  In applications of Gaussian processes where quantification of uncertainty is
a strict requirement, it is necessary to accurately characterize the posterior
distribution over Gaussian process covariance parameters. Normally, this is
done by means of standard Markov chain Monte Carlo (MCMC) algorithms. Motivated
by the issues related to the complexity of calculating the marginal likelihood
that can make MCMC algorithms inefficient, this paper develops an alternative
inference framework based on Adaptive Multiple Importance Sampling (AMIS). This
paper studies the application of AMIS in the case of a Gaussian likelihood, and
proposes the Pseudo-Marginal AMIS for non-Gaussian likelihoods, where the
marginal likelihood is unbiasedly estimated. The results suggest that the
proposed framework outperforms MCMC-based inference of covariance parameters in
a wide range of scenarios and remains competitive for moderately large
dimensional parameter spaces.

Computation