Monte Carlo simulation

Monte Carlo simulation

still in the probability side

method of generating random data using the rules of probability

what is randomness

anything that isn’t perfectly predictable is subject to randomness, even things that are somewhat regular

random variable

any variable defined by:

• a domain: possible values it can take on

• function: way of mapping possible values onto numerical outcomes

• probability distribution: rules governing how likely each numerical outcome is

random number generation in R

typically start with r

simulate single Bernoulli trial: rbinom(n = 1, size = 1, prob = .5)

n is the number of “draws”/samples taken

size number of trials per draw

prob probability of success on each trial

ifelse()

takes a vector and checks if a test condition is met (yes or no)

ifelse(test = event == 1, yes = "heads", no = "tails")

Monte Carlo procedure

proposed by Stanislow Ulam, John von Neumann and Nicholas Metropolis in the 40s

1. define domain

2. define probability distribution

3. draw random numbers

4. perform computation on random numbers

5. repeat many times

6. analyze distribution of computation outputs from each iteration

for loop

repeats a procedure for a finite number of times, each iteration is indexed

indexed outputs can thus be saved and analyzed after loop is complete