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Institute of Mathematics, UZH

Reinhard Furrer's Publications and Proceedings

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Selected publications on ZORA,   arXiv ,   Google Scolar  or ResearcherID or   Scopus .

2014

Gerber, F. and Furrer, R. (2014). Pitfalls in the implementation of Bayesian hierarchical modeling of areal count data. An illustration using BYM and Leroux models. Journal of Statistical Software, accepted.    
Abstract:
BibTeX:
@ARTICLE{Gerb:Furr:14,
  AUTHOR = 	 {Gerber, F. and Furrer,  R.},
  TITLE = 	 {Pitfalls in the implementation of {Bayesian} hierarchical modeling of areal count data. 
         An illustration using {BYM} and {Leroux} models},
  JOURNAL = 	 {J. Stat. Softw.},
  FJOURNAL = 	 {Journal of Statistical Software},
  YEAR = 	 {},
  DOI =          {},
  PMID =         {}, 
  VOLUME = 	 {},
  NUMBER = 	 {},
  PAGES = 	 {},
}
Geinitz, S., Furrer, R. and Sain, S. R. (2014). Bayesian multilevel analysis of variance for relative comparison across sources of global climate model variability. International Journal of Climatology, in press.     [Abstract] [BibTeX]
Abstract:
BibTeX:
@ARTICLE{Gein:Furr:Sain:14,
  AUTHOR = 	 {Geinitz, S. and Furrer,  R. and Sain, S. R.},
  TITLE = 	 {Bayesian multilevel analysis of variance for relative comparison across sources of global climate model variability},
  JOURNAL = 	 {Int. J. Climatol.},
  FJOURNAL = 	 {International Journal of Climatology},
  YEAR = 	 {2014},
  DOI =          {},
  PMID =         {}, 
  VOLUME = 	 {},
  NUMBER = 	 {},
  PAGES = 	 {},
}
Torgerson, P. R., Paul, M. and Furrer, R. (2014). Evaluating faecal egg count reduction using a specifically designed package "eggCounts" in R and a user friendly web interface International Journal for Parasitology, 44(5), 299-303.     [Abstract] [BibTeX]
Abstract: The seemingly straightforward task of analysing faecal egg counts resulting from laboratory procedures such as the McMaster technique has, in reality, a number of complexities. These include Poisson errors in the counting technique which result from eggs being randomly distributed in well mixed faecal samples. In addition, counts between animals in a single experimental or observational group are nearly always over-dispersed. We describe the R package “eggCounts” that we have developed that incorporates both sampling error and over-dispersion between animals to calculate the true egg counts in samples of faeces, the probability distribution of the true counts and summary statistics such as the 95% uncertainty intervals. Based on a hierarchical Bayesian framework, the software will also rigorously estimate the percentage reduction of faecal egg counts and the 95% uncertainty intervals of data generated by a faecal egg count reduction test. We have also developed a user friendly web interface that can be used by those with limited knowledge of the R statistical computing environment. We illustrate the package with three simulated data sets of faecal egg count reduction experiments.

KEYWORDS: Faecal egg count reduction test; Anthelmintic resistance; Mathematical techniques; Statistical analysis; Bayesian hierarchical model

BibTeX:
@ARTICLE{Torg:Paul:Furr:14,
  AUTHOR = 	 {Torgerson, P. R., and Paul, M., and Furrer, R.},
  TITLE = 	 {Evaluating faecal egg count reduction using a specifically designed package "eggCounts" in R and a user friendly web interface},
  JOURNAL = 	 {Int. J. Parasitol.},
  FJOURNAL = 	 {International Journal of Parasitology},
  YEAR = 	 {2014},
  DOI =          {10.1016/j.ijpara.2014.01.005},
  PMID =         {24556564}, 
  volume = 	 {44},
  number = 	 {5},
  pages = 	 {299--303},
}
Furrer, R., Kirchner, N. and Jakobsson, M. (2014). A Cross-polar Modeling Approach to Hindcast Paleo-Arctic Mega Icebergs: a Storyboard In: Pardo-Igúzquiza, E., et al. (Eds.) Mathematics of Planet Earth, Springer, 41-44.     [Abstract] [BibTeX]
Abstract: Recent geophysical mapping of the Arctic seafloor has revealed extensive erosion caused by ice and glacial landforms on ridge crests and plateaus where present water depths are shallower than $\approx$1000\,m. Such erosion stems from thick outlet glaciers and massive ice shelf complexes. Cores and glacigenic landforms suggest that the largest ice shelf complex was confined to the Amerasian sector of the Arctic Ocean, roughly 135'000 years ago. We apply a peak over threshold approach to assess whether the calving fronts of this ice shelf complex comprise a likely source of the deep draft icebergs responsible for the mapped plow marks. This approach is novel to modeling Arctic paleoglacial configurations. Predicted extreme calving front drafts match observed deep-draft iceberg marks if the ice shelf complex is sufficiently large.
We explain the methodology of Kirchner, Furrer, Jakobsson and coauthors \cite{kirc:furr:etal:13} in a storyboard framework, i.e., with figures and sketches. Here, we extend their approach by using shelf specific threshold selection, an alternative estimate to scale `coastlines', supervised pooling of estimates and uncertainty estimates based on parametric bootstrap. For theoretical details as well as details about the precise origin and preprocessing of the data we refer to \cite{kirc:furr:etal:13}, much of the statistical theory is covered in \cite{coles,Embr:etal}.
BibTeX:
@InProceedings{Furr:Kirc:Jako:14,
    AUTHOR = {Furrer,  R. and Kirchner, N. and Jakobsson,  M.},
      YEAR = {2014},
     TITLE = {Statistical modeling of a former {Arctic Ocean} ice shelf 
             complex using {Antarctic} analogies},
 BOOKTITLE = {Mathematics of Planet Earth},
     PAGES = {41-44},
       DOI = {10.1007/978-3-642-32408-6_10},
    EDITOR = {Pardo-Igúzquiza, E. and Guardiola-Albert, C. and Heredia, J.
             and Moreno-Merino, L. and Durán, J.J. and Vargas-Guzmán, J.A.},
    SERIES = {Lecture Notes in Earth System Sciences},
 PUBLISHER = {Springer},
      NOTE = {Proceedings of the 15th Annual Conference of the International 
              Association for Mathematical Geosciences},
      ISBN = {978-3-642-32407-9}
}
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2013

Gerber, F.,+ Marty, F.,+ Eijkel, G. B.,+ Basler, K., Brunner, E., Furrer, R.| and Heeren, R. M. A.| (2013). Multi order correction algorithms to remove image distortions from mass spectrometry imaging datasets, Analytical Chemistry 85(21), 10249-10254.      [Abstract] [BibTeX]
Abstract: Time-of-flight secondary ion mass spectrometry imaging is a rapidly evolving technology. Its main application is the study of the distribution of small molecules on biological tissues. The sequential image acquisition process remains susceptible to measurement distortions that can render imaging data less analytically useful. Most of these artifacts show a repetitive nature from tile to tile. Here we statistically describe these distortions and derive two different algorithms to correct them. Both a generalized linear model approach and the linear discriminant analysis approach are able to increase image quality for negative and positive ion mode data sets. Additionally, performing simulation studies with repetitive and nonrepetitive tiling error we show that both algorithms are only removing repetitive distortions. It is further shown that the spectral component of the data set is not altered by the use of these correction methods. Both algorithms presented in this work greatly increase the image quality and improve the analytical usefulness of distorted images dramatically.
BibTeX:
@ARTICLE{Gerb:etal:13,
    AUTHOR = {Florian Gerber and Florian Marty and Gert B. Eijkel and Konrad Basler and Erich Brunner and Reinhard Furrer and Ron M. A. Heeren},
      YEAR = {2013},
     TITLE = {Multi order correction algorithms to remove image distortions from mass spectrometry imaging datasets},
   JOURNAL = {Anal. Chem.},
  FJOURNAL = {Analytical Chemistry},
    VOLUME = {85},
    NUMBER = {21},
     PAGES = {10249-10254},
       DOI = {10.1021/ac402018e},
      PMID = {24093946}, 
}
Heersink, D. K. and Furrer, R. (2013). Sequential spatial analysis of large datasets with applications to modern earthwork compaction roller measurement values, Spatial Statistics, 6, 41-56.     [Abstract] [BibTeX]
Abstract: In the context of road construction, modern earthwork compaction rollers equipped with sensors collect a virtually continuous flow of soil property measurements. This sequential, spatial data can be utilized to improve the quality control of the compaction process through the introduction of intelligent compaction. These roller measurement values are observed indirectly through non-linear measurement operators, non-stationary, inherently multivariate with complex correlation structures, and collected in huge quantities. The problem of modeling and estimation in a spatially correlated setting with large amounts of data is well known and many approaches can be found in the literature. Very few studies have been completed investigating sequential, spatially correlated data outside of a point process framework. We propose a sequential, spatial mixed-effects model and develop a sequential, spatial backfitting algorithm to estimate fixed effects and several independent, spatially correlated processes. This new algorithm is demonstrated in a simulation study and applied to earthwork compaction data.

