## Gaussian Process Regression (Draft)

### Uncertainty quantification

Reader level: Advanced Gaussian Distributions A Gaussian distribution exists over variables, i.e. the distribution explains how (relatively) frequently the values for those variables show up in observations. A Gaussian distribution for a n-dimensional vector variable is fully specified by a mean vector, μ, and covariance matrix Σ
$$ \mathrm{x} = (x_{1},....x_{n})^{T} \sim \mathcal{N}(\mu,\Sigma) $$ A univariate Gaussian distribution is given by $$ p(x|\mu,\sigma^2) = \dfrac{1}{2\pi \sigma^2} e^{ \dfrac{ -(x - \mu)^2 }{2 \sigma^2} } $$ where μ is the mean and σ is the standard deviation for the Gaussian.
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