64th ISI World Statistics Congress - Ottawa, Canada

64th ISI World Statistics Congress - Ottawa, Canada

Hierarchical, non-stationary, spatial modelling to account for model error in computational models

Author

DH
Dave Higdon

Co-author

  • S
    Stephen Walsh
  • M
    Marco Ferreira
  • A
    Annie Sauer

Conference

64th ISI World Statistics Congress - Ottawa, Canada

Format: IPS Abstract

Keywords: bayesian hierarchical model

Session: IPS 219 - Statistical inference for computer models

Wednesday 19 July 10 a.m. - noon (Canada/Eastern)

Abstract

It has been noted that deep machine learning models are closely connected to spatial hierarchical models (e.g. Wikle (2019)). In both approaches, complex spatial fields are developed through dependence on simpler on simpler spatial fields. The dependence is commonly additive in hierarchical modelling settings, but can be more general in a deep ML model. In this talk we explore the use of deep Gaussian processes in settings where a hierarchical spatial model seems appropriate. We'll explore the basic deep GP formulation and computing required to carry out a fully Bayesian analysis and compare this to a more standard hierarchical model. We'll consider examples in cosmology and rainfall from tropical cyclones.