Keywords: Backfitting; Hierarchical multivariate spatial models; Quasi-Kronecker; Sparse matrix; Spatial mixed-effects

BibTeX:
@ARTICLE{Heer:Furr:13,
    AUTHOR = {Heersink, D. K. and Furrer,  R.},
      YEAR = {2013},
     TITLE = {Sequential spatial analysis of large datasets with
              applications to modern earthwork compaction
              roller measurement values},
   JOURNAL = {Spatial Statistics},
  FJOURNAL = {Spatial Statistics},
    VOLUME = {6},
     PAGES = {41-56},
       DOI = {10.1016/j.spasta.2013.07.002},
}
Kirchner, N.,+ Furrer, R.,+ Jakobsson, M., Zwally, H. J. and Robbins, J. W. (2013). Statistical modeling of a former Arctic Ocean ice shelf complex using Antarctic analogies. Journal of Geophysical Research: Earth Surface, 118(2), 1105-1117.     [Abstract] [BibTeX]
Abstract: Geophysical mapping and coring of the central Arctic Ocean seafloor provide evidence for repeated occurrences of ice sheet/ice shelf complexes during previous glacial periods. Several ridges and bathymetric highs shallower than present water depths of ∼1000 m show signs of erosion from deep-drafting (armadas of) icebergs, which originated from thick outlet glaciers and ice shelves. Mapped glacigenic landforms and dates of cored sediments suggest that the largest ice shelf complex was confined to the Amerasian sector of the Arctic Ocean during Marine Isotope Stage (MIS) 6. However, the spatial extent of ice shelves can not be well reconstructed from occasional groundings on bathymetric highs. Therefore, we apply a statistical approach to provide independent support for an extensive MIS 6 ice shelf complex, which previously was inferred only from interpretation of geophysical and geological data. Specifically, we assess whether this ice shelf complex comprises a likely source of the deep-draft icebergs responsible for the mapped scour marks. The statistical modeling is based on exploiting relations between contemporary Antarctic ice shelves and their local physical environments and the assumption that Arctic Ocean MIS 6 ice shelves scale similarly. Analyzing ice thickness data along the calving front of contemporary ice shelves, a peak over threshold method is applied to determine sources of deep-drafting icebergs in the Arctic Ocean MIS 6 ice shelf complex. This approach is novel to modeling Arctic paleoglacial configurations. Predicted extreme calving front drafts match observed deep-draft iceberg scours if the ice shelf complex is sufficiently large.

Keywords: Arctic Ocean ice shelves; extreme value theory; deep-draft ice berg scours; multivariate linear model; ICESat data in Arctic-Antarctic analogy approach

BibTeX:
@ARTICLE{Kirc:Furr:etal:13,
    AUTHOR = {Kirchner, N. and Furrer, R. and Jakobsson, M. and Zwally, H. J. and Robbins, J. W.},
      YEAR = {2013},
     TITLE = {Statistical modeling of a former {Arctic Ocean} ice shelf complex using {Antarctic} analogies},
   JOURNAL = {J. Geophys. Res. Earth Surf.},
  FJOURNAL = {Journal of Geophysical Research: Earth Surface},
    VOLUME = {118},
    NUMBER = {2},
     PAGES = {1105-1117},
       DOI = {10.1002/jgrf.20077},
}
de Jong, R., Schaepman, M. E., Furrer, R. de Bruin, S. and Verburg, P. H. (2013). Spatial relationship between climatologies and changes in global vegetation activity. Global Change Biology, 19(6), 1953–1964.     [Abstract] [BibTeX]
Abstract: Vegetation forms a main component of the terrestrial biosphere and plays a crucial role in land-cover and climate-related studies. Activity of vegetation systems is commonly quantified using remotely sensed vegetation indices (VI). Extensive reports on temporal trends over the past decades in time series of such indices can be found in literature. However, little remains known about the processes underlying these changes at large spatial scales. In this study, we aimed at quantifying the spatial relationship between changes in potential climatic growth constraints (i.e. temperature, precipitation and incident solar radiation) and changes in vegetation activity (1982–2008). We demonstrate an additive spatial model with 0.5° resolution, consisting of a regression component representing climate-associated effects and a spatially correlated field representing the combined influence of other factors, including land-use change. Little over 50% of the spatial variance could be attributed to changes in climatologies; conspicuously, many greening trends and browning hotspots in Argentina and Australia. The nonassociated model component may contain large-scale human interventions, feedback mechanisms or natural effects, which were not captured by the climatologies. Browning hotspots in this component were especially found in subequatorial Africa. On the scale of land-cover types, strongest relationships between climatologies and vegetation activity were found in forests, including indications for browning under warming conditions (analogous to the divergence issue discussed in dendroclimatology).

Keywords: climate- and human-induced change; climatologies; Gaussian random field; growth constraints; regression; spatial additive model; vegetation-activity trends

BibTeX:
@ARTICLE{deJo:etal:13,
    AUTHOR = {de Jong, Rogier and Schaepman, Michael E. and Furrer, Reinhard and de Bruin, Sytze and Verburg, Peter H.},
      YEAR = {2013},
     TITLE = {Spatial relationship between climatologies and changes in global vegetation activity},
   JOURNAL = {Glob. Change Biol.},
  FJOURNAL = {Global Change Biology},
    VOLUME = {19},
    NUMBER = {6},
     PAGES = {1953–1964},
       DOI = {10.1111/gcb.12193},
      PMID = {23512439}, 
}
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2012

Benigni, M. and Furrer, R. (2012). Spatio-temporal improvised explosive device monitoring: improving detection to minimise attacks. Journal of Applied Statistics, 39(11) 2493-2508.     [Abstract] [BibTeX]
Abstract:

The improvised explosive device (IED) is a weapon of strategic influence on today's battlefield. IED detonations occur predominantly on roads, footpaths, or trails. Therefore, locations are best described when constrained to the road network, and some spaces on the network are more dangerous at specific times of the day. We propose a statistical model that reduces the spatial location to one dimension and uses a cyclic time as a second dimension. Based on the Poisson process methodology, we develop normalised, inhomogeneous, bivariate intensity functions measuring the threat of attack to support resourcing decisions. A simulation and an analysis of attacks on a main supply route in Baghdad are given to illustrate the proposed methods. Additionally, we provide an overview of the growing demand for the analysis efforts in support of operations in Afghanistan and Iraq, and provide an extensive literature review of developments in counter-IED analysis.

Keywords: Periodic spatio-temporal cluster, linear referencing, Poisson process, risk, intensity function.

BibTeX:
@ARTICLE{Beni:Furr:12,
    AUTHOR = {Benigni, Matthew and Furrer, Reinhard},
     TITLE = {Spatio-temporal improvised explosive device monitoring: improving detection to minimise attacks},
      YEAR = {2012},
   JOURNAL = {J. Appl. Stat.},
  FJOURNAL = {Journal of Applied Statistics},
    VOLUME = {39},
    NUMBER = {11},
     PAGES = {2493--2508},
       DOI = {10.1080/02664763.2012.719222},
}
Furrer, R., Genton, M. G. and Nychka, D. (2012). Erratum and Addendum to: “Covariance Tapering for Interpolation of Large Spatial Datasets” published in the Journal of Computational and Graphical Statistics, 15, 502–523. Journal of Computational and Graphical Statistics 21(3), 823-824.     [Summary] [BibTeX] [Auxiliary material]
Summary:

The Taper Condition stated in Furrer et al. (2006) (FGN hereafter) should either exclude the case ε = 0 or be slightly rephrased. The proof of Proposition 1 in FGN shows that the limit superior of (A.1) is bounded but it does not explicitly show that it is equal to the limit inferior for ε = 0. It is, moreover, possible to construct tapers satisfying the taper condition which lead to non-existing limits (A.1), an example is the sum of a spherical and triangular covariance function in IR. To include the case ε = 0 a slightly stronger tail condition on the spectral density of the taper is required. The supplementary material gives a proof of Proposition 1 of FGN under this modified taper condition combining the cases k > ν + d/2 (ε > 0) and k = ν + d/2 (ε = 0).

BibTeX:
 @ARTICLE{Furr:Gent:Nych:12,
    AUTHOR = {R. Furrer and M. G. Genton and D. Nychka},
     TITLE = {Erratum and Addendum to: “Covariance Tapering for Interpolation of Large Spatial Datasets” published in the Journal of Computational and Graphical Statistics, 15, 502–523},
      YEAR = {2012},	
   JOURNAL = {J. Comput. Graph. Stat.},
  FJOURNAL = {Journal of Computational and Graphical Statistics},
    VOLUME = {21},
    NUMBER = {3},
     PAGES = {823-824},
       DOI = {10.1080/10618600.2012.712502},
}
Furrer, R., Geinitz, S. and Sain, S. R. (2012). Assessing variance components of general circulation model output field. Environmetrics, 23(5), 440-450.     [Abstract] [BibTeX]
Abstract:

Recent internationally coordinated efforts have used deterministic climate models for a common set of experiments and have produced large datasets of future climate projections. These ensembles are subject to many sources of variability, and we propose an analysis of variance procedure to quantify the contribution from several sources to the overall variation. This procedure is based on a Bayesian linear model parameterization and is applicable for large spatial data. A key feature is that individual sources of variability are modeled through batches and assessed through the batches' superpopulation variance, individual batch level predictions, and finite population covariance. Further, for a large class of models, we show that the full posterior can be factored into conditionally independent distributions, consisting of a batch's superpopulation and batch levels. By doing so, the need for MCMC methods is obviated. Finally, this approach is applied to decadal summer temperatures for different climate models and various scenarios.

