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National Institute for Applied Statistics Research Australia Seminar Series
November 29 @ 2:00 pm - 3:00 pm
A/Prof Lassi Roininen
Lappeenranta University of Technology
Posterior inference for sparse hierarchical non-stationary models
Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed. While removing this assumption can improve prediction, fitting such models is challenging. In this work, hierarchical models are constructed based on Gaussian Markov random fields with stochastic spatially varying parameters. Importantly, this allows for non-stationarity while also addressing the computational burden through a sparse representation of the precision matrix. The prior field is chosen to be Matérn, and two hyperpriors, for the spatially varying parameters, are considered. One hyperprior is Ornstein-Uhlenbeck, formulated through an autoregressive process. The other corresponds to the widely used squared exponential. In this setting, efficient Markov chain Monte Carlo (MCMC) sampling is challenging due to the strong coupling a posteriori of the parameters and hyperparameters. We develop and compare three MCMC schemes, which are adaptive and therefore free of parameter tuning. Furthermore, a novel extension to higher-dimensional settings is proposed through an additive structure that retains the flexibility and scalability of the model, while also inheriting interpretability from the additive approach. A thorough assessment of the ability of the methods to efficiently explore the posterior distribution and to account for non-stationarity is presented, in both simulated experiments and a real-world computer emulation problem. https://arxiv.org/abs/1804.01431
After the seminar, NIASRA will sponsor coffee for the audiences. All welcome!