We propose a new modeling framework for highly multivariate spatial processes that synthesizes ideas from recent multiscale and spectral approaches with graphical models. The basis graphical lasso writes a univariate ...
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We propose a new modeling framework for highly multivariate spatial processes that synthesizes ideas from recent multiscale and spectral approaches with graphical models. The basis graphical lasso writes a univariate Gaussian process as a linear combination of basisfunctions weighted with entries of a Gaussian graphical vector whose graph is estimated from optimizing an l1 penalized likelihood. This article extends the setting to a multivariate Gaussian process where the basisfunctions are weighted with Gaussian graphical vectors. We motivate a model where the basisfunctions represent different levels of resolution and the graphical vectors for each level are assumed to be independent. Using an orthogonal basis grants linear complexity and memory usage in the number of spatial locations, the number of basisfunctions, and the number of realizations. An additional fusion penalty encourages a parsimonious conditional independence structure in the multilevel graphical model. We illustrate our method on a large climate ensemble from the National Center for Atmospheric Research's Community Atmosphere Model that involves 40 spatial processes. for this article are available online.
The presence and establishment of a tree species at a particular spatial location is influenced by multiple physiological and environmental filters such as propagule pressure (seed availability), light and moisture av...
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The presence and establishment of a tree species at a particular spatial location is influenced by multiple physiological and environmental filters such as propagule pressure (seed availability), light and moisture availability, and slope and elevation. However, a less understood environmental filter to species-specific establishment is competition or facilitation between dominant tree species. For example, certain tree species may compete for resources at spatial locations where such resources are scarce while less competition may occur at resource-rich areas. Using data from the Forest Inventory and Analysis (FIA) program of the United States Department of Agriculture (USDA) Forest Service, we develop a multivariate spatial Bernoulli model to investigate the space-varying relationship between extant tree species in Utah. Additionally, we propose a novel modeling strategy that explains the spatially varying relationships by regressing the associated between-species correlation matrix on available covariate data. Positive definite conditions of the covariate-varying correlation matrix are ensured by defining the regression in terms of the unique partial correlation matrix. Results indicate that correlations between species are dependent upon elevation.
Spectral methods are among the most extensively used techniques for model reduction of distributed parameter systems in various fields, including fluid dynamics, quantum mechanics, heat conduction, and weather predict...
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Spectral methods are among the most extensively used techniques for model reduction of distributed parameter systems in various fields, including fluid dynamics, quantum mechanics, heat conduction, and weather prediction. However, the model dimension is not minimized for a given desired accuracy because of general spatial basis functions. New spatial basis functions are obtained by linear combination of general spatial basis functions in spectral method, whereas the basisfunction transformation matrix is derived from straightforward optimization techniques. After the expansion and truncation of spatial basis functions, the present spatial basis functions can provide a lower dimensional and more precise ordinary differential equation system to approximate the dynamics of the systems. The numerical example shows the feasibility and effectiveness of the optimal combination of spectral basisfunctions for model reduction of nonlinear distributed parameter systems. (C) 2012 Elsevier B.V. All rights reserved.
The aggregative basisfunctions (ABFs) are introduced to construct a size-reduced system for the marching-on-in-order (MOO) time-domain integral equation (TDIE) method to analyse transient electromagnetic scattering f...
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The aggregative basisfunctions (ABFs) are introduced to construct a size-reduced system for the marching-on-in-order (MOO) time-domain integral equation (TDIE) method to analyse transient electromagnetic scattering from conducting objects. Based on the previously developed characteristic basisfunction method (CBFM), a set of orthogonal vectors that expand the original unknown current coefficients are obtained via the singular value decomposition (SVD). The ABF method can be considered as an application and counterpart of CBFM in TDIE with some differences. The ABFs are aggregations of the weighted Laguerre polynomials and RWG basisfunctions, which are the elemental temporal and spatial basis functions, respectively. The ABFs are defined over the entire geometry and effective in each order of the MOO scheme. The proposed method gives significant reduction to matrix size and also the storage by several orders of magnitude. This is achieved because of the much less number of ABFs or the orthogonal vectors than the inner edges of the geometry. Several numerical results are presented to illustrate the validity of the proposed method.
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