Dec 6. 11:00-12:40. 14SCO Theatre 2

IPS1: Addressing challenges in Bayesian analysis for complex data

Organiser: Matias Quiroz

IN THIS SESSION

11:00-11:25

Bayesian Generalized Additive Model Selection Including a Fast Variational Option

Virginia He

We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be categorized as either zero, linear or non-linear. Employment of carefully tailored auxiliary variables results in Gibbsian Markov chain Monte Carlo schemes for practical implementation of the approach. In addition, mean field variational algorithms with closed form updates are obtained. Whilst not as accurate, this fast variational option enhances scalability to very large data sets. A package in the R language aids use in practice.

11:25-11:50

Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks

Andrew Zammit-Mangion, University of Wolloongong

Neural Bayes estimators are neural networks that approximate Bayes estimators in a fast and likelihood-free manner. Neural Bayes estimators are appealing to use with spatial models and data, where estimation is often a computational bottleneck. However, neural Bayes estimation in spatial applications has, to date, been restricted to data collected over a regular grid. These estimators are currently also implicitly dependent on a prescribed set of sampling locations, which means that the neural network needs to be re-trained for new spatial locations; this renders them impractical in many applications and impedes their widespread adoption. In this work, we employ graph neural networks to tackle the important problem of spatial-model-parameter estimation from arbitrary spatial sampling locations. In addition to extending neural Bayes estimation to irregular spatial data, our architecture leads to substantial computational benefits, since the estimator can be used with any arrangement or number of locations and independent replicates, thus amortising the cost of training for a given spatial model. We also facilitate fast uncertainty quantification by training an accompanying neural Bayes estimator for the marginal posterior quantiles. We illustrate our methodology on Gaussian and max-stable processes, where the latter have an intractable likelihood function. Finally, we showcase our methodology in a global sea-surface temperature application, where we estimate the parameters of a Gaussian process model in 2,161 regions of the globe, each containing a few hundred to more than 12,000 irregularly-spaced data points, in just a few minutes with a single graphics processing unit. :::