Slice sampling covariance hyperparameters of latent Gaussian models

TL;DR

This paper introduces a slice sampling method for hyperparameters in Gaussian process models that simplifies tuning and improves mixing, especially with non-Gaussian data, enhancing Bayesian inference efficiency.

Contribution

The paper proposes a novel slice sampling technique for covariance hyperparameters in latent Gaussian models, reducing tuning effort and improving convergence in MCMC sampling.

Findings

Slice sampling requires minimal tuning.

Method performs well in both strong- and weak-data regimes.

Improves convergence speed over traditional methods.

Abstract

The Gaussian process (GP) is a popular way to specify dependencies between 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 explanations for the data when making predictions. This integration is often performed 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.