Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors

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 models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS478 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hierarchical spatial models for predicting tree species assemblages across large domains

Spatially explicit data layers of tree species assemblages, referred to as forest types or forest type groups, are a key component in large-scale assessments of forest sustainability, biodiversity, timber biomass, carbon sinks and forest health monitoring. This paper explores the utility of coupling georeferenced national forest inventory (NFI) data with readily available and spatially complete environmental predictor variables through spatially-varying multinomial logistic regression models to predict forest type groups across large forested landscapes. These models exploit underlying spatial associations within the NFI plot array and the spatially-varying impact of predictor variables to improve the accuracy of forest type group predictions. The richness of these models incurs onerous computational burdens and we discuss dimension reducing spatial processes that retain the richness in modeling. We illustrate using NFI data from Michigan, USA, where we provide a comprehensive analysis of this large study area and demonstrate improved prediction with associated measures of uncertainty.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS250 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

Daily minimum and maximum temperature simulation over complex terrain

Spatiotemporal simulation of minimum and maximum temperature is a fundamental requirement for climate impact studies and hydrological or agricultural models. Particularly over regions with variable orography, these simulations are difficult to produce due to terrain driven nonstationarity. We develop a bivariate stochastic model for the spatiotemporal field of minimum and maximum temperature. The proposed framework splits the bivariate field into two components of "local climate" and "weather." The local climate component is a linear model with spatially varying process coefficients capturing the annual cycle and yielding local climate estimates at all locations, not only those within the observation network. The weather component spatially correlates the bivariate simulations, whose matrix-valued covariance function we estimate using a nonparametric kernel smoother that retains nonnegative definiteness and allows for substantial nonstationarity across the simulation domain. The statistical model is augmented with a spatially varying nugget effect to allow for locally varying small scale variability. Our model is applied to a daily temperature data set covering the complex terrain of Colorado, USA, and successfully accommodates substantial temporally varying nonstationarity in both the direct-covariance and cross-covariance functions.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS602 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org