Solved – About the “a prior over the parameters” why always Gaussian distribution

I have the following problem.
I'm reading through the Gaussian Process book In the bayesian linear regression it is suggested to use the Gaussian prior over the parameters. For the Gaussian process regression we also don't know the distribution of the process, it can be not gaussian. Can GPR always work well? I just don't understand why should we use gaussian distribution? Is there any paper or book?

I can't exactly define what you ask in this question. However, I have two hypothesis.

Why do we use Gaussian prior for Bayesian linear regression?

We use this prior as convenient one and one that has nice interpretation. Really, it is a quadratic penalty for parameters values.

Why do we use Gaussian process as a model for the data?

Realizations of Gaussian processes with a proper covariance function can provide nearly all functions we can encounter in "real life". Also, they are convenient and provide exact inference and marginal distribution.

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