Novel Methods for High-Dimensional Space-Time Data

Jonathan Hobbs Chair
Jet Propulsion Laboratory
 
Sunday, Aug 2: 2:00 PM - 3:50 PM
6409 
Contributed Papers 

Main Sponsor

Section on Statistics and the Environment

Presentations

A Bayesian hierarchical model for CO₂ surface-flux estimation from multivariate satellite data

Quantifying the natural components of CO₂ surface flux is key to understanding Earth's carbon dynamics. Existing inverse methods struggle to isolate the natural components, which cannot be individually constrained using atmospheric CO₂ concentrations alone. However, the advent of solar-induced fluorescence (SIF) satellite data provides an opportunity to improve identifiability by constraining the distribution of the gross primary production (GPP) component. Here, we develop a spatio-temporal hierarchical model linking GPP to SIF and embed it within the WOMBAT v2.0 (WOllongong Methodology for Bayesian Assimilation of Trace-gases, version 2.0) statistical flux-inversion framework. We call the new framework WOMBAT v2.S, and we apply it to multivariate data from NASA's OCO-2 satellite to estimate natural flux components over the globe during a six-year period. In a simulation experiment that mimics OCO-2's retrieval characteristics, the inclusion of SIF substantially improves posterior accuracy and uncertainty quantification. Comparing real-data estimates from WOMBAT v2.S, v2.0, and an alternative method, we observe a reversal in the inferred trends of global CO₂ absorption. 

Keywords

flux inversion

spatio-temporal modeling

remote sensing

carbon cycle

gross primary production (GPP)

solar-induced fluorescence (SIF) 

Speaker

Josh Jacobson, University of Colorado Boulder

Co-Author(s)

Michael Bertolacci, University of Western Australia
Andrew Zammit-Mangion, University of Wollongong
Andrew Schuh, Colorado State University (CIRA)
Noel Cressie, University of Wollongong

Bayesian inference for the automultinomial model

Multicategory lattice data arise in a wide variety of disciplines such as image analysis, biology, and forestry. We consider modeling such data with the automultinomial model, which can be viewed as a natural extension of the autologistic model to multicategory responses, or as an extension of the Potts model that incorporates covariate information into a pure-intercept model. The automultinomial model has the advantage of having a unique parameter that controls the spatial correlation. However, the model's likelihood involves an intractable normalizing function of the model parameters that pose serious computational problems for likelihood-based inference. We address this difficulty by performing Bayesian inference through the Double-Metropolis Hastings algorithm, and implement diagnostics to assess the convergence to the target posterior distribution. Through simulation studies and an application to land cover data, we found the automultinomial model to be highly flexible across a wide range of spatial correlation levels while maintaining a relatively simple specification. We also provide practical recommendations for model specification and computational implementation. 

Keywords

Spatial modeling

Multinomial spatial data

Automodels

Asymptotically inexact algorithms

Intractable normalizing functions 

Speaker

Maria Paula Duenas Herrera, The Pennsylvania State University

Co-Author(s)

Stephen Berg
Murali Haran, The Pennsylvania State University

Connecting reflective asymmetries in multivariate spatial and spatio-temporal covariances

In the analysis of multivariate spatial and univariate spatio-temporal data, it is commonly recognized that asymmetric dependence may exist, which can be addressed using an asymmetric (matrix or space-time, respectively) covariance function within a Gaussian process framework. This paper introduces a new paradigm for constructing asymmetric space-time covariances, which we refer to as "reflective asymmetric," by leveraging recently-introduced models for multivariate spatial data. We first provide new results for reflective asymmetric multivariate spatial models that extends their applicability. We then propose their asymmetric space-time extension, which come from a substantially different perspective than Lagrangian asymmetric space-time covariances. There are fewer parameters in the new models, one controls both the spatial and temporal marginal covariances, and the standard separable model is a special case. In simulation studies and analysis of the frequently-studied Irish wind data, these new models also improve model fit and prediction performance, and they can be easier to estimate. These features indicate broad applicability for improved analysis in environ 

