arXiv subjects

Pulong Ma

Publications and source records attributed to Pulong Ma.

12 recordsLinked to original sources

arXiv2026

Locally stationary Argo ocean heat content estimates: Modeling, validation and uncertainty quantification

Argo profiling floats measure seawater temperature and salinity in the upper 2000 meters of the ocean. These floats are uniquely capable of measuring the global Ocean Heat Content (OHC), a quantity that is of central importance for understanding Earth Energy Imbalance. Yet, producing Argo-based OHC estimates with reliable uncertainties is statistically challenging due to the complex structure and large size of the Argo dataset. Here we present an end-to-end mapping and uncertainty quantification framework for Argo-based OHC estimation using state-of-the-art methods from spatio-temporal statistics. The framework is based on modeling vertically integrated Argo temperature profiles as a locally stationary Gaussian process defined over space and time. This enables us to produce computationally tractable OHC anomaly maps based on data-driven decorrelation scales estimated from the Argo observations. Our modeling choices are validated using statistical cross-validation, which demonstrates the importance of including a climatological time trend in the mean field and accounting for time in the covariance function. We quantify the uncertainty of these maps using local conditional simulation ensembles, a novel approach that leads to principled spatially and temporally correlated uncertainty quantification. A new paired cross-validation technique is presented to validate these uncertainties. The mapping framework is implemented in an open-source codebase that is designed to be modular, reproducible and extensible. To demonstrate the mapping and uncertainty quantification capabilities of this approach, we present new Argo OHC maps with uncertainties for 2004-2022 and report on various downstream climatological estimates and their uncertainties.

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arXiv2026

Multivariate Gaussian process emulation for multifidelity computer models with high-dimensional spatial outputs

Risk assessment of hurricane-driven storm surge relies on deterministic computer models that produce outputs over a large spatial domain. The surge models can often be run at a range of fidelity levels, with greater precision yielding more accurate simulations. Improved accuracy comes with a significant increase in computational expense, necessitating the development of an emulator which leverages information from the more plentiful low-fidelity outputs to provide fast and accurate predictions of high-fidelity simulations. To properly assess the risk of storm surge over a geographic region at aggregated spatial resolution, an emulator must account for spatial dependence between outputs yet remain computationally feasible for high-dimensional simulations. To address this challenge, we exploit the autoregressive cokriging framework to develop two cross-covariance structures to account for spatial dependence. One approach uses a separable covariance structure with a sparse Cholesky prior for the inverse of the cross-covariance matrix; the other involves a low-rank approximation via basis representations. We demonstrate their predictive performance in the storm surge application and a testbed example.

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arXiv2025

Asymmetric Space-Time Covariance Functions via Hierarchical Mixtures

This work is focused on constructing space-time covariance functions through a hierarchical mixture approach that can serve as building blocks for capturing complex dependency structures. This hierarchical mixture approach provides a unified modeling framework that not only constructs a new class of asymmetric space-time covariance functions with closed-form expressions, but also provides corresponding space-time process representations, which further unify constructions for many existing space-time covariance models. This hierarchical mixture framework decomposes the complexity of model specification at different levels of hierarchy, for which parsimonious covariance models can be specified with simple mixing measures to yield flexible properties and closed-form derivation. A characterization theorem is provided for the hierarchical mixture approach on how the mixing measures determine the statistical properties of covariance functions. Several new covariance models resulting from this hierarchical mixture approach are discussed in terms of their practical usefulness. A theorem is also provided to construct a general class of valid asymmetric space-time covariance functions with arbitrary and possibly different degrees of smoothness in space and in time and flexible long-range dependence. The proposed covariance class also bridges a theoretical gap in using the Lagrangian reference framework. The superior performance of several new parsimonious covariance models over existing models is verified with the well-known Irish wind data and the U.S. air temperature data.

