  The hyperparameters in Gaussian process regression (GPR) model with a
specified kernel are often estimated from the data via the maximum marginal
likelihood. Due to the non-convexity of marginal likelihood with respect to the
hyperparameters, the optimization may not converge to the global maxima. A
common approach to tackle this issue is to use multiple starting points
randomly selected from a specific prior distribution. As a result the choice of
prior distribution may play a vital role in the predictability of this
approach. However, there exists little research in the literature to study the
impact of the prior distributions on the hyperparameter estimation and the
performance of GPR. In this paper, we provide the first empirical study on this
problem using simulated and real data experiments. We consider different types
of priors for the initial values of hyperparameters for some commonly used
kernels and investigate the influence of the priors on the predictability of
GPR models. The results reveal that, once a kernel is chosen, different priors
for the initial hyperparameters have no significant impact on the performance
of GPR prediction, despite that the estimates of the hyperparameters are very
different to the true values in some cases.
