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Gaussian processes are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Scientific data are often heterogeneous in their inputs and contain multiple known discrete groups of samples; thus, it is desirable to leverage the similarity among groups while accounting for heterogeneity across groups. We propose multi-group Gaussian processes (MGGPs) defined over Rp×C , where C is a finite set representing the group label, by developing general classes of valid (positive definite) covariance functions on such domains. MGGPs are able to accurately recover relationships between the groups and efficiently share strength across samples from all groups during inference, while capturing distinct group-specific behaviors in the conditional posterior distributions. We demonstrate inference in MGGPs through simulation experiments, and we apply our proposed MGGP regression framework to gene expression data to illustrate the behavior and enhanced inferential capabilities of multi-group Gaussian processes by jointly modeling continuous and categorical variables. 

Abstract Cities are concentrators of complex, multi‐sectoral interactions. As keystones in the interconnected human‐Earth system, cities have an outsized impact on the Earth system. We describe a multi‐lens framework for organizing our understanding of the complexity of urban systems and scientific research on urban systems, which may be useful for natural system scientists exploring the ways their work can be made more actionable. We then describe four critical dimensions along which improvements are needed to advance the urban research that addresses urgent climate challenges: (a) solutions‐oriented research, (b) equity‐centered assessments which rely on fine‐scale human and ecological data, (c) co‐production of knowledge, and (d) better integration of human and natural systems occurring through theory, observation, and modeling. 

Tropical glaciers have retreated over recent decades, but whether the magnitude of this retreat exceeds the bounds of Holocene fluctuations is unclear. We measured cosmogenic beryllium-10 and carbon-14 concentrations in recently exposed bedrock at the margin of four glaciers spanning the tropical Andes to reconstruct their past extents relative to today. Nuclide concentrations are near zero in almost all samples, suggesting that these locations were never exposed during the Holocene. Our data imply that many glaciers in the tropics are probably now smaller than they have been in at least 11,700 years, making the tropics the first large region where this milestone has been documented. 

Abstract BackgroundSingle-cell RNA-sequencing (scRNA-seq) technologies allow for the study of gene expression in individual cells. Often, it is of interest to understand how transcriptional activity is associated with cell-specific covariates, such as cell type, genotype, or measures of cell health. Traditional approaches for this type of association mapping assume independence between the outcome variables (or genes), and perform a separate regression for each. However, these methods are computationally costly and ignore the substantial correlation structure of gene expression. Furthermore, count-based scRNA-seq data pose challenges for traditional models based on Gaussian assumptions. ResultsWe aim to resolve these issues by developing a reduced-rank regression model that identifies low-dimensional linear associations between a large number of cell-specific covariates and high-dimensional gene expression readouts. Our probabilistic model uses a Poisson likelihood in order to account for the unique structure of scRNA-seq counts. We demonstrate the performance of our model using simulations, and we apply our model to a scRNA-seq dataset, a spatial gene expression dataset, and a bulk RNA-seq dataset to show its behavior in three distinct analyses. ConclusionWe show that our statistical modeling approach, which is based on reduced-rank regression, captures associations between gene expression and cell- and sample-specific covariates by leveraging low-dimensional representations of transcriptional states.