Spatially-Varying Bayesian Predictive Synthesis for Flexible and
Interpretable Spatial Prediction
- URL: http://arxiv.org/abs/2203.05197v1
- Date: Thu, 10 Mar 2022 07:16:29 GMT
- Title: Spatially-Varying Bayesian Predictive Synthesis for Flexible and
Interpretable Spatial Prediction
- Authors: Danielle Cabel, Masahiro Kato, Kenichiro McAlinn, Shonosuke Sugasawa,
Kosaku Takanashi
- Abstract summary: We propose a novel methodology that captures spatially-varying model uncertainty, which we call spatial Bayesian predictive synthesis.
We show that our proposed spatial Bayesian predictive synthesis outperforms standard spatial models and advanced machine learning methods.
- Score: 6.07227513262407
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Spatial data are characterized by their spatial dependence, which is often
complex, non-linear, and difficult to capture with a single model. Significant
levels of model uncertainty -- arising from these characteristics -- cannot be
resolved by model selection or simple ensemble methods, as performances are not
homogeneous. We address this issue by proposing a novel methodology that
captures spatially-varying model uncertainty, which we call spatial Bayesian
predictive synthesis. Our proposal is defined by specifying a latent factor
spatially-varying coefficient model as the synthesis function, which enables
model coefficients to vary over the region to achieve flexible spatial model
ensembling. Two MCMC strategies are implemented for full uncertainty
quantification, as well as a variational inference strategy for fast point
inference. We also extend the estimations strategy for general responses. A
finite sample theoretical guarantee is given for the predictive performance of
our methodology, showing that the predictions are exact minimax. Through
simulation examples and two real data applications, we demonstrate that our
proposed spatial Bayesian predictive synthesis outperforms standard spatial
models and advanced machine learning methods, in terms of predictive accuracy,
while maintaining interpretability of the prediction mechanism.
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