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arXiv2022

Multifidelity Computer Model Emulation with High-Dimensional Output: An Application to Storm Surge

Hurricane-driven storm surge is one of the most deadly and costly natural disasters, making precise quantification of the surge hazard of great importance. Surge hazard quantification is often performed through physics-based computer models of storm surges. Such computer models can be implemented with a wide range of fidelity levels, with computational burdens varying by several orders of magnitude due to the nature of the system. The threat posed by surge makes greater fidelity highly desirable, however such models and their high-volume output tend to come at great computational cost, which can make detailed study of coastal flood hazards prohibitive. These needs make the development of an emulator combining high-dimensional output from multiple complex computer models with different fidelity levels important. We propose a parallel partial autoregressive cokriging model to predict highly-accurate storm surges in a computationally efficient way over a large spatial domain. This emulator has the capability of predicting storm surges as accurately as a high-fidelity computer model given any storm characteristics over a large spatial domain.

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arXiv2021

Beyond Matérn: On A Class of Interpretable Confluent Hypergeometric Covariance Functions

The Matérn covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matérn class is that it is possible to get precise control over the degree of mean-square differentiability of the random process. However, the Matérn class possesses exponentially decaying tails, and thus may not be suitable for modeling polynomially decaying dependence. This problem can be remedied using polynomial covariances; however one loses control over the degree of mean-square differentiability of corresponding processes, in that random processes with existing polynomial covariances are either infinitely mean-square differentiable or nowhere mean-square differentiable at all. We construct a new family of covariance functions called the \emph{Confluent Hypergeometric} (CH) class using a scale mixture representation of the Matérn class where one obtains the benefits of both Matérn and polynomial covariances. The resultant covariance contains two parameters: one controls the degree of mean-square differentiability near the origin and the other controls the tail heaviness, independently of each other. Using a spectral representation, we derive theoretical properties of this new covariance including equivalent measures and asymptotic behavior of the maximum likelihood estimators under infill asymptotics. The improved theoretical properties of the CH class are verified via extensive simulations. Application using NASA's Orbiting Carbon Observatory-2 satellite data confirms the advantage of the CH class over the Matérn class, especially in extrapolative settings.

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arXiv2020

Computer Model Emulation with High-Dimensional Functional Output in Large-Scale Observing System Uncertainty Experiments

Observing system uncertainty experiments (OSUEs) have been recently proposed as a cost-effective way to perform probabilistic assessment of retrievals for NASA's Orbiting Carbon Observatory-2 (OCO-2) mission. One important component in the OCO-2 retrieval algorithm is a full-physics forward model that describes the mathematical relationship between atmospheric variables such as carbon dioxide and radiances measured by the remote sensing instrument. This forward model is complicated and computationally expensive but large-scale OSUEs require evaluation of this model numerous times, which makes it infeasible for comprehensive experiments. To tackle this issue, we develop a statistical emulator to facilitate large-scale OSUEs in the OCO-2 mission with independent emulation. Within each distinct spectral band, the emulator represents radiances output at irregular wavelengths via a linear combination of basis functions and random coefficients. These random coefficients are then modeled with nearest-neighbor Gaussian processes with built-in input dimension reduction via active subspace. The proposed emulator reduces dimensionality in both input space and output space, so that fast computation is achieved within a fully Bayesian inference framework. Validation experiments demonstrate that this emulator outperforms other competing statistical methods and a reduced order model that approximates the full-physics forward model.

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arXiv2020

Objective Bayesian Analysis of a Cokriging Model for Hierarchical Multifidelity Codes

Autoregressive cokriging models have been widely used to emulate multiple computer models with different levels of fidelity. The dependence structures are modeled via Gaussian processes at each level of fidelity, where covariance structures are often parameterized up to a few parameters. The predictive distributions typically require intensive Monte Carlo approximations in previous works. This article derives new closed-form formulas to compute the means and variances of predictive distributions in autoregressive cokriging models that only depend on correlation parameters. For parameter estimation, we consider objective Bayesian analysis of such autoregressive cokriging models. We show that common choices of prior distributions, such as the constant prior and inverse correlation prior, typically lead to improper posteriors. We also develop several objective priors such as the independent reference prior and the independent Jeffreys prior that are shown to yield proper posterior distributions. This development is illustrated with a borehole function in an eight-dimensional input space and applied to an engineering application in a six-dimensional input space.

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arXiv2020

Analyzing Stochastic Computer Models: A Review with Opportunities

In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer models -- providing a catalogue of statistical methods for practitioners, an introductory view for statisticians (whether familiar with deterministic computer models or not), and an emphasis on open questions of relevance to practitioners and statisticians. Gaussian process surrogate models take center stage in this review, and these, along with several extensions needed for stochastic settings, are explained. The basic issues of designing a stochastic computer experiment and calibrating a stochastic computer model are prominent in the discussion. Instructive examples, with data and code, are used to describe the implementation of, and results from, various methods.