Keywords: Multivariate ANOVA; Spatial data; Mixed model; Bayesian inference.

BibTeX:
@ARTICLE{Furr:Gein:Sain:12,
    AUTHOR = {Reinhard Furrer and Steven Geinitz and Stephan R. Sain},
     TITLE = {Assessing variance components of general circulation model output field},
      YEAR = {2012},
   JOURNAL = {Environmetrics},
  FJOURNAL = {Environmetrics},
    VOLUME = {23},
    NUMBER = {5},
     PAGES = {440--450},
       DOI = {10.1002/env.2139},
}
Heersink, D. K. and Furrer, R. (2012). On Moore-Penrose Inverses of Quasi-Kronecker Structured Matrices. Linear Algebra and its Applications, 436(3), 561-570.     [Abstract] [BibTeX]
Abstract: The Moore--Penrose inverse and generalized inverse of $\A+\X_1\X_2^*$, where $\A$, $\X_1$, $\X_2$ are complex matrices are given under various assumptions. We use the result to derive the Moore--Penrose inverse and inverse for $\bdiag(\A_k)+ \bfu\v^*\otimes\bfE$ with $p$ complex matrices $\A_k$, two complex $p$-vectors $\bfu$ and $\v$ and a complex matrix $\bfE$. Such block structured matrices occur in hierarchical modeling of multivariate spatial or space-time Gaussian processes. For the latter we also give expressions of the determinant and of conditional variances.

Keywords: block-partitioned matrix, likelihood, hierarchical multivariate spatial models.

MSC: 15A09, 15A15, 62M30

BibTeX:
@ARTICLE{Heer:Furr:12,
    AUTHOR = {Heersink, D. K. and Furrer, R.},
      YEAR = {2012},
     TITLE = {On {Moore--Penrose} Inverses of Quasi-{Kronecker} Structured Matrices},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {436},
    NUMBER = {3},
     PAGES = {561-570},
       DOI = {10.1016/j.laa.2011.07.009},
}
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2011

Furrer, R. and Genton, M. G. (2011). Aggregation-cokriging for Highly-Multivariate Spatial Data. Biometrika, 98(3), 615--631.     [Abstract] [BibTeX]
Abstract: Best linear unbiased prediction of spatially correlated multivariate random processes, often called cokriging in geostatistics, requires the solution of a large linear system based on the covariance and cross-covariance matrix of the observations. For many problems of practical interest it is impossible to solve the linear system with direct methods. We propose an efficient linear unbiased predictor based on a linear aggregation of the covariables. The primary variable together with this single meta-covariable is used to perform cokriging. We discuss the optimality of the approach under different covariance structures, and use it to create re-analysis type high-resolution historical temperature fields.

Keywords: Climate; Cokriging; Eigendecomposition; Intrinsic process; Linear unbiased prediction.

BibTeX:
@ARTICLE{Furr:Gent:11,
    AUTHOR = {Furrer, R. and Genton, M. G.},
      YEAR = {2011},
     TITLE = {Aggregation-cokriging for Highly-Multivariate Spatial Data},
   JOURNAL = {Biometrika},
  FJOURNAL = {Biometrika},
    VOLUME = {98},
    NUMBER = {3},
     PAGES = {615--631},
       DOI = {10.1093/biomet/asr029},
}
Holmström, L., Pasanen, L., Furrer, R. and Sain, S. R. (2011). Scale Space Multiresolution Analysis of Random Signals. Computational Statistics and Data Analysis, 55, 2840-2855.     [Abstract] [BibTeX]
Abstract: A method to capture the scale-dependent features in a random signal is proposed with the main focus on images and spatial fields defined on a regular grid. A technique based on scale space smoothing is used. However, where the usual scale space analysis approach is to suppress detail by increasing smoothing progressively, the proposed method instead considers differences of smooths at neighboring scales. A random signal can then be represented as a sum of such differences, a kind of a multiresolution analysis, each difference representing details relevant at a particular scale or resolution. Bayesian analysis is used to infer which details are credible and which are just artifacts of random variation. The applicability of the method is demonstrated using noisy digital images as well as global temperature change fields produced by numerical climate prediction models.

Keywords: Scale space smoothing, Bayesian methods, Image analysis, Climate research

BibTeX:
@ARTICLE{Holm:etal:11,
    AUTHOR = {Holmstr\"om, L. and Pasanen, L. and Furrer, R. and Sain, S. R.},
      YEAR = {2011},
     TITLE = {Scale Space Multiresolution Analysis of Random Signals},
   JOURNAL = {Comput. Stat. Data An.},
  FJOURNAL = {Computational Statistics \& Data Analysis},
    VOLUME = {55},
    NUMBER = {},
     PAGES = {2840--2855},
       DOI = {10.1016/j.csda.2011.04.011},
}
Sain, S. R., Furrer, R., Cressie, N. (2011). A Spatial Analysis of Multivariate Output from Regional Climate Models. Annals of Applied Statistics, 5(1), 150-175.     [Abstract] [BibTeX]
Abstract: 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 eld. This approach allows for exible 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.

Keywords: Lattice Data, Markov Random Field (MRF), Conditional Autoregressive (CAR) Model, Bayesian Hierarchical Model, Climate Change.

BibTeX:
@ARTICLE{Sain:Furr:Cres:11,
    AUTHOR = {Sain, S. R. and Furrer, R. and Cressie, N.},
      YEAR = {2011},
     TITLE = {A Spatial Analysis of Multivariate Output from Regional Climate Models},
   JOURNAL = {Ann. Appl. Stat.},
  FJOURNAL = {Annals of Applied Statistics},
    VOLUME = {5},
    NUMBER = {1},
     PAGES = {150-175},
       DOI = {10.1214/10-AOAS369},
}
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2010

Furrer, E. M., Katz, R. W., Walter, M. D. and Furrer, R. (2010). Statistical modeling of hot spells and heat waves. Climate Research, 43(3), 191-205. [Abstract] [BibTeX]
Abstract: Although hot spells and heat waves are considered extreme meteorological phenomena, the statistical theory of extreme values has only rarely, if ever, been applied. To address this shortcoming, we extended the point process approach to extreme value analysis to model the frequency, duration, and intensity of hot spells. The annual frequency of hot spells was modeled by a Poisson distribution, and their length by a geometric distribution. To account for the temporal dependence of daily maximum temperatures within a hot spell, the excesses over a high threshold were modeled by a conditional generalized Pareto distribution, whose scale parameter depends on the excess on the previous day. Requiring only univariate extreme value theory, our proposed approach is simple enough to be readily generalized to incorporate trends in hot spell characteristics. Through a heat wave simulator, the statistical modeling of hot spells can be extended to apply to more full-fledged heat waves, which are difficult to model directly. Our statistical model for hot spells was fitted to time series of daily maximum temperature during the summer heat wave season in Phoenix, Arizona (USA), Fort Collins, Colorado (USA), and Paris, France. Trends in the frequency, duration, and intensity of hot spells were fitted as well. The heat wave simulator was used to convert any such trends into the corresponding changes in the characteristics of heat waves. By being based at least in part on extreme value theory, our proposed approach is both more realistic and more flexible than techniques heretofore applied to model hot spells and heat waves.

Keywords: Climate change; Clustering of extremes; Generalized Pareto distribution; Point process approach; Heat wave simulator.

