for the longest time i thought it was just a dessert. gordon ramsay has failed me
In: Mathematics
Monte Carlo is in fact a dessert! However, the simulation is a way of building your probabilistic models to introduce uncertainty/randomness into them. It’s named after the casino, which is actually no longer named Monte Carlo. The dessert is named after the city in France.
Monte Carlo is a city famous for casinos (games of chance). As a process it is the randomization (chance) of all the variables and denoting the outcome. I used it in electronic circuit analysis. Varying all the electronic components within the design tolerances to make sure the circuit works as expected. In basic electronics the components are assumed to be exact but in reality the physical parts have slight variances in values, usually 5-10% variance. It is important to make sure the the design works not just in theory but in the physical.
It’s a way of approximating something by doing lots and lots of trials. The idea is after many randomized trials a pattern will emerge. It’s very useful for complex systems where there is no closed formula.
A simple example would be suppose you wanted to know the probability of each poker hand. You could write a computer program that generates thousands of random 5 card draws and counts each type of poker hand. Eventually the number of each poker hand divided by the number of trials will approach the theoretical probability.
For reference, Monte Carlo is famous for a casino. In mathematics, a Monte Carlo simulation is just a probabilistic method for finding a solution, especially useful when an exact or traditional approximate method would be computationally expensive.
One simple example: let’s say you want to find the area of a circle of radius 1. You can pick two random numbers between -1 and 1, and let those be x-y coordinates. Do this thousands or millions of times (or even more), and see what proportion of those fall inside the circle (i.e. satisfy `x^2+y^2<1`). Multiply that by the area of the square with sides going from -1 to 1 (area is 4), and there’s a Monte Carlo simulation for the area of the circle.
Of course, circles are easy, but this can be done with more complex shapes, with more complex types of problems (such as weather forecasting from certain models).
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