![]() ![]() Important: If you re-run the preceding command you will, in general, get a different result. To make repeats particularly likely, I’ll change size to 20: numbers = 1:10 If I instead set replace = TRUE I can get repeats of the same number. This example draws 5 numbers between 1 and 10 without replacement: sample(x = 1:10, size = 5, replace = FALSE) # 9 8 5 2 6 In the preceding example, marbles was a character vector, but we can also use sample with a numeric vector. (For those of you who know a bit more about computer science, technically they’re only pseudo-random draws, but this will suffice for Monte Carlo Simulations.) This is because the command sample simulates a random draw, meaning the result won’t be the same each time you use the command. IMPORTANT: You may get a different result than I did when you run the previous command. Notice that we didn’t get any repeats since I set replace = FALSE. Sample(x = marbles, size = 2, replace = FALSE) # "red" "blue" Let’s look at an example in which I simulate drawing two marbles from a bowl containing one red, one blue and one green marble, without replacement: marbles = c('red', 'blue', 'green') What do I mean by a “vector containing marbles”? You can use any vector at all as the argument x: it simply plays the role of the label we give to each of our hypothetical marbles. Of these three arguments x is the most mysterious. The function sample takes three arguments: x is a vector containing the “marbles” in our hypothetical bowl, size tells R how many marbles we want to draw, and replace is set to TRUE or FALSE depending on whether we want to draw marbles from the bowl with replacement, which means putting the marble back after each draw, or without replacement, which means keeping each marble after we draw it and not returning it to the bowl. It turns out that there are many random experiments that can be reduced to thinking about a bowl containing different kinds of marbles, so sample is ipso facto a fairly general command. ![]() ![]() The R command sample simulates drawing marbles from a bowl. This is why Monte Carlo Simulation is such a valuable tool. But simulating a million coin flips in R takes less than a second. A colleague of… Ulam, Nicholas Metropolis, suggested using the name Monte Carlo, which refers to the Monte Carlo Casino in Monaco where Ulam’s uncle would borrow money from relatives to gamble.įlipping a coin one million times by hand would be tedious in the extreme. The modern version of the… Monte Carlo method was invented in the late 1940s by Stanislaw Ulam, while he was working on nuclear weapon projects at the Los Alamos National Laboratory. Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results i.e., by running simulations many times over in order to calculate those same probabilities heuristically just like actually playing and recording your results in a real casino situation: hence the name.īut where did the name come from? Monte Carlo is a region in the tiny principality of Monaco famed for its casino. Here’s what Wikipedia has to say on the matter: Remember: our definition of probability is “long-run relative frequency.” If we repeat an experiment (like flipping a coin) a large number of times and tabulate the outcomes, the relative frequencies will “converge,” in a sense that will be made clearer later in the semester, to the probabilities of each outcome. Roughly speaking, Monte Carlo Simulation means using a computer to repeatedly carry out a random experiment and keeping track of the outcomes.
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