BibTeX:
@ARTICLE{Furr:etal:10,
    AUTHOR = {Furrer, E. M. and Katz, R. W. and  Walter, M. D. and Furrer, R},
      YEAR = {2010},
     TITLE = {Statistical modeling of hot spells and heat waves},
   JOURNAL = {Clim. Res.},
  FJOURNAL = {Climate Research},
    VOLUME = {43},
    NUMBER = {3},
     PAGES = {191--205},
       DOI = {10.3354/cr00924},
}
Krembs, F. J., Siegrist, R. L., Crimi, M. L., Furrer, R. and Petri, B. G. (2010). ISCO for Groundwater Remediation: Analysis of Field Applications and Performance. Ground Water Monitoring & Remediation, 30(4): 42–53. [Abstract] [BibTeX]
Abstract: A critical analysis of in situ chemical oxidation (ISCO) projects was performed to characterize situations in which ISCO is being implemented, how design and operating parameters are typically employed, and to determine the performance results being achieved. This research involved design of a database, acquisition and review of ISCO project information, population of the database, and analyses of the database using statistical methods. Based on 242 ISCO projects included in the database, ISCO has been used to treat a variety of contaminants; however, chlorinated solvents are by far the most common. ISCO has been implemented at sites with varied subsurface conditions with vertical injection wells and direct push probes being the most common delivery methods. ISCO has met and maintained concentrations below maximum contaminant levels (MCLs), although not at any sites where dense nonaqueous phase liquids (DNAPL) were presumed to be present. Alternative cleanup levels and mass reduction goals have also been attempted, and these less stringent goals are met with greater frequency than MCLs. The use of pilot testing is beneficial in heterogeneous geologic media, but not so in homogeneous media. ISCO projects cost $220,000 on average, and cost on average $94/yd3 of target treatment zone. ISCO costs vary widely based on the size of the treatment zone, the presence of DNAPL, and the oxidant delivery method. No case studies were encountered in which ISCO resulted in permanent reductions to microbial populations or sustained increases in metal concentrations in groundwater at the ISCO-treated site.
BibTeX:
@ARTICLE{Krem:etal:10,
    AUTHOR = {Krembs, F. J., Siegrist, R. L., Crimi, M. L., Furrer, R. and Petri, B. G.},
      YEAR = {2010},
     TITLE = {ISCO for Groundwater Remediation: Analysis of Field Applications and Performance},
   JOURNAL = {Ground Water Monitoring \& Remediation},
  FJOURNAL = {Ground Water Monit. Remediat.},
    VOLUME = {30},
    NUMBER = {4},
     PAGES = {42--53},
       DOI = {10.1111/j.1745-6592.2010.01312.x},
}
Facas, N., Mooney, M. A. and Furrer, R. (2010). Anisotropy in the Spatial Distribution of Roller-Measured Soil Stiffness. International Journal of Geomechanics, 10(4), 129-135.      [Abstract] [BibTeX]
Abstract: Geostatistical analysis of roller-measured soil properties (from continuous compaction control and intelligent compaction) is required for advanced quality control/quality assurance of earthwork and asphalt compaction. This paper explores the existence of anisotropy in the spatial distribution of roller-measured soil stiffness and the effect of anisotropy on kriging. Field testing was conducted to collect roller measurement value (MV) data over typical roadway embankment evaluation areas and on a large square area to enable a robust investigation of anisotropy. Semi-variogram analysis of the field data clearly indicates that range anisotropy exists. The spatial distribution of roller MV data is different in the longitudinal x direction than in the transverse y direction. Magnitudes of range anisotropy (x range/y range) varied from 2.4 to over 5. The observed range anisotropy is not due to the roller measurement system; rather, it is likely due to the directional nature of earthwork construction activities and to alignment geometry. The influence of anisotropy on kriging was found to be significant when considering the use of kriged data in earthwork specifications. The error introduced by not accounting for anisotropy in kriging varied from 5% to 17% when considering pass to pass or layer to layer map analysis. Anisotropy in the spatial distribution of roller MV data should be factored into kriging and other geostatistical analyses. For typical earthwork area geometries, the roller mapping procedure requires slight modification to determine the y range and anisotropy ratio.

BibTeX:
@ARTICLE{Faca:Moon:Furr:10,
    AUTHOR = {Facas, N. and Mooney, M. A. and Furrer, R.},
      YEAR = {2010},
     TITLE = {Anisotropy in the Spatial Distribution of Roller-Measured Soil Stiffness},
   JOURNAL = {Int. J. Geomech.},
  FJOURNAL = {International Journal of Geomechanics},
    VOLUME = {10},
    NUMBER = {4},
     PAGES = {129-135},
       DOI = {10.1061/(ASCE)GM.1943-5622.0000053},
}
Furrer, R. and Sain, S. R. (2010). spam: A Sparse Matrix R Package with Emphasis on MCMC Methods for Gaussian Markov Random Fields. Journal of Statistical Software, 36(10), 1--25.     [Abstract] [BibTeX]
Abstract: 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 S4 and S3 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 sparseness 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.

Keywords: Cholesky factorization, Compactly supported covariance function, Compressed sparse row format, Symmetric positive-definite matrix, Stochastic modeling, S3/S4.

BibTeX:
@ARTICLE{Furr:Sain:10,
    AUTHOR = {Furrer, R. and Sain, S. R.},
      YEAR = {2010},
     TITLE = {{spam}: {A} Sparse Matrix {R} Package with Emphasis on {MCMC} Methods for {G}aussian {M}arkov Random Fields},
   JOURNAL = {J. Stat. Softw.},
  FJOURNAL = {Journal of Statistical Software},
    VOLUME = {36},
    NUMBER = {10},
     PAGES = {1--25},
       URL = {http://www.jstatsoft.org/v36/i10/},
}
Sain, S. R. and Furrer, R. (2010). Combining Climate Model Output via Model Correlations, Stochastic Environmental Research and Risk Assessment, 24(6), 821--829.      [Abstract] [BibTeX]
Abstract: In climate science, collections of climate model output, usually referred to as ensembles, are commonly used devices to study uncertainty in climate model experiments. The ensemble members may reflect variation in initial conditions, different physics implementations, or even entirely different climate models. However, there is a need to deliver a unified product based on the ensemble members that reflects the information contained in whole of the ensemble. We propose a technique for creating linear combinations of ensemble members where the weights are constructed from estimates of variation and correlation both within and between ensemble members. At the heart of this approach is a Bayesian hierarchical model that allows for estimation of the correlation between ensemble members as well as the study of the impact of uncertainty in the parameter estimates of the hierarchical model on the weights. The approach is demonstrated on an ensemble of regional climate model (RCM) output.

Keywords: Model averaging, Model correlations, Total variation, Regional climate models, Bayesian hierarchical model

BibTeX:
@ARTICLE{Sain:Furr:10,
    AUTHOR = {Sain, S. R. and Furrer, R.},
      YEAR = {2010},
     TITLE = {Combining climate model output via model correlations},
   JOURNAL = {Stoch. Environ. Res. Risk Assess.},
  FJOURNAL = {Stochastic Environmental Research and Risk Assessment},
    VOLUME = {24},
    NUMBER = {6},
     PAGES = {821--829},
       DOI = {10.1007/s00477-010-0380-5},
}
Knutti, R. and Furrer, R. and Tebaldi, C. and Cermak, J. and Meehl, G. A. (2010). Challenges in combining projections from multiple climate models. Journal of Climate, 23(10), 2739-2758.     [Abstract] [BibTeX]
Abstract: Recent coordinated efforts, in which numerous general circulation climate models have been run for a common set of experiments, have produced large datasets of projections of future climate for various scenarios. Those multimodel ensembles sample initial conditions, parameters, and structural uncertainties in the model design, and they have prompted a variety of approaches to quantifying uncertainty in future climate change. International climate change assessments also rely heavily on these models. These assessments often provide equal-weighted averages as best-guess results, assuming that individual model biases will at least partly cancel and that a model average prediction is more likely to be correct than a prediction from a single model based on the result that a multimodel average of present-day climate generally outperforms any individual model. This study outlines the motivation for using multimodel ensembles and discusses various challenges in interpreting them. Among these challenges are that the number of models in these ensembles is usually small, their distribution in the model or parameter space is unclear, and that extreme behavior is often not sampled. Model skill in simulating present-day climate conditions is shown to relate only weakly to the magnitude of predicted change. It is thus unclear by how much the confidence in future projections should increase based on improvements in simulating present-day conditions, a reduction of intermodel spread, or a larger number of models. Averaging model output may further lead to a loss of signal—for example, for precipitation change where the predicted changes are spatially heterogeneous, such that the true expected change is very likely to be larger than suggested by a model average. Last, there is little agreement on metrics to separate “good” and “bad” models, and there is concern that model development, evaluation, and posterior weighting or ranking are all using the same datasets. While the multimodel average appears to still be useful in some situations, these results show that more quantitative methods to evaluate model performance are critical to maximize the value of climate change projections from global models.

Keywords: Climate models, Ensembles, Diagnostics, Climate prediction

BibTeX:
@ARTICLE{Knut:etal:10,
    AUTHOR = {Knutti, R. and Furrer, R. and  Tebaldi, C. and Cermak, J. and  Meehl, G. A.},
      YEAR = {2010},
     TITLE = {Challenges in combining projections from multiple climate models},
   JOURNAL = {J. Clim.},
  FJOURNAL = {Journal of Climate},
    VOLUME = {23},
    NUMBER = {10},
     PAGES = {2739-2758},
       DOI = {10.1175/2009JCLI3361.1},
}
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2009

Furrer, R. and Sain, S. R. (2009). Spatial Model Fitting for Large Datasets with Applications to Climate and Microarray Problems. Statistics and Computing, 19(2), 113-128, doi:10.1007/s11222-008-9075-x.     [Abstract] [BibTeX]
Abstract: Many problems in the environmental and biological sciences involve the analysis of large quantities of data. Further, the data in these problems are often subject to various types of structure and, in particular, spatial dependence. Traditional model fitting often fails due to the size of the datasets since it is difficult to not only specify but also to compute with the full covariance matrix describing the spatial dependence. We propose a very general type of mixed model that has a random spatial component. Recognizing that spatial covariance matrices often exhibit a large number of zero or near-zero entries, covariance tapering is used to force near-zero entries to zero. Then, taking advantage of the sparse nature of such tapered covariance matrices, backfitting is used to estimate the fixed and random model parameters. The novelty of the paper is the combination of the two techniques, tapering and backfitting, to model and analyze spatial datasets several orders of magnitude larger than those datasets typically analyzed with conventional approaches. Results will be demonstrated with two datasets. The first consists of regional climate model output that is based on an experiment with two regional and two driver models arranged in a two-by-two layout. The second is microarray data used to build a profile of differentially expressed genes relating to cerebral vascular malformations, an important cause of hemorrhagic stroke and seizures.

