Gaussian Processes
The Gaussian Distribution Gaussian distributions, better knows as normal distributions , are important in all types of science. The terms normal and Gaussian distributions are used interchangeably. They are often used to represent real valued variables whose underlying distributions are not known. The central limit theorem says that in most situations, when independent random variables are added, their sum tends toward a normal distribution. If you don't know anything else, a normal distribution is often the default guess for the underlying distribution. The Gaussian distribution for a single variable is defined \[f(x|\mu ,{\sigma ^2}) = \frac{1}{{\sqrt {2\pi {\sigma ^2}} }}{e^ - }^{\frac{{{{(x - \mu )}^2}}}{{2{\sigma ^2}}}}\] where $ \mu $ is the mean of the distribution and $\sigma $ is the standard deviation . ${\sigma ^2}$ is the variance . The distribution is typically written $X \sim N(\mu ,{\sigma ^2})$. Plotting the normal distribution shows the familiar bell ...