Slice sampling covariance hyperparameters of latent Gaussian models

The Gaussian process (GP) is a popular way to specify dependencies be-tween random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these hyperparameters considers different possible expla-nations for the data when making predictions. This integration is often per-formed using Markov chain Monte Carlo (MCMC) sampling. However, with non-Gaussian observations standard hyperparameter sampling approaches require careful tuning and may converge slowly. In this paper we present a slice sampling approach that requires little tuning while mixing well in both strong- and weak-data regimes.