Keywords: Mixed effects; Backfitting; Covariance Tapering; Sparse matrices.

BibTeX:
@ARTICLE{Furr:Sain:09,
    AUTHOR = {Furrer, R. and Sain, S. R.},
      YEAR = {2009},
     TITLE = {Spatial Model Fitting for Large Datasets with Applications to Climate and Microarray Problems},
   JOURNAL = {Stat. Comput.},
  FJOURNAL = {Statistics and Computing},
    VOLUME = {19},
    NUMBER = {2},
     PAGES = {113-128},
       DOI = {10.1007/s11222-008-9075-x},
}
Facas. N., Mooney, M. A., and Furrer, R. (2009). Geostatistical Analysis of Roller-Integrated Continuous Compaction Control Data. Bearing Capacity of Roads, Railways and Airfields, Tutumluer and Al-Qadi (eds.), Taylor and Francis Group, London, 1, 755-762.     
Abstract:

Keywords: Mixed effects; Backfitting; Covariance Tapering; Sparse matrices.

BibTeX:
@ARTICLE{Furr:Sain:09,
    AUTHOR = {Furrer, R. and Sain, S. R.},
      YEAR = {2009},
     TITLE = {Spatial Model Fitting for Large Datasets with Applications to Climate and Microarray Problems},
   JOURNAL = {Stat. Comput.},
  FJOURNAL = {Statistics and Computing},
    VOLUME = {19},
    NUMBER = {2},
     PAGES = {113-128},
       DOI = {10.1007/s11222-008-9075-x},
}
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2008

Mendez, P. F., Furrer, R., Ford, R. and Ordóñez, F. (2008). Scaling Laws as a Tool of Materials Informatics. JOM, 60(03), 60-66, doi:10.1007/s11837-008-0036-9.      [Abstract] [BibTeX]
Abstract: This paper discusses the utility of scaling laws to materials informatics and presents the algorithm Scaling LAW (SLAW), useful to obtain scaling laws from statistical data. These laws can be used to extrapolate known materials property data to untested materials by using other more readily available information. This technique is independent of a characteristic length or time scale, so it is useful for a broad diversity of problems. In some cases, SLAW can reproduce the mathematical expression that would have been obtained through an analytical treatment of the problem. This technique was originally designed for mining statistical data in materials processing and materials behavior at a system level, and it shows promise for the study of the relationship between structure and properties in materials.
BibTeX:
@ARTICLE{Mend:etal:08,
    AUTHOR = {Mendez, P. F. and Furrer, R. and Ford, R. and Ord\'o\~nez, F.},
      YEAR = {2008},
     TITLE = {Scaling Laws as a Tool of Materials Informatics},
   JOURNAL = {JOM},
  FJOURNAL = {JOM},
    VOLUME = {60},
    NUMBER = {3},
     PAGES = {60-66},
       DOI = {http://dx.doi.org/10.1007/s11837-008-0036-9},
}
Kupper, T., de Alencastro, L. F., Gatsigazi, R., Furrer, R., Grandjean D. and Tarradellas J. (2008). Concentrations and specific loads of brominated flame retardants in sewage sludge. Chemosphere, 71(6), 1173-1180, doi:10.1016/j.chemosphere.2007.10.019.     [Abstract] [BibTeX]
Abstract: Many substances related to human activities end up in wastewater and accumulate in sewage sludge. The present study focuses on two classes of brominated flame retardants: polybrominated diphenyl ethers (BDE28, BDE47, BDE49, BDE66, BDE85, BDE99, BDE100, BDE119, BDE138, BDE153, BDE154, BDE183, BDE209) and hexabromocyclododecane (HBCD) detected in sewage sludge collected from a monitoring network in Switzerland. Mean concentrations (n = 16 wastewater treatment plants) were 310, 149, 95 and 17 mu g per kg dry matter for decaBDE, HBCD, penta- and octaBDE, respectively. These numbers correspond well with other studies from European countries. DecaBDE, HBCD, penta- and octaBDE showed average specific loads (load per connected inhabitant per year) in sludge of 6.1, 3.3, 2.0 and 0.3 mg cap-1 yr-1, respectively. This is in line with consumption and storage of the compounds in the environment and the anthroposphere. Discrepancies observed for octaBDE and HBCD can be explained by the release from materials where these compounds are incorporated in and/or their degradation during anaerobic sludge treatment. Loads from different types of monitoring sites showed that brominated flame retardants ending up in sewage sludge originate mainly from surface runoff, industrial and domestic wastewater.

Keywords: Sources; Wastewater treatment plant; Polybrominated diphenyl ethers; Hexabromocyclododecane; Flux

BibTeX:
@ARTICLE{Kupp:etal:08,
    AUTHOR = {Kupper, T. and  De Alencastro, L.F. and Gatsigazi, R. and Furrer, R. and Grandjean, D. and Tarradellas J.},
      YEAR = {2008},
     TITLE = {Concentrations and specific loads of brominated flame retardants in sewage sludge},
   JOURNAL = {Chemosphere},
  FJOURNAL = {Chemosphere},
    VOLUME = {71},
    NUMBER = {6},
     PAGES = {1173-1180},
       DOI = {10.1016/j.chemosphere.2007.10.019},
      PMID = {18035395},
}
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2007

Contributing author to Chapter 10 Global Climate Projections of the Working Group I contribution to the Intergovernmental Panel on Climate Change Fourth Assessment Report: Climate Change 2007: The Physical Science Basis, Cambridge University Press; ISBN 0521705967/0521880092.
Furrer, R, Sain, S. R., Nychka, D. and Meehl, G. A. (2007). Multivariate Bayesian Analysis of Atmosphere-Ocean General Circulation Models. Environmental and Ecological Statistics, 14(3), 249-266, doi:10.1007/s10651-007-0018-z.     [Abstract] [BibTeX]
Abstract: Numerical experiments based on atmosphere-ocean general circulation models (AOGCMs) are one of the primary tools in deriving projections for future climate change. Although each AOGCM has the same underlying partial differential equations, modelling large scale effects, they have different small scale parameterisations and different discretisations to solve the equations, resulting in different climate projections. This motivates climate projections synthesized from results of several AOGCMs' output. We combine present day observations, present day and future climate projections in a single highdimensional hierarchical Bayes model. The challenging aspect is the modeling of the spatial processes on the sphere, the number of parameters and the amount of data involved. We pursue a Bayesian hierarchical model that separates the spatial response into a large scale climate change signal and an isotropic process representing small scale variability among AOGCMs. Samples from the posterior distributions are obtained with computer-intensive MCMC simulations. The novelty of our approach is that we use gridded, high resolution data covering the entire sphere within a spatial hierarchical framework. The primary data source is provided by the Coupled Model Intercomparison Project (CMIP) and consists of 9 AOGCMs on a 2.8 by 2.8 degree grid under several different emission scenarios. In this article we consider mean seasonal surface temperature and precipitation as climate variables. Extensions for our model are also discussed.

Keywords: Climate change; Spatial process; Spherical covariance, Hierarchical model; Large datasets; MCMC.

