Wednesday, Aug 6: 10:30 AM - 12:20 PM
0482
Invited Paper Session
Music City Center
Room: CC-104E
Applied
Yes
Main Sponsor
Section on Statistics and the Environment
Co Sponsors
Environmental and Ecological Statistics
The International Environmetrics Society
Presentations
Process (physics)-informed neural models have become ubiquitous across many areas of science in recent years due to the value of regularizing neural-networks based on an underlying partial differential equation physical constraint. This talk discusses a generalization in which mechanistic information about the process can be incorporated via a Bayesian hierarchical approach. In many scientific applications where there is substantial a priori process knowledge, incorporating this information can improve model performance and efficiency. The notion of including process knowledge in data-driven models for spatio-temporal data is not new (e.g., data assimilation, physical-statistical modeling, etc.), and considering hybrid statistical/neural approaches can provide more realistic modeling of complex processes while quantifying uncertainty. This talk presents a brief overview of neural and statistical approaches and presents a unifying hierarchical modeling structure that can accommodate flexible mechanistically informed neural or statistical models for spatio-temporal dynamic processes.
Keywords
spatio-temporal
dynamics
large-language model
attention mechanism
stochastic antecedent
Hawkes process is a popular point process model for applications such as earthquakes, crime and conflict data, due to its self-exciting nature via triggering functions. However, many Hawkes process models in the literature concern with temporal point patterns only and they often consider univariate problems. Recently, there have been some developments on spatio-temporal Hawkes process models, but many of them deal with restrictive triggering structure. In this work, we adapt the neural Hawkes process models that are proven to be flexible with complex triggering structure and extend them to multivariate spatio-temporal point patterns. We apply our proposed approach to modeling multivariate terrorism occurrences in the middle eastern region.
This is a joint work with Hojun You and Lingling Chen.
Keywords
Hawkes process
Spatio-temporal point process
neural network
Terrorism data
In geostatistical inference, preferential sampling takes place when the locations of point-referenced data are related to the latent spatial process of interest. Traditional geostatistical models can lead to biased inferences and predictions under preferential sampling. We introduce an extended Bayesian hierarchical framework that models both the observation locations and the observed data jointly, using a spatial point process for the locations and a geostatistical process for the observations. We illustrate extensions beyond the classical log-Gaussian Cox process for the sampling locations, combined with a Gaussian process for the observations. We also introduce simpler methods for accounting for preferential sampling that are less computationally demanding at the expense of prediction accuracy. We validate our models through simulation, demonstrating their effectiveness in correcting biases and improving prediction accuracy. We apply our models to decadal average temperature data from the Global Historical Climate Network in Southwestern United States and show that preferential sampling could be present in some spatial regions.
Keywords
Geostatistical processes
Point processes
Log Gaussian Cox processes
Bayesian inference
Climate
We consider the problem of spatial downscaling when aggregated values of the response variable and of a large number of potential covariates are observed. We show that a naïve application of standard regularization methods can lead to misleading predictions at finer resolutions. We develop a novel regularization methodology that provides dimension reduction as well as scale-adaptive predictions at finer scales with minimal computational overhead. We study theoretical properties of the method under a mixed increasing domain spatial asymptotic structure and also report results from a moderately large simulation study.
Keywords
Spatial downscaling
LASSO
Spatial prediction
Mixed Increasing Domain Asymptotics