Related papers: A Flexible Class of Non-separable Cross-Covariance…
The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivotal role. While models such as Whittle-Mat\'ern fields have…
We develop two new classes of space-time Gaussian process models by specifying covariance functions using what we call a half-spectral representation. The half-spectral representation of a covariance function, $K$, is a special case of…
Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…
We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…
In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…
Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of p-splines, we propose a Bayesian framework for choosing the smoothing parameter which…
Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and…
Accurately specifying covariance structures is critical for valid inference in longitudinal and functional data analysis, particularly when data are sparsely observed. In this study, we develop a global goodness-of-fit test to assess…
We study covariance functions in the Gauss hypergeometric ($\mathcal{GH}$) class, a flexible family that encompasses the Generalized Wendland ($\mathcal{GW}$) and Mat\'ern ($\mathcal{MT}$) models. We derive sharp validity conditions,…
Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the…
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…
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
Fine particulate matter (PM$_{2.5}$) has become a great concern worldwide due to its adverse health effects. PM$_{2.5}$ concentrations typically exhibit complex spatio-temporal variations. Both the mean and the spatio-temporal dependence…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
We propose a Bayesian modeling framework for jointly analyzing multiple functional responses of different types (e.g. binary and continuous data). Our approach is based on a multivariate latent Gaussian process and models the dependence…
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the…
The random matrix theory method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, firstly in the form of master…
The Mat\'ern covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Mat\'ern class is that it is possible to get precise control over the degree of…
This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate…
In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global…