Keywords

asymmetric dependence

Gaussian processes

multivariate covariances

space-time data

spatial statistics 

Speaker

Drew Yarger, Purdue University

Highly Multivariate Large-scale Spatial Stochastic Processes – A Cross-Markov Random Field Approach

Key challenges in the analysis of highly multivariate large-scale spatial stochastic processes, where both the number of components (p) and spatial locations (n) can be large, include achieving maximal sparsity in the joint precision matrix, ensuring efficient computational cost for its generation, accommodating asymmetric cross-covariance in the joint covariance matrix, and delivering scientific interpretability. We propose a cross-Markov Random Field model class, consisting of a mixed spatial graphical model framework and cross-Markov Random Field theory, to collectively address these challenges in one unified framework. We demonstrate with 1D simulated comparative studies and 2D real-world data. 

Keywords

auto-neighbourhood

cross-neighbourhood

cross-Markov Random Field

doubly conditional independence

mixed spatial graph

spatial stochastic processes 

Speaker

Xiaoqing Chen, The Alan Turing Institute; University of Exeter

Co-Author(s)

Peter Diggle, Lancaster University
James Zidek, University of British Columbia
Gavin Shaddick, University of Exeter

Introducing a Tensor Product Cubic B-Spline Basis Function to the Gaussian Process Model LatticeKrig

Remotely sensed observations of the atmosphere play an important role in climate research since they have more extensive spatial coverage than surface measurements. However, multiple challenges arise from the large quantities of data needed to provide the necessary spatial coverage. A useful framework for spatial models involves expanding the field using basis functions and making distributional assumptions about the basis coefficients. This approach forms the foundation of the successful fixed rank kriging methodology, which has been adopted and extended by models such as LatticeKrig. We introduce a tensor product cubic B-spline basis for representing a multi-resolution Gaussian process model. Surprisingly, the use of B-splines as spatial basis functions has not been extensively explored, despite their several advantages. The cubic B-spline basis function presented here is compactly supported, preserving the efficient sparse linear algebra used in LatticeKrig. In addition, we leverage the partition of unity property of B-splines to reduce basis function artifacts and develop more accurate numerical integration over irregular spatial regions for change-of-support methods. 

Keywords

Gaussian process model

Basis function

Multi-resolution

Cubic B-splines

Change-of-support 

Speaker

Ryan Peterson, Colorado School Of Mines

Co-Author(s)

Douglas Nychka, Colorado School of Mines
Dorit Hammerling, Colorado School of Mines

Scalable Uncertainty Quantification for Multisource Remote-Sensing Data Products

A wide array of data products from many Earth-observing satellite platforms are providing valuable insights on a range of geophysical processes at fine spatial and temporal resolution. Leveraging complementary information from multiple remote-sensing instruments, along with geophysical models, can provide substantial utility for science and applications. The added utility from these derived science data products often comes with added complexity and computational cost for uncertainty quantification (UQ) due to variable fidelity of input uncertainty and nonstationary spatio-temporal correlation. This work outlines a framework for UQ for these derived products that combines generative flexibility of transport maps (TMs) with scalable spatial statistical methods for dense geophysical fields. The presentation will illustrate the approach for estimates of atmospheric aerosols for NASA's upcoming Multi-Angle Imager for Aerosols (MAIA) mission. These aerosol estimates will be delivered for 1-km footprints for multiple mission target areas across the globe, providing information for air quality and health applications. 

Keywords

Uncertainty quantification

Remote sensing

Generative model

Transport map

Air quality 

Speaker

Jonathan Hobbs, Jet Propulsion Laboratory

Co-Author(s)

Otto Lamminpää
Margaret Johnson, Jet Propulsion Laboratory
Ricardo Baptista, California Institute of Technology
Meredith Franklin, University of Toronto
Gregory Halverson, Jet Propulsion Laboratory
Olga Kalashnikova, Jet Propulsion Laboratory
Kerry Cawse-Nicholson, Jet Propulsion Laboratory