Monte Carlo Integration in Python
What is Monte Carlo Integration?
Monte Carlo, is in fact, the name of the world-famous casino located in the eponymous district of the principality of Monaco on the world-famous French Riviera.
It turns out that the casino inspired the minds of famous scientists to devise an intriguing mathematical technique for solving complex problems in statistics, numerical computing, and system simulation.
One of the first and most famous uses of this technique was during the Manhattan Project when the chain-reaction dynamics in highly enriched uranium presented an unimaginably complex theoretical calculation to the scientists. Even the genius minds such as John Von Neumann, Stanislaw Ulam, and Nicholas Metropolis could not tackle it in the traditional way. They, therefore, turned to the wonderful world of random numbers and let these probabilistic quantities tame the originally intractable calculations.
Amazingly, these random variables could solve the computing problem, which stymied the sure-footed deterministic approach. The elements of uncertainty actually won.
Today, it is a technique used in a wide swath of fields:
- Risk analysis
- Financial engineering
- Supply chain logistics
- Healthcare research, drug development
- Statistical learning and modeling
- Computer graphics, image processing, game design
- Large system simulations
- Computational physics, astronomy, etc.
For all its successes and fame, the basic idea is deceptively simple and easy to demonstrate. This story demonstrates it with a simple set of Python code.
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