Emily L. Kang

Fixed Rank Filtering for Spatio-Temporal Data

Datasets from remote-sensing platforms and sensor networks are often spatial, temporal, and very large. Processing massive amounts of data to provide current estimates of the (hidden) state from current and past data is challenging, even for the Kalman filter. A large number of spatial locations observed through time can quickly lead to an overwhelmingly high-dimensional statistical model. Dimension reduction without sacrificing complexity is our goal in this article. We demonstrate how a Spatio-Temporal Random Effects (STRE) component of a statistical model reduces the problem to one of fixed dimension with a very fast statistical solution, a methodology we call Fixed Rank Filtering (FRF). This is compared in a simulation experiment to successive, spatial-only predictions based on an analogous Spatial Random Effects (SRE) model, and the value of incorporating temporal dependence is quantified. A remote-sensing dataset of aerosol optical depth (AOD), from the Multi-angle Imaging SpectroRadiometer (MISR) instrument on the Terra satellite, is used to compare spatio-temporal FRF with spatial-only prediction. FRF achieves rapid production of optimally filtered AOD predictions, along with their prediction standard errors. In our case, over 100,000 spatio-temporal data were processed: Parameter estimation took 64.4 seconds and optimal predictions and their standard errors took 77.3 seconds to compute. Supplemental materials giving complete details on the design and analysis of a simulation experiment, the simulation code, and the MISR data used are available on-line.

Computational and statistical analysis of metabolomics data

Metabolomics is the comprehensive study of small molecule metabolites in biological systems. By assaying and analyzing thousands of metabolites in biological samples, it provides a whole picture of metabolic status and biochemical events happening within an organism and has become an increasingly powerful tool in the disease research. In metabolomics, it is common to deal with large amounts of data generated by nuclear magnetic resonance (NMR) and/or mass spectrometry (MS). Moreover, based on different goals and designs of studies, it may be necessary to use a variety of data analysis methods or a combination of them in order to obtain an accurate and comprehensive result. In this review, we intend to provide an overview of computational and statistical methods that are commonly applied to analyze metabolomics data. The review is divided into five sections. The first two sections will introduce the background and the databases and resources available for metabolomics research. The third section will briefly describe the principles of the two main experimental methods that produce metabolomics data: MS and NMR, followed by the fourth section that describes the preprocessing of the data from these two approaches. In the fifth and the most important section, we will review four main types of analysis that can be performed on metabolomics data with examples in metabolomics. These are unsupervised learning methods, supervised learning methods, pathway analysis methods and analysis of time course metabolomics data. We conclude by providing a table summarizing the principles and tools that we discussed in this review.

Bayesian Inference for the Spatial Random Effects Model

Spatial statistical analysis of massive amounts of spatial data can be challenging because computation of optimal procedures can break down. The Spatial Random Effects (SRE) model uses a fixed number of known but not necessarily orthogonal (multiresolutional) spatial basis functions, which gives a flexible family of nonstationary covariance functions, results in dimension reduction, and yields optimal spatial predictors whose computations are scalable. By modeling spatial data in a hierarchical manner with a process model that includes the SRE model, the choice is whether to estimate the SRE model’s parameters or to take a Bayesian approach and put a prior distribution on them. In this article, we develop Bayesian inference for the SRE model when the spatial basis functions are multiresolutional. Then the covariance matrix of the random effects decomposes naturally in terms of Givens angles and eigenvalues, for which a new class of prior distributions is developed. This approach to prior specification of a spatial covariance matrix offers remarkable improvement over other types of priors used in the random-effects literature (e.g., Wishart priors), as demonstrated in a simulation experiment. Further, a large remote-sensing dataset of aerosol optical depth (AOD), from the Multi-angle Imaging SpectroRadiometer (MISR) instrument on the Terra satellite, is analyzed in a fully Bayesian framework, using the new prior, and compared to an empirical-Bayesian analysis.

High-Resolution Digital Soil Mapping: Kriging for Very Large Datasets

The ability to take many observations at precisely known spatial locations has given birth to precision agriculture and transformed traditional agriculture into a spatial science. An important aspect of precision agriculture is its intersection with pedometrics. Maps of soil properties are in great demand, but there is a point at which datasets from proximal soil sensors can, when very large, overload and ‘break’ the algorithms designed for production of the statistically optimal (kriging) maps. In this research, we present a geostatistical method that relies on highly flexible, nonstationary spatial covariances, for which exact kriging can be carried out for very large datasets (on the order of tens of thousands to hundreds of thousands of elements). The methodology is applied to total counts obtained from gamma radiometer readings in several fields of Nowley Farm, New South Wales, Australia.

Bayesian hierarchical ANOVA of regional climate-change projections from NARCCAP Phase II

Abstract We consider current (1971–2000) and future (2041–2070) average seasonal surface temperature fields from two regional climate models (RCMs) driven by the same atmosphere–ocean general circulation model (GCM) in the North American Regional Climate Change Assessment Program (NARCCAP) Phase II experiment. We analyze the difference between future and current temperature fields for each RCM and include the factor of season, the factor of RCM, and their interaction in a two-way ANOVA model. Noticing that classical ANOVA approaches do not account for spatial dependence, we assume that the main effects and interactions are spatial processes that follow the Spatial Random Effects (SRE) model. This enables us to model the spatial variability through fixed spatial basis functions, and the computations associated with an ANOVA of high-resolution RCM outputs can be carried out without having to resort to approximations. We call the resulting model a spatial two-way ANOVA model. We implement it in a Bayesian framework, and we investigate the variability of climate-change projections over seasons, RCMs, and their interactions. We find that projected temperatures in North America are credibly higher, that the associated warming effects differ in spatial areas and in seasons, and that they are of much larger magnitude than the variability between RCMs.

Filtering Partially Observed Multiscale Systems with Heterogeneous Multiscale Methods-Based Reduced Climate Models

AbstractThis paper presents a fast reduced filtering strategy for assimilating multiscale systems in the presence of observations of only the macroscopic (or large scale) variables. This reduced filtering strategy introduces model errors in estimating the prior forecast statistics through the (heterogeneous multiscale methods) HMM-based reduced climate model as an alternative to the standard expensive (direct numerical simulation) DNS-based fully resolved model. More importantly, this approach is not restricted to any analysis (or Bayesian updating) step from various ensemble-based filters. In a regime where there is a distinctive separation of scales, high filtering skill is obtained through applying the HMM alone with any desirable analysis step from ensemble Kalman filters. When separation of scales is not apparent as typically observed in geophysical turbulent systems, an additional procedure is proposed to reinitialize the microscopic variables to statistically reflect pseudo-observations that are co...

Hot Enough for You? A Spatial Exploratory and Inferential Analysis of North American Climate-Change Projections

Climate models have become the primary tools for scientists to project climate-change into the future and to understand its potential impact. Continental-scale General Circulation Models (GCMs) oversimplify the regional climate processes and geophysical features such as topography and land cover. The consequences of local/regional climate change are particularly relevant to natural resource management and environmental-policy decisions, for which Regional Climate Models (RCMs) have been developed. RCMs simulate, for example, three-hourly “weather” over long time periods, from which long-run averages (e.g., over 30 years) are commonly computed to estimate a region’s future climate. With anthropogenic forcings incorporated, RCMs provide a means to assess a combination of natural and anthropogenic influences on climate variability. The North American Regional Climate Change Assessment Program ran RCMs into the future, until 2070, for 11,760 contiguous regions, each of which is approximately

Cokriging method for spatio-temporal assimilation of multi-scale satellite data

50~\mathrm {km}\times 50~\mathrm {km}