BibTeX:
@ARTICLE{Furr:Sain:Nych:Meeh:07,
  AUTHOR = {Furrer, R. and  Sain, S. R. and Nychka, D. W. and Meehl, G. A.},
   TITLE = {Multivariate {B}ayesian Analysis of Atmosphere-Ocean General Circulation Models},
    YEAR = {2007},
 JOURNAL = {Environ. Ecol. Stat.},
FJOURNAL = {Environmental and Ecological Statistics},
  VOLUME = {14},
  NUMBER = {3},
   PAGES = {249-266},
     DOI = {10.1007/s10651-007-0018-z},
}
Furrer, R., Knutti, R., Sain, S. R., Nychka, D. W. and Meehl, G. A. (2007). Spatial patterns of probabilistic temperature change projections from a multivariate Bayesian analysis. Geophysical Research Letters, 34, L06711, doi:10.1029/2006GL027754.     [Abstract] [BibTeX]
Abstract: We present probabilistic projections for spatial patterns of future temperature change using a multivariate Bayesian analysis. The methodology is applied to the output from 21 global coupled climate models used for the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. The statistical technique is based on the assumption that spatial patterns of climate change can be separated into a large scale signal related to the true forced climate change and a small scale signal due to model bias and variability. The different scales are represented via dimension reduction techniques in a hierarchical Bayesian model. Posterior probabilities are obtained with a Markov chain Monte Carlo simulation. We show that with 66% (90%) probability 79% (48%) of the land areas warm by more than 2oC by the end of the century for the SRES A1B scenario.
BibTeX:
@ARTICLE{Furr:Knut:Sain:Nych:Meeh:07,
    AUTHOR = {Furrer, R. and Knutti, R. and Sain, S. R. and Nychka, D. W. and Meehl, G. A.},
     TITLE = {Spatial patterns of probabilistic temperature change projections from a multivariate {B}ayesian analysis},
      YEAR = {2007},
   JOURNAL = {Geophys. Res. Lett.},
  FJOURNAL = {Geophysical Research Letters},
    VOLUME = {34},
     PAGES = {L06711},
       DOI = {10.1029/2006GL027754},
}
Brändli, R. C., Bucheli, T. D., Kupper, T., Furrer, R., Stahel, W. A., Stadelmann, F. X. and Tarradellas, J. (2007). Organic pollutants in compost and digestate. Part 1. Polychlorinated biphenyls, polycyclic aromatic hydrocarbons and markers. Journal of Environmental Moniting, 9, 456-464, doi:10.1039/b617101j.     [Abstract] [BibTeX]
Abstract: In Europe, 9.3x106tdry weight (dw) of compost and digestate are produced per year. Most of this is applied to agricultural land, which can lead to considerable inputs of organic pollutants, such as polychlorinated biphenyls (PCB) and polycyclic aromatic hydrocarbons (PAH) to soil. This paper presents an inventory of the pollutant situation in source-separated composts, digestates and presswater in Switzerland by a detailed analysis of over 70 samples. PCB concentrations (sum PCB 28, 52, 101, 118, 138, 153, 180) were significantly higher in urban (median: 30 mg kgdw-1, n = 52) than in rural samples (median: 14 mg kgdw-1, n = 16). Together with low concentrations in general, this points to aerial deposition on compost input material as the major contamination pathway. Enantiomeric fractions of atropisometric PCB were close to racemic. Median PAH concentration was 3010 mg kgdw-1 (sum 15PAH, n = 69), and one quarter of the samples exhibited concentrations above the relevant Swiss guide value for compost (4000 mg kgdw-1). The levels were influenced by the treatment process (digestate > compost), the season of input material collection (spring-summer > winter > autumn), the particle size (coarse-grained > fine-grained), and maturity (mature > less mature). The main source of PAH in compost was pyrogenic, probably influenced mainly by liquid fossil fuel combustion and some asphalt abrasion, as suggested by multiple linear regression. This study, together with a companion paper reporting on other organic contaminates including emerging compound classes, provides a starting point for a better risk-benefit estimation of the application of compost and digestate to agricultural soil in Switzerland.
BibTeX:
@ARTICLE{Brae:Buch:Kupp:Furr:Stah:Stad:Tarr:07,
    AUTHOR = {Br\"andli, R. C. and Bucheli, T. D. and Kupper, T. and Furrer, R. and Stahel, W. A. and Stadelmann, F. X. and Tarradellas, J.},
     TITLE = {Organic pollutants in compost and digestate.  {P}art 1. {P}olychlorinated biphenyls, polycyclic aromatic hydrocarbons and markers},
      YEAR = {2007},
   JOURNAL = {J. Environ. Monit.},
  FJOURNAL = {Journal of Environmental Moniting},
    VOLUME = {9},
     PAGES = {456-464},
       DOI = {10.1039/b617101j},
      PMID = {17492091},
}
Furrer, R. and Naveau, P. (2007). Probability Weighted Moments Properties for Small Samples. Statistics and Probability Letters, 77(2), 190-195, doi:10.1016/j.spl.2006.06.009.     [Abstract] [BibTeX]
Abstract: Probability weighted moments (PWM) are classically used in hydrology. Here we study their properties for small samples. Links between PWMs and the hazard rate ordering are identified. We propose PWM tail equivalences and derive explicit variances for PWM unbiased estimators.

Keywords: Generalized Pareto distribution; U-statistics

BibTeX:
@ARTICLE {Furr:Nave:07,
    AUTHOR = {Furrer, R. and Naveau, P.},
     TITLE = {Probability Weighted Moments Properties for Small Samples},
   JOURNAL = {Statist. Probab. Lett.},
  FJOURNAL = {Statistics and Probability Letters},
    VOLUME = {77},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {190-195},
}
Furrer, R. and Bengtsson, T. (2007). Estimation of High-dimensional Prior and Posteriori Covariance Matrices in Kalman Filter Variants. Journal of Multivariate Analysis, 98(2), 227-255, doi:10.1016/j.jmva.2006.08.003.     [Abstract] [BibTeX]
Abstract: This work studies the effects of sampling variability in Monte Carlo-based methods to estimate very highdimensional systems. Recent focus in the geosciences has been on representing the atmospheric state using a probability density function, and, for extremely high-dimensional systems, various sample-based Kalman filter techniques have been developed to address the problem of real-time assimilation of system information and observations. As the employed sample sizes are typically several orders of magnitude smaller than the system dimension, such sampling techniques inevitably induce considerable variability into the state estimate, primarily through prior and posterior sample covariance matrices. In this article, we quantify this variability with mean squared error measures for two Monte Carlo-based Kalman filter variants: the ensemble Kalman filter and the ensemble square-root Kalman filter. Expressions of the error measures are derived under weak assumptions and show that sample sizes need to grow proportionally to the square of the system dimension for bounded error growth. To reduce necessary ensemble size requirements and to address rank-deficient sample covariances, covariance-shrinking (tapering) based on the Schur product of the prior sample covariance and a positive definite function is demonstrated to be a simple, computationally feasible, and very effective technique. Rules for obtaining optimal taper functions for both stationary as well as non-stationary covariances are given, and optimal taper lengths are given in terms of the ensemble size and practical range of the forecast covariance. Results are also presented for optimal covariance inflation. The theory is verified and illustrated with extensive simulations.

Keywords: Ensemble Kalman filter; Square-root filter; Matrix expansions; Shrinking; Tapering; Covariance boosting

BibTeX:
@ARTICLE{Furr:Beng:05,
    AUTHOR = {Furrer, R. and Bengtsson, T.},
      YEAR = {2007},
     TITLE = {Estimation of High-dimensional Prior and Posteriori Covariance Matrices in Kalman Filter Variants},
   JOURNAL = {J. Multivariate Anal.},
  FJOURNAL = {Journal of Multivariate Analysis},
    VOLUME = {98},
    NUMBER = {2},
     PAGES = {227-255},
       DOI = {10.1016/j.jmva.2006.08.003},
}
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2006

Furrer, R., Genton, M. G. and Nychka, D. (2006). Covariance Tapering for Interpolation of Large Spatial Datasets. Journal of Computational and Graphical Statistics 15(3), 502-523.     [Abstract] [BibTeX] [precipitation dataset, "read me"]
Abstract: Interpolation of a spatially correlated random process is used in many scientific areas. The best unbiased linear predictor, often called a kriging predictor in geostatistical science, requires the solution of a (possibly large) linear system based on the covariance matrix of the observations. In this article, we show that tapering the correct covariance matrix with an appropriate compactly supported positive definite function reduces the computational burden significantly and still leads to an asymptotically optimal mean squared error. The effect of tapering is to create a sparse approximate linear system that can then be solved using sparse matrix algorithms. Monte Carlo simulations support the theoretical results. An application to a large climatological precipitation dataset is presented as a concrete and practical illustration.

Keywords: asymptotic optimality, compactly supported covariance, kriging, large linear systems, sparse matrix.

