R package for Nearest Neighbor Gaussian Process models

This paper describes and illustrates functionality of the spNNGP R package. The package provides a suite of spatial regression models for Gaussian and non-Gaussian point-referenced outcomes that are spatially indexed. The package implements several Markov chain Monte Carlo (MCMC) and MCMC-free Nearest Neighbor Gaussian Process (NNGP) models for inference about large spatial data. Non-Gaussian outcomes are modeled using a NNGP Polya-Gamma latent variable. OpenMP parallelization options are provided to take advantage of multiprocessor systems. Package features are illustrated using simulated and real data sets

Wildlife infectious disease dynamics in the context of seasonality and bird migration

The thesis contains chapters that elucidate questions with regards to wildlife infectious disease dynamics - avian influenza in particular - and how those dynamics are affected by seasonality and avian migration

Statistical Methods for Large Complex Datasets

University of Minnesota Ph.D. dissertation. 2016. Major: Biostatistics. Advisors: Sudipto Banerjee, Hui Zou. 1 computer file (PDF); 175 pages.Modern technological advancements have enabled massive-scale collection, processing and storage of information triggering the onset of the `big data' era where in every two days now we create as much data as we did in the entire twentieth century. This thesis aims at developing novel statistical methods that can efficiently analyze a variety of large complex datasets. Underlying the umbrella theme of big data modeling, we present statistical methods for two different classes of large complex datasets. The first half of the thesis focuses on the 'large n' problem for large spatial or spatio-temporal datasets where observations exhibit strong dependencies across space and time. In the second half of this thesis we present methods for high-dimensional regression in the `large p small n' setting for datasets that contain measurement errors or change points

Theory and Application of Dynamic Spatial Time Series Models

Stochastic economic processes are often characterized by dynamic interactions between variables that are dependent in both space and time. Analyzing these processes raises a number of questions about the econometric methods used that are both practically and theoretically interesting. This work studies econometric approaches to analyze spatial data that evolves dynamically over time. The book provides a background on least squares and maximum likelihood estimators, and discusses some of the limits of basic econometric theory. It then discusses the importance of addressing spatial heterogeneity in policies. The next chapters cover parametric modeling of linear and nonlinear spatial time series, non-parametric modeling of nonlinearities in panel data, modeling of multiple spatial time series variables that exhibit long and short memory, and probabilistic causality in spatial time series settings

Handbook of Mathematical Geosciences

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences

The Role of Climate Variability in Duck Population Ecology

Climate change is having profound impacts on animal populations globally, and is expected to become a stronger stressor in future, influencing abundance and persistence of many species. In northern hemisphere bird populations, local weather and climate cycles play important roles via effects on components of individual fitness (i.e., survival and reproductive success), and thus annual fluctuations in population sizes. I used congruent long-term data for duck populations, individuals, and climatic variables to test hypotheses about the relative roles of climate and other factors in population dynamics, variation in vital rates, and timing of breeding. Where possible I used interspecific comparisons to evaluate whether responses were mediated by life-history traits. First, I examined annual variation in the timing, length, and productivity of growing seasons on duck population growth rates in North American boreal forest, 1982-2013. I found limited evidence that spring phenology, growing season length or productivity influenced annual population growth rates, and effects were not always in the direction predicted based on species-specific timing of breeding. Second, I evaluated impacts and potential synchronizing forces of shared trends in temperature and precipitation on widely separated populations of ecologically equivalent duck species in North America and western Europe, 1976-2011. Several duck species-pairs shared increasing time trends but growth rates were not synchronized among years. This pattern of shared trends but no annual synchrony was mirrored in climate variables recorded over the major breeding areas on each continent. Third, at the individual-level, I found that ducklings of a late-breeding species, lesser scaup (Aythya affinis), had slower growth rates when hatched late relative to their cohort but I detected no effect of spring phenology. Hatch date effects did not carryover to influence postfledging survival. In contrast, a negative effect of conspecific density on prefledging growth seemed to carryover to influence postfledging survival, and possibly first-year breeding probability. Fourth, examining breeding dates of individually marked females, I found that early-nesting species tracked spring phenology, while late-nesting species did not. Yet, annual variation in the timing of breeding in late-nesting species suggests that females respond to other unmeasured cues not related to spring phenology. Collectively, results indicate that individual ducks are resilient to annual fluctuations in climatic drivers, so populations respond more strongly to sustained long-term trends in climate cycles. Species I studied have varying capacity to respond to annual phenological cues, but it may be that density dependence in vital rates mediates adverse environmental effects that occur in only one season. Therefore, climate trends that impact per capita resource availability (e.g., wetland area, food quality and quantity) may be the primary concern for conservationists assuming that annual climatic fluctuations remain within the range observed during my study periods. Experimental studies that manipulate environmental variables may be necessary to gain further insights into how ducks will respond to climate change predicted in this century

Applications of Bayesian computational statistics and modeling to large-scale geoscientific problems

Climate change is one of the most important, pressing, and furthest reaching global challenges that humanity faces in the 21st century. Already affecting daily lives of many directly and everyone indirectly, changes in climate are projected to have many catastrophic consequences. For this reason, researching climate and climate change is needed. Studying complex geoscientific phenomena such as climate change consists of a patchwork of challenging mathematical, statistical, and computational problems. To solve these problems, local and global process models and statistical models are combined with both small in situ observation data sets with only few observations, and equally well with enormous global remote sensing data products containing hundreds of millions of data points. This integration of models and data can be done in a Bayesian inverse modeling setting if the algorithms and computational methods used are chosen and implemented carefully. The methods used in the four publications on which this thesis is based range from high-dimensional Bayesian spatial statistical models and Markov chain Monte Carlo methods to time series modeling and point estimation via optimization. The particular geoscientific problems considered are: finding the spatio-temporal distribution of atmospheric carbon dioxide based on sparse remote sensing data, quantifying uncertainties in modeling methane emissions from boreal wetlands, analyzing and quantifying the effect of climate change on growing season in the boreal region, and using statistical methods to calibrate a terrestrial ecosystem model. In addition to analyzing these problems, the research and the results help to understand model performance and how modeling uncertainties in very large computational problems can be approached, also providing algorithm implementations on top of which future efforts may be built

Quantitative Techniques in Participatory Forest Management

Forest management has evolved from a mercantilist view to a multi-functional one that integrates economic, social, and ecological aspects. However, the issue of sustainability is not yet resolved. Quantitative Techniques in Participatory Forest Management brings together global research in three areas of application: inventory of the forest variables that determine the main environmental indices, description and design of new environmental indices, and the application of sustainability indices for regional implementations. All these quantitative techniques create the basis for the development of scientific methodologies of participatory sustainable forest management