spam: A Sparse Matrix R Package with Emphasis on MCMC Methods for Gaussian Markov Random Fields

spam is an R package for sparse matrix algebra with emphasis on a Cholesky factorization of sparse positive definite matrices. The implemantation of spam is based on the competing philosophical maxims to be competitively fast compared to existing tools and to be easy to use, modify and extend. The first is addressed by using fast Fortran routines and the second by assuring S3 and S4 compatibility. One of the features of spam is to exploit the algorithmic steps of the Cholesky factorization and hence to perform only a fraction of the workload when factorizing matrices with the same sparsity structure. Simulations show that exploiting this break-down of the factorization results in a speed-up of about a factor 5 and memory savings of about a factor 10 for large matrices and slightly smaller factors for huge matrices. The article is motivated with Markov chain Monte Carlo methods for Gaussian Markov random fields, but many other statistical applications are mentioned that profit from an efficient Cholesky factorization as well.

A spatial analysis of multivariate output from regional climate models

Climate models have become an important tool in the study of climate and climate change, and ensemble experiments consisting of multiple climate-model runs are used in studying and quantifying the uncertainty in climate-model output. However, there are often only a limited number of model runs available for a particular experiment, and one of the statistical challenges is to characterize the distribution of the model output. To that end, we have developed a multivariate hierarchical approach, at the heart of which is a new representation of a multivariate Markov random field. This approach allows for flexible modeling of the multivariate spatial dependencies, including the cross-dependencies between variables. We demonstrate this statistical model on an ensemble arising from a regional-climate-model experiment over the western United States, and we focus on the projected change in seasonal temperature and precipitation over the next 50 years.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS369 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

spam: A Sparse Matrix R Package with Emphasis on MCMC Methods for Gaussian Markov Random Fields

spam is an R package for sparse matrix algebra with emphasis on a Cholesky factorization of sparse positive definite matrices. The implemantation of spam is based on the competing philosophical maxims to be competitively fast compared to existing tools and to be easy to use, modify and extend. The first is addressed by using fast Fortran routines and the second by assuring S3 and S4 compatibility. One of the features of spam is to exploit the algorithmic steps of the Cholesky factorization and hence to perform only a fraction of the workload when factorizing matrices with the same sparsity structure. Simulations show that exploiting this break-down of the factorization results in a speed-up of about a factor 5 and memory savings of about a factor 10 for large matrices and slightly smaller factors for huge matrices. The article is motivated with Markov chain Monte Carlo methods for Gaussian Markov random fields, but many other statistical applications are mentioned that profit from an efficient Cholesky factorization as well

Regional climate model assessment using statistical upscaling and downscaling techniques

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/92355/1/env_2145_sm.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/92355/2/env2145.pd

Downscaling extremes: A comparison of extreme value distributions in point-source and gridded precipitation data

There is substantial empirical and climatological evidence that precipitation extremes have become more extreme during the twentieth century, and that this trend is likely to continue as global warming becomes more intense. However, understanding these issues is limited by a fundamental issue of spatial scaling: most evidence of past trends comes from rain gauge data, whereas trends into the future are produced by climate models, which rely on gridded aggregates. To study this further, we fit the Generalized Extreme Value (GEV) distribution to the right tail of the distribution of both rain gauge and gridded events. The results of this modeling exercise confirm that return values computed from rain gauge data are typically higher than those computed from gridded data; however, the size of the difference is somewhat surprising, with the rain gauge data exhibiting return values sometimes two or three times that of the gridded data. The main contribution of this paper is the development of a family of regression relationships between the two sets of return values that also take spatial variations into account. Based on these results, we now believe it is possible to project future changes in precipitation extremes at the point-location level based on results from climate models.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS287 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

On locally adaptive density estimation.

Abstract Multivariate versions of variable bandwidth kernel density estimators can lead to improvement over kernel density estimators using global bandwidth choices. These estimators are more exible and better able to model complex (multimodal) densities. In this work, two variable bandwidth estimators are discussed: the balloon estimator which varies the smoothing matrix with each estimation point and the sample point estimator which uses a di erent smoothing matrix for each data point. A binned version of the sample point estimator is developed that, for various situations in low to moderate dimensions, exhibits less error (MISE) than the ÿxed bandwidth estimator and the balloon estimator. A practical implementation of the sample point estimator is shown through simulation and example to do a better job at reconstructing features of the underlying density than ÿxed bandwidth estimators. Computational details, including parameterization of the smoothing matrix, are discussed throughout