  Gaussian Process Networks (GPNs) are a class of directed graphical models
which employ Gaussian processes as priors for the conditional expectation of
each variable given its parents in the network. The model allows the
description of continuous joint distributions in a compact but flexible manner
with minimal parametric assumptions on the dependencies between variables.
Bayesian structure learning of GPNs requires computing the posterior over
graphs of the network and is computationally infeasible even in low dimensions.
This work implements Monte Carlo and Markov Chain Monte Carlo methods to sample
from the posterior distribution of network structures. As such, the approach
follows the Bayesian paradigm, comparing models via their marginal likelihood
and computing the posterior probability of the GPN features. Simulation studies
show that our method outperforms state-of-the-art algorithms in recovering the
graphical structure of the network and provides an accurate approximation of
its posterior distribution.
