Suppose I have a Gaussian Process $f \sim GP(\mu, k)$ with given mean function $\mu(x)$ and covariance function $k(x, x')$. I also have a trajectory $\textbf{p} = (p_1, \dots, p_n) \in \mathbb{R}^n$.
Question: What is the best way to calculate the probability that $\textbf{p}$ was generated by given Gaussian Process $f$?
I heard about Monte-Carlo methods, but I do not fully understand how they are applicable here. I also was thinking about some likelihood estimations, but formally I have just one point (my path $\textbf{x}$, so it doesn't really make sense to calculate this type of likelihood.