arXiv subjects

Reinhard Furrer

Publications and source records attributed to Reinhard Furrer.

43 records · Page 3Linked to original sources

arXiv2016

On the smallest eigenvalues of covariance matrices of multivariate spatial processes

There has been a growing interest in providing models for multivariate spatial processes. A majority of these models specify a parametric matrix covariance function. Based on observations, the parameters are estimated by maximum likelihood or variants thereof. While the asymptotic properties of maximum likelihood estimators for univariate spatial processes have been analyzed in detail, maximum likelihood estimators for multivariate spatial processes have not received their deserved attention yet. In this article we consider the classical increasing-domain asymptotic setting restricting the minimum distance between the locations. Then, one of the main components to be studied from a theoretical point of view is the asymptotic positive definiteness of the underlying covariance matrix. Based on very weak assumptions on the matrix covariance function we show that the smallest eigenvalue of