R Tutorial: Gaussian mixture models (GMM)

Key Takeaways

now that you have learned how to simulate observations from a Gaussian distribution it is time to simulate a simple mixture of two Gaussian components to do so we will imagine we have a coin and samples from two different couchant distributions we flip the coin and whenever comes up hits we take a sample from the first Gaussian distribution otherwise would take a sample from the second Gaussian for the moment don't mind what are representing the gaussians we repeat this procedure until we reach the desired number of samples to simulate the results from a coin we use the function sample where the first argument is the vector of values from which to choose the second is the number of items to choose the third if the sampling should be with replacement or not here we consider with and last is the vector of probability weights corresponding to each element of the vector bin sample here we simulate 500 coin tosses representing the number one as heads and zero as tails both with equal probabilities using the function table we summarized the number of each result once we have simulated the coin tosses we proceed to simulate two different Gaussian distributions the first one with a mean of 5 and a standard deviation of 2 the second with a mean of 0 and a SD of 1 which corresponds to the standard normal distribution the default distribution for our norm then we create the object mixture underscore simulation which takes the values from the first caution when the coin comes up one or heads and from the second when the coin comes up zero or tails the table combines the result with the function C vine and shows the first six rows with the function head observe that the last column is the resulting mixture of two gaussians to plug the histogram of the simulated mixture we follow the same path as before that is to say we transform the object into a data frame and use geom histogram you can see from the plot that two peaks appear each of them accounting for the same area instead of having equal probabilities for each side of the coin as before we give now more chances to details then we would expect that the second peak on the last blood decreases to do it in R we just changed the weight in the prov argument here we give zero point a to the number zero the mixture is then created as before in fact from the plot you can see that the second peak has decreased the probability weights represent the importance of the distributions that form the mixture if the way for a particular distribution is high the sub population explained by that distribution is important we can also incorporate as many distributions as we want into our mixture in this example we simulate a mixture of three gaussians first we create the proportions object which is analogous to the flipping coin process but now with three outcomes then we include a third gaussian option with a mean of 10 and a SD of 1 to plot it we use the GM histogram as before from the plot we see a suspected three different Peaks now is your turn to simulate a mixture of gas