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arXiv2019

A Fused Gaussian Process Model for Very Large Spatial Data

With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model large or massive spatial datasets. In particular, a Gaussian process with additive components is proposed, with its covariance structure consisting of two components: one component is flexible without assuming a specific parametric covariance function but is able to achieve dimension reduction; the other is parametric and simultaneously induces sparsity. The inference algorithm for parameter estimation and spatial prediction is devised. The resulting spatial prediction methodology that we call fused Gaussian process (FGP), is applied to simulated data and a massive satellite dataset. The results demonstrate the computational and inferential benefits of FGP over competing methods and show that FGP is robust against model misspecification and captures spatial nonstationarity. The supplemental materials are available online.

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arXiv2019

An Additive Approximate Gaussian Process Model for Large Spatio-Temporal Data

Motivated by a large ground-level ozone dataset, we propose a new computationally efficient additive approximate Gaussian process. The proposed method incorporates a computational-complexity-reduction method and a separable covariance function, which can flexibly capture various spatio-temporal dependence structure. The first component is able to capture nonseparable spatio-temporal variability while the second component captures the separable variation. Based on a hierarchical formulation of the model, we are able to utilize the computational advantages of both components and perform efficient Bayesian inference. To demonstrate the inferential and computational benefits of the proposed method, we carry out extensive simulation studies assuming various scenarios of underlying spatio-temporal covariance structure. The proposed method is also applied to analyze large spatio-temporal measurements of ground-level ozone in the Eastern United States.

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arXiv2019

Spatio-Temporal Data Fusion for Massive Sea Surface Temperature Data from MODIS and AMSR-E Instruments

Remote sensing data have been widely used to study various geophysical processes. With the advances in remote-sensing technology, massive amount of remote sensing data are collected in space over time. Different satellite instruments typically have different footprints, measurement-error characteristics, and data coverages. To combine datasets from different satellite instruments, we propose a dynamic fused Gaussian process (DFGP) model that enables fast statistical inference such as filtering and smoothing for massive spatio-temporal datasets in a data-fusion context. Based upon a spatio-temporal-random-effects model, the DFGP methodology represents the underlying true process with two components: a linear combination of a small number of basis functions and random coefficients with a general covariance matrix, together with a linear combination of a large number of basis functions and Markov random coefficients. To model the underlying geophysical process at different spatial resolutions, we rely on the change-of-support property, which also allows efficient computations in the DFGP model. To estimate model parameters, we devise a computationally efficient stochastic expectation-maximization (SEM) algorithm to ensure its scalability for massive datasets. The DFGP model is applied to a total of 3.7 million sea surface temperature datasets in the tropical Pacific Ocean for a one-week time period in 2010 from MODIS and AMSR-E instruments.

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arXiv2018

Spatial Statistical Downscaling for Constructing High-Resolution Nature Runs in Global Observing System Simulation Experiments

Observing system simulation experiments (OSSEs) have been widely used as a rigorous and cost-effective way to guide development of new observing systems, and to evaluate the performance of new data assimilation algorithms. Nature runs (NRs), which are outputs from deterministic models, play an essential role in building OSSE systems for global atmospheric processes because they are used both to create synthetic observations at high spatial resolution, and to represent the "true" atmosphere against which the forecasts are verified. However, most NRs are generated at resolutions coarser than actual observations. Here, we propose a principled statistical downscaling framework to construct high-resolution NRs via conditional simulation from coarse-resolution numerical model output. We use nonstationary spatial covariance function models that have basis function representations. This approach not only explicitly addresses the change-of-support problem, but also allows fast computation with large volumes of numerical model output. We also propose a data-driven algorithm to select the required basis functions adaptively, in order to increase the flexibility of our nonstationary covariance function models. In this article we demonstrate these techniques by downscaling a coarse-resolution physical NR at a native resolution of $1^{\circ} \text{ latitude} \times 1.25^{\circ} \text{ longitude}$ of global surface $\text{CO}_2$ concentrations to 655,362 equal-area hexagons.

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