Related Issue:

• This PR introduces a draft for the implementation of Gaussian processes, as outlined in issue Gaussian Processes #190.

Description:

• This PR defines a Gaussian process using AbstractGPs.jl, where you can specify a mean function, a kernel function, and optionally add observational noise.
• The Gaussian process can be fitted to data directly or have its hyperparameters optimized using maximum likelihood estimation (MLE).
• Hyperparameters are automatically extracted from the Gaussian process model during optimization.

Current State:

• A gaussian process can be fitted to data stored in a DataFrame.
• A gaussian process can be fitted with an UQInput, a UQModel and an experimental design.
• The hyperparameters of the Gaussian process can optionally be optimized using MLE.
• Both input and output standardization are supported.

What’s Left to Do:

• The automatic hyperparameter-extraction is not implemented for every possible mean and kernel function.
• The current optimization method is unstable and heavily relies on a good initial guess for the hyperparameters.
• Occasionally, UQInput standardization can break the fitting procedure due to -Inf or Inf values arising from the inverse standard normal CDF.
• There is no documentation yet
• There are no recent tests implemented