Although using real high-dimensional data is also an option, we more often than not do not know the true distribution of these data points, so what we observe from real data might not always align nicely with theory. This method of simulation is useful for our project because it enables us to sample high-dimensional vectors from a known distribution-the standard normal distribution-so that we can compare our simulated results with our theory. The Monte Carlo methods are basically a class of computational algorithms that rely on repeated random sampling to obtain certain numerical results, and can be used to solve problems that have a probabilistic interpretation.
In this section, we will discuss some aspects of the Monte Carlo method our team used to simulate high dimensional data.
