Splines and Gaussians [closed]

1. Why would we want to use splines as opposed to polynomials?
2. How does Gaussian process regression work?

Why would we want to use splines as opposed to polynomials?

In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.

How does Gaussian process regression work?

Gaussian process regression is nonparametric (i.e. not limited by a functional form), so rather than calculating the probability distribution of parameters of a specific function, GPR calculates the probability distribution over all admissible functions that fit the data.