Gaussian processes compared with state-of-the-art nonlinear parametric models

Easy to use
predictions correspond to model with infinite number of parameters
Equally good, or better, on a large range of datasets
GPs have many standard regression methods as special cases
Radial basis functions
Splines
Feed-forward neural networks with one hidden layer

Problems:
Ill-conditioned
N^3 complexity is bad news for N>1000
approximate methods