Monday, Aug 5: 10:30 AM - 12:20 PM
5057
Contributed Papers
Oregon Convention Center
Room: CC-C122
Main Sponsor
Section on Statistics and the Environment
Presentations
For modeling non-stationary spatial processes, spatial deformation is a popular approach in the literature, which characterizes the underlying non-stationary process as a stationary counterpart in the deformed space through proper space mapping. Existing studies often follow a two-step procedure, involving space mapping exploration in the initial step and spatial covariance estimation in the subsequent step. The first step typically involves estimating local variograms from data, followed by applying a multi-dimensional scaling technique with spline fittings to construct a smoothed deformed space. This study introduces a novel approach to estimate the space deformation, considering affine coupling for space mapping. The proposed method applies to both single and multiple realizations of spatial data where the spatial locations may vary across different realizations, offering flexibility and ensuring a bijective mapping. For inference, we use maximum likelihood to simultaneously estimate the deformation space mapping and the spatial covariance function. The effectiveness of the proposed method is demonstrated through simulations and real data examples.
Keywords
Affine coupling
gradient descent
non-stationarity
regularization
spatial deformation
Computer models are often run at different fidelities or resolutions due to tradeoffs between computational cost and accuracy. For example, global circulation models can simulate climate on a global scale, but they are too expensive to be run at a fine spatial resolution. Hence, regional climate models (RCMs) forced by GCM output are used to simulate fine-scale climate behavior in regions of interest. We propose a highly scalable generative approach for learning high-fidelity or high-resolution spatial distributions conditional on low-fidelity fields from training data consisting of both high and low-fidelity output. Our method learns the relevant high-dimensional conditional distribution from a small number of training samples via autoregressive Gaussian processes with suitably chosen regularization-inducing priors. We demonstrate our method on simulated examples and for emulating the RCM distribution corresponding to GCM forcing using past data, which is then applied to future GCM forecasts
Keywords
Gaussian Processes
Spatial Fields
Downscaling
Bayesian Transport Map
Climate-model emulation
Generative Modelling
This study presents an advancement in geostatistical modeling for environmental data, focusing specifically on oceanic temperature and salinity from the Argo project. By incorporating a correlation term in the nugget effect and employing a bivariate Matérn-SPDE model with both Gaussian and non-Gaussian driving noises, we effectively address the challenges of analyzing complex environmental datasets. This extension primarily tackles issues arising from correlated measurement errors and pronounced small-scale variability. Using both simulated and real-world Argo project data from 2007-2020 for temperature and salinity, we demonstrate how this enhanced correlation parameterization impacts variable estimation and spatial predictions in bivariate Matérn-SPDE models.
Relaxing the independent noise assumption, our approach shows significant shifts in dependence characterization. We validate our model with global temperature and salinity predictions, employing a combined approach of a Matérn-SPDE model and a moving-window model. This integration refines geostatistical analysis and underscores the merit of our methodology for environmental science.
Keywords
Multivariate random fields
Non-Gaussian models
Matérn covariances
Nugget effect
Stochastic partial differential equations
Spatial statistics
Predicting animal trajectories poses a significant challenge due to the intricate nature of their behaviors, unpredictable environmental elements, individual differences, and the scarcity of precise movement data. Further complexities arise from factors such as migration, hunting, reproduction, and social interactions, making precise trajectory prediction challenging. Various models in the literature attempt to investigate animal telemetry by either modeling the velocity or position, or both concurrently using Gaussian processes. In this work, we consider multi-dimensional trajectories with respect to longitude, latitude and altitude. Our approach involves modeling the velocity of each dimension as a fractional Ornstein-Uhlenbeck (fOU) process, where correlation is induced from an associated multi-dimensional fractional Brownian motion. We propose fast simulation and prediction algorithms, and present the feasibility of maximum likelihood estimation. The applicability of our model for animal movement is presented through simulation studies and by modeling the trajectory of bats in Germany.
Keywords
Animal tracking
fractional Brownian motion
Gaussian process simulations
telemetry data
trajectory prediction
Abstracts
The classical Matérn model has been a staple in spatial statistics. We offer a new perspective to extending the Matérn covariance model to the vector-valued setting. We adopt a spectral, stochastic integral approach, which allows us to address challenging issues on the validity of the covariance structure and at the same time to obtain new, flexible, and interpretable models. In particular, our multivariate extensions of the Matérn model allow for time-irreversible or, more generally, asymmetric covariance structures. Moreover, the spectral approach provides an essentially complete flexibility in modeling the local structure of the process. We establish closed-form representations of the cross-covariances when available, compare them with existing models, simulate Gaussian instances of these new processes, and demonstrate estimation of the model's parameters through maximum likelihood. An application of the new class of multivariate Matérn models to environmental data indicate their success in capturing inherent covariance-asymmetry phenomena.
Keywords
Multivariate spatial statistics
cross-covariance functions
spectral analysis
In the realm of frequency domain analysis for spatial data, estimators based on the periodogram often exhibit complex variance structures originating from aggregated periodogram covariances. Previous attempts to bootstrap these statistics face challenges in capturing these variances and quantifying estimation uncertainty. This difficulty arises because achieving consistency for various periodogram-based statistics requires evaluating the periodogram at an increasing number of frequencies as the sample size grows. Despite the diminishing dependence between periodogram ordinates, the decay rate balances the growing frequencies, preserving a dependence structure in the limiting distribution. Consequently, the validity of frequency domain bootstrap (FDB) approaches for spatial data is confined to a specific class of processes and statistics. To overcome this challenge, we propose cutting-edge FDB methods based on subsampling which can accurately capture uncertainty without necessitating additional stringent assumptions beyond those required for the existence of a target limit distribution, filling a gap in the theory by providing distributional approximations for spectral statistics.
Keywords
Frequency Domain Bootstrap
Periodogram
Subsampling
Spatial Process
Spectral Mean Statistic