18, 2010

Certain types of molecules form patterns when deposited onto substrates. Photovoltaic and sensor devices from organic compounds depend on this phenomenon of self-organization. Physicists of Ludwig-Maximilians-Universitaet ...

#### More precise measurements of the W boson

Dec 21, 2009

(PhysOrg.com) -- "The W boson is one of the very few major building blocks of matter," Dmitri Denisov tells PhysOrg.com. "It is a member of a family of particles that is the most fundamental in nature. The W boson is res ...

## Recommended for you

#### Magic and symmetry in mathematics

8 hours ago

We live in a three-dimensional world. Despite the many benefits this presents, it also makes for a complicated math problem, according to Northeastern associate professor of mathematics Ivan Loseu. The best ...

#### Optimising the future with mathematics

Mar 11, 2014

How will science address the challenges of the future? In collaboration with Australia's chief scientist Ian Chubb, we're asking how each science discipline will contribute to Australia now and in the fu ...

#### Strong teams attract crowds for international cricket

Mar 06, 2014

The strength of the team—not the promise of a close contest—is the biggest draw to crowds in international cricket, new research has found.

#### Improving radiation therapies for cancer mathematically

Mar 05, 2014

In a paper published in December in the SIAM Journal on Scientific Computing, authors Li-Tien Cheng, Bin Dong, Chunhua Men, Xun Jia, and Steve Jiang propose a method to optimize radiation therapy treatments in cancer patien ...

#### Computational study finds maximum packing density of 55,000 different shapes

Mar 05, 2014

A team of researchers at the University of Michigan has used computational and analytical analysis to find the maximum packing density of 55,000 uniquely shaped particles. In their paper published in the ...

##### EponymousDave
not rated yet May 18, 2010
The heavy metal ball is called a 'shot.' 'Put' is the transitive verb nickname for throwing the shot.

## More news stories

#### Researchers discover evidence in bones that shows ancient sloths returned to the sea

(Phys.org) —A team of researchers from the Sorbonne Universités have found evidence of an ancient sloth returning to the sea to survive. In their paper published in Proceedings of the Royal Society B: ...

#### Researchers reconstruct a cheese recipe from the Early Bronze Age

Normally, Andrej Shevchenko and his team at the Max Planck Institute of Molecular Cell Biology and Genetics in Dresden analyse proteins and fats in the cells of fruit flies or roundworms. In this case, however, ...

#### Chemical ghosts of dinosaurs may help reveal new secrets

Most of life is carbon-based, that is, organic. These organic molecules containing mostly carbon and hydrogen are delicate to the ravages of time, relatively speaking. They aren't usually preserved in fossils ...

#### Promoting love can punish sales

Valentine's Day has come and gone. But those images of romance are still everywhere : a happy couple holding hands in an eharmony ad, two lovebirds sharing a tender kiss in a Nikon camera commercial.

#### Magic and symmetry in mathematics

We live in a three-dimensional world. Despite the many benefits this presents, it also makes for a complicated math problem, according to Northeastern associate professor of mathematics Ivan Loseu. The best ...

#### 'Ultracold' molecules promising for quantum computing, simulation

(Phys.org) —Researchers have created a new type of "ultracold" molecule, using lasers to cool atoms nearly to absolute zero and then gluing them together, a technology that might be applied to quantum computing, precise ...

#### Can material rivaling graphene be mined out of rocks? Yes, if...

Will one-atom-thick layers of molybdenum disulfide, a compound that occurs naturally in rocks, prove to be better than graphene for electronic applications? There are many signs that might prove to be the ...

#### Relationship between gut bacteria, blood cell development helps immune system fight infection

The human relationship with microbial life is complicated. At almost any supermarket, you can pick up both antibacterial soap and probiotic yogurt during the same shopping trip. Although there are types of ...

#### Protein key to cell motility has implications for stopping cancer metastasis

A Penn team describes how a key cell-movement protein called IRSp53 is regulated in a resting and active state, and what this means for cancer-cell metastasis. They characterized how IRSp53 connects to the ...

#### Transition to ICD-10 may cause information, financial losses for providers

Health providers may experience information and financial loss during the mandated conversion from the current International Classification of Diseases to its new and improved version, report researchers at the University ...