Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming

Abstract Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when number of observations large, especially estimated with fully Bayesian methods such as Markov chain Monte Carlo. In this paper, we focus on low-rank approximate processes, based basis function approximation via Laplace eigenfunctions stationary covariance The main contribution paper detailed analysis performance, and practical recommendations how to select functions boundary factor. Intuitive visualizations recommendations, make it easier users improve accuracy computational performance. We also propose diagnostics checking factor adequate given data. approach simple exhibits an attractive due its linear structure, easy implement in programming frameworks. Several illustrative examples performance applicability method language Stan presented together underlying model code.