BibTeX:
 @ARTICLE{Furr:Gent:Nych:06,
    AUTHOR = {R. Furrer and M. G. Genton and D. Nychka},
     TITLE = {Covariance Tapering for Interpolation of Large Spatial Datasets},
      YEAR = {2006},	
   JOURNAL = {J. Comput. Graph. Stat.},
  FJOURNAL = {Journal of Computational and Graphical Statistics},
    VOLUME = {15},
    NUMBER = {3},
     PAGES = {502-523},
}
Feingold, G., Furrer, R., Pilewskie, P., Remer L. A., Min, Q. and Jonsson H. (2006). Aerosol Indirect Effect Studies at Southern Great Plains during the May 2003 Intensive Operation Period. Journal of Geophysical Research. 111, D05S14, doi:10.1029/2004JD005648.     [Abstract] [BibTeX]
Abstract: During May 2003 the Department of Energy's Atmospheric Radiation Measurement Program conducted an Intensive Operations Period (IOP) to measure the radiative effects of aerosol and clouds. A suite of both in situ and remote sensing measurements were available to measure aerosol and cloud parameters. This paper has three main goals: First, it focuses on comparison between in situ retrievals of the radiatively important drop effective radius re and various satellite, airborne, and surface remote sensing retrievals of the same parameter. On 17 May 2003, there was a fortuitous, near-simultaneous sampling of a stratus cloud by five different methods. The retrievals of re agree with one another to within ~20%, which is approximately the error estimate for most methods. Second, a methodology for deriving a best estimate of re from these different instruments, with their different physical properties and sampling volumes, is proposed and applied to the 17 May event. Third, the paper examines the response of re to changes in aerosol on 3 days during the experiment and examines the consistency of remote sensing and in situ measurements of the effect of aerosol on re. It is shown that in spite of the generally good agreement in derived re, the magnitude of the response of re to changes in aerosol is quite sensitive to the method of retrieving re and to the aerosol proxy for cloud condensation nuclei. Nonphysical responses are sometimes noted, and it is suggested that further work needs to be done to refine these techniques.
BibTeX:
@ARTICLE{Fein:Furr:Pile:Reme:Min:Jons:07,
    AUTHOR = {Feingold, G. and Furrer, R. and Pilewskie, P. and Remer, L. A. and Min, Q. and Jonsson, H.},
      YEAR = {2006},
     TITLE = {Aerosol Indirect Effect Studies at Southern Great Plains during the May 2003 Intensive Operation Period},
   JOURNAL = {J. Geophys. Res.},
  FJOURNAL = {Journal of Geophysical Research},
    VOLUME = {111},
     PAGES = {D05S14},
       DOI = {10.1029/2004JD005648},
}
Plagellat, C., Kupper, T., Furrer, R., de Alencastro, L. F., Grandjean, D. and Tarradellas, J. (2006). Concentrations and Specific Loads of UV Filters in Sewage Sludge Originating from a Monitoring Network in Switzerland. Chemosphere, 62, 915-925, doi:10.1016/j.chemosphere.2005.05.024.     [Abstract] [BibTeX]
Abstract: Many substances related to human activities end up in wastewater and accumulate in sewage sludge. The present study focuses on the analysis of widely used UV filters 3-(4-methylbenzylidene) camphor (4-MBC), octyl-methoxycinnamate (OMC), octocrylene (OC) and octyl-triazone (OT) in sewage sludge originating from a monitoring network in Switzerland. Mean concentrations in stabilised sludge from 14 wastewater treatment plants were 1780, 110, 4840 and 5510 lg/kg dry matter for 4-MBC, OMC, OC and OT, respectively. Specific loads in sewage sludge show that UV filters originate mainly from private households, but surface runoff and industries may be considered as additional sources. This indicates that besides use for sunscreens and cosmetics UV filters might occur in plastics and other materials and be released to the environment by volatilization or leaching. Differences between the modeled per capita loads of UV filters in sewage sludge and the observed specific loads in sewage sludge are probably due to erroneous figures of production volumes, degradation and sorption during wastewater treatment as well as degradation processes during transport in the sewer or sludge treatment. Thus, further research is needed to elucidate the fate of UV filters after application and release into the environment. Other compounds used as UV filters should be included in future studies.

Keywords: Chemical analysis; Sources; Wastewater treatment plant; Sunscreen agents; UV screens; Personal care products

BibTeX:
@ARTICLE{Plag:Kupp:Furr:deAl:Gran:Tarr:06,
    AUTHOR = "C\'ecile Plagellat and Thomas Kupper and Reinhard Furrer and Luiz Felippe de Alencastro and Dominique Grandjean and Joseph Tarradellas",
     TITLE = "Concentrations and specific loads of UV filters in sewage sludge originating from a monitoring network in Switzerland",
   JOURNAL = "Chemosphere",
  FJOURNAL = "Chemosphere", 
    VOLUME = "62",
    NUMBER = "6",
     PAGES = "915-925",
      YEAR = "2006", 
       DOI = "10.1016/j.chemosphere.2005.05.024",
      PMID = {15996716},
}
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2005

Fournier, B. and Furrer, R. (2005). Automatic Mapping in the Presence of Substitutive Errors: A Robust Kriging Approach. Extended Abstract in Automatic mapping algorithms for routine and emergency monitoring data. Report on the Spatial Interpolation Comparison (SIC2004) exercise, Dubois, G. ed. Office for Official Publications of the European Communities, Luxembourg, EUR 21595 EN, ISBN: 92-894-9400-X.    
Fournier, B. and Furrer, R. (2005). Automatic Mapping in the Presence of Substitutive Errors: A Robust Kriging Approach. Applied GIS 1(2), doi:10.2104/ag050012.     [Abstract] [BibTeX]
Abstract: Interpolation of a spatially correlated random process is used in many scientific domains. The best unbiased linear predictor (BLUP), often called kriging predictor in geostatistical science, is sensitive to outliers. The literature contains a few attempts to robustify the kriging predictor, however none of them is completely satisfactory. In this article, we present a new robust linear predictor for a substitutive error model. First, we derive a BLUP, which is computationally very expensive even for moderate sample sizes. A forward search type algorithm is used to derive the predictor resulting in a linear likelihood-weighted mean procedure that is robust with respect to substitutive errors. Monte Carlo simulations support the theoretical results. The new predictor is applied to the two SIC2004 data sets and is evaluated with respect to automatic interpolation and monitoring.
BibTeX:
@ARTICLE{Four:Furr:05a,
    AUTHOR = {Fournier, B. and Furrer, R.},
      YEAR = {2005},
     TITLE = {Automatic Mapping in the Presence of Substitutive Errors: A Robust Kriging Approach},
   JOURNAL = {Applied GIS},
  FJOURNAL = {Applied GIS},
    VOLUME = {1},
    NUMBER = {2},
       DOI = {10.2104/ag050012},  
}
Brändli, R., Kupper, T., Bucheli, T. D., Furrer, R., Stadelmann, F. X. and Tarradellas, J. (2005). Persistent Organic Pollutants in Compost and its Input Materials - A Review of Field Studies. Journal of Environmental Quality 34(3), 735-760, doi:10.2134/jeq2004.0333.     [Abstract] [BibTeX]
Abstract: Received for publication August 27, 2004. Composting and the application of compost to the soil follow the principle of recycling and sustainability. Compost can also have a positive effect on physical, chemical, and biological soil parameters. However, little is known about the origin, concentration, and transformation of persistent organic pollutants (POPs) in compost. We therefore compiled literature data on some priority POPs in compost and its main feedstock materials from more than 60 reports. Our data evaluation suggests the following findings. First, median concentrations of {Sigma} 16 polycyclic aromatic hydrocarbons (PAHs), {Sigma} 6 polychlorinated biphenyls (PCBs), and {Sigma} 17 polychlorinated dibenzo-p-dioxins and -furans (PCDD/Fs) were higher in green waste (1803, 15.6 µg/kg dry wt., and 2.5 ng international toxicity equivalent [I-TEQ]/kg dry wt.) than in organic household waste (635, 14.6 µg/kg dry wt., and 2.2 ng I-TEQ/kg dry wt.) and kitchen waste (not available [NA], 14.9 µg/kg dry wt., 0.4 ng I-TEQ/kg dry wt.). The POP concentrations in foliage were up to 12 times higher than in other feedstock materials. Second, in contrast, compost from organic household waste and green waste contained similar amounts of {Sigma} 16 PAHs, {Sigma} 6 PCBs, and {Sigma} 17 PCDD/Fs (1915, 39.8 µg/kg dry wt., and 9.5 ng I-TEQ/kg dry wt., and 1715, 30.6 µg/kg dry wt., and 8.5 ng I-TEQ/kg dry wt., respectively). Third, concentrations of three-ring PAHs were reduced during the composting process, whereas five- to six-ring PAHs and {Sigma} 6 PCBs increased by roughly a factor of two due to mass reduction during composting. {Sigma} 17 PCDD/Fs had accumulated by up to a factor of 14. Fourth, urban feedstock and compost had higher POP concentrations than rural material. Fifth, the highest concentrations of POPs were usually observed in summer samples. Finally, median compost concentrations of POPs were greater by up to one order of magnitude than in arable soils, as the primary recipients of compost, but were well within the range of many urban soils. In conclusion, this work provides a basis for the further improvement of composting and for future risk assessments of compost application.
BibTeX:
@ARTICLE{Brae:Kupp:Buch:Furr:Stad:Tarr:05,
    AUTHOR = {Rahel C. Br\"andli and Thomas D. Bucheli and Thomas Kupper and Reinhard Furrer and Franz X. Stadelmann and Joseph Tarradellas},
      YEAR = {2005},
     TITLE = {Persistent Organic Pollutants in Source-Separated Compost and Its Feedstock Materials—A Review of Field Studies},
   JOURNAL = {J. Environ. Qual.},
  FJOURNAL = {Journal of Environmental Quality},
    VOLUME = {34},
     PAGES = {735-760},
       DOI = {10.2134/jeq2004.0333},  
      PMID = {15843638},
}
Furrer, R. (2005). Covariance Estimation under Spatial Dependence. Journal of Multivariate Analysis, 94(2), 366-381, doi:10.1016/j.jmva.2004.05.009.     [Abstract] [BibTeX]
Abstract:
BibTeX:
@ARTICLE{Furr:05,
    AUTHOR = {Furrer, R.},
      YEAR = {2005},
     TITLE = {Covariance Estimation under Spatial Dependence},
   JOURNAL = {J. Multivariate Anal.},
  FJOURNAL = {Journal of Multivariate Analysis},
    VOLUME = {94},
    NUMBER = {2},
     PAGES = {366-381},
       DOI = {10.1016/j.jmva.2004.05.009},  
}
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2004

