Bias variance tradeoff in Gaussian process regression Can someone explain in simple terms the bias and variance tradeoff of Gaussian Process regression?

While it's not exactly what you asked, Rasmussen and Williams talk about (essentially) this briefly in chapter 5 of Gaussian Processes for machine learning.
In particular:

Notice that the trade-off between data-fit and model complexity is automatic;
there is no need to set a parameter externally to fix the trade-off.

For a mathematical explanation of how this occurs, you can check out the "interpretation" paragraph (in subsection 5.4.1) on page 113 of the same chapter, though the whole of chapter 5 would probably be useful reading.
A very brief summary is that the likelihood function contains two terms: one encouraging "a good fit for the data" (Rasmussen and Williams call this the "data fit" term), and one penalising complexity (the "complexity penalty").