Sain, S. R. and Furrer, R. (2004). Fitting Large-Scale Spatial Models with Applications to Microarray Data Analysis. Computing Science and Statistics (Proceedings of Interface 2004: Computational Biology and Bioinformatics), 36, 869--883.     [Abstract] [BibTeX]
Abstract:
BibTeX:
@INPROCEEDINGS{Sain:Furr:04,
     AUTHOR = {S. R. Sain and R. Furrer},
      title = {Fitting Large-Scale Spatial Models with Applications to Microarray Data Analysis},
  BOOKTITLE = {Proceedings Interface 2004},
   FJOURNAL = {Computing Science and Statistics},
       YEAR = {2004},
     VOLUME = {36},
      PAGES = {869--883},
        URL = {http://www.interfacesymposia.org/I04/I2004Proceedings/SainStephan/SainStephan.paper.pdf}
 }
Kupper, T., Berset, J. D., Etter-Holzer, R., Furrer, R. and Tarradellas, J. (2004). Concentrations and Specific Loads of Polycyclic Musks in Sewage Sludge Originating from a Monitoring Network in Switzerland. Chemosphere, 54(8), 1111-1120, doi:10.1016/j.chemosphere.2003.09.023.     [Abstract] [BibTeX]
Abstract:
BibTeX:
@ARTICLE{Kupp:Bers:Ette:Furr:Tarr:04,
  AUTHOR = "T. Kupper and J. D. Berset and R. Etter-Holzer and R. Furrer and J. Tarradellas",
   TITLE = "Concentrations and specific loads of polycyclic musks in sewage sludge originating from a monitoring network in {S}witzerland",
 JOURNAL = "Chemosphere",
FJOURNAL = "Chemosphere",
  VOLUME = "54",
  NUMBER = "8",
   PAGES = "1111-1120",
    YEAR = "2004",
     DOI = "10.1016/j.chemosphere.2003.09.023",
    PMID = {14664839},
}
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2003

Fournier, B., Furrer, R., Gsponer, T. and Restle, E.-M. (2003), Editors. Proceedings of the 13th European Young Statisticans Meeting, September 21-26, Ovronnaz, Switzerland, Stämpfli AG, ISBN 3-908152-17-8.    
Naveau, P., Furrer, R. and Keckhut, P. (2003). The spatio-temporal influence of the vortex on Artic Total Column Ozone variability, in The ISI International Conference on Environmental Statistics and Health, Mateu, J., Holland, D. González-Manteiga, W. (eds), 131-140.     [Abstract]
Genton, M. G. and Furrer, R. (2003). Analysis of Rainfall Data by Simple Good Sense: is Spatial Statistics Worth the Trouble?, in Mapping radioactivity in the environment - Spatial Interpolation Comparison 97, Dubois, G., Malczewski, J., and De Cort M. (eds), 45-50.     [Abstract]
Genton, M. G. and Furrer, R. (2003). Analysis of Rainfall Data by Robust Spatial Statistics using S+SpatialStats, in Mapping radioactivity in the environment - Spatial Interpolation Comparison 97, G. Dubois, J. Malczewski, M. De Cort (eds), 118-129.     [Abstract]
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2002

Furrer, R. (2002). M-Estimation for Dependent Random Variables. Statistics and Probabability Letters, 57(4), 337-341, doi:10.1016/S0167-7152(02)00084-6. [Abstract] [BibTeX]
BibTeX:
@ARTICLE{Furr:02b,
  AUTHOR = "Reinhard Furrer",
   TITLE = "M-Estimation for dependent random variables",
 JOURNAL = "Statist. Probab. Lett.",
FJOURNAL = "Statistics & Probability Letters",
  VOLUME = "57",
  NUMBER = "4",
   PAGES = "337-341",
    YEAR = "2002",
     DOI = "10.1016/S0167-7152(02)00084-6",
}
Furrer, R. (2002). Aspects of Modern Geostatistics: Nonstationarity, Covariance Estimation and State-Space Decompositions. Doctoral thesis under the supervision of Prof. Stephan Morgenthaler.     [Abstract] [BibTeX]
Abstract:
BibTeX:
@PHDTHESIS{Furr:02,
  AUTHOR = {R. Furrer},
   TITLE = {Aspects of Modern Geostatistics: Nonstationarity, Covariance Estimation and State-Space Decompositions},
  SCHOOL = {Swiss Federal Insitute of Technology},
    YEAR = {2002},
}
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2001

Furrer, R. (2001). Observation-State Representation of Non Stationary Spatial Processes. Proceedings of the 12th European Young Statisticians Meeting, Jánska Dolina, Slovakia, 15.    
Furrer, R. (2001). Non Parametric Estimation within Decomposed Spatial Processes. Proceedings of the International Conference of the Royal Statistical Society (RSS2001), University of Glasgow, Scotland, 51.    
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2000

Furrer, R. (2000). On the Implementation of the Decomposition of Spatial Processes in Matlab. Computing Science and Statistics. Vol. 32, 64-77.     [Abstract]
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1999

Furrer, R. (1999). Covariance Estimation under Spatial Dependence. Proceedings in Spatial Temporal Modelling and its Applictions. Edited by Mardia, K. V., Aykroyd, R. G. and Dryden, I. L. Leeds University Press, Leeds, 137-140.     [Abstract]
Furrer, R. and Genton, M. G. (1999). Robust Spatial Data Analysis of Lake Geneva Sediments with S+SpatialStats. Systems Research and Information Science, Special Issue on Spatial Data: Neural Nets/Statistics, 8(4), 257-272.     [Abstract] [BibTeX]
Abstract: This paper discusses the use of robust geostatistical methods on a multivariate data set of sediments in the Lake Geneva in Switzerland. Each variable is detrended via nonparametric estimation penalized with a smoothing parameter. The optimal trend is computed with a smoothing parameter based on cross-validation. Then, variograms are estimated by a highly robust estimator of scale. The parametric variogram models are fitted by generalized least squares, thus taking account of the variance-covariance structure of the variogram estimates. Kriging has been performed inside the Lake Geneva boundaries, and results are in close agreements with the geographical surroundings. The comparison of the kriging results with and without detrending the data relieved the importance of the trend detection and tren d removing, and that a simple model with constant trend for this data set is not satisfactory. All these computations are done with the software {\sc S+SpatialStats}, extended with new functions in {\sc S+} that are made available.
BibTeX:
@ARTICLE{Furr:Gent:99,
  AUTHOR = 	 {Furrer, R. and Genton, M. G.},
  TITLE = 	 {Robust Spatial Data Analysis of Lake Geneva Sediments with S+SpatialStats},
  JOURNAL = 	 {Syst. Res. Inform. Sci.},
  FJOURNAL = 	 {Systems Research and Information Science},
  YEAR = 	 {1999},
  VOLUME = 	 {8},
  NUMBER = 	 {4},
  PAGES = 	 {257--272},
  OPTannote = 	 {Special Issue on Spatial Data: Neural Nets/Statistics}
}
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1998

Furrer, R. (1998). Principal Component Analysis of Lake Geneva Sediments. Proceedings of the Fourth Annual Conference of the International Association for Mathematical Geology . Edited by, Buccianti, A., Nardi, G. and Potenza, R., De Frede Editore, Napoli, 421-426.     [Abstract]
Genton, M. G. and Furrer, R. (1998). Analysis of Rainfall Data by Robust Spatial Statistics using S+SpatialStats. Journal of Geographic Information and Decision Analysis, Vol. 2, No. 2, 126-136.     [Abstract] [BibTeX]
BibTeX:
@ARTICLE{Gent:Furr:98b,
  AUTHOR =       "M. G. Genton and R. Furrer",
  TITLE =        "Analysis of Rainfall Data by Robust Spatial Statistics using {S+SpatialStats}",
  JOURNAL =      "Journal of Geographic Information and Decision Analysis",
  VOLUME =       "2",
  YEAR =         "1998",
  NUMBER =       "2",
  PAGES =        "126--136",
}
Genton, M. G. and Furrer, R. (1998). Analysis of Rainfall Data by Simple Good Sense: is Spatial Statistics Worth the Trouble?. Journal of Geographic Information and Decision Analysis, Vol. 2, No. 2, 11-17.     [Abstract] [BibTeX]
BibTeX:
@ARTICLE{Gent:Furr:98a,
  AUTHOR =       "M. G. Genton and R. Furrer",
  TITLE =        "Analysis of Rainfall Data by Simple Good Sense: Is Spatial Statistics Worth the Trouble?",
  JOURNAL =      "Journal of Geographic Information and Decision Analysis",
  VOLUME =       "2",
  YEAR =         "1998",
  NUMBER =       "2",
  PAGES =        "11--17",
}
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top home Last modified May 19 2014 by reinhard. furrer @ math. uzh. ch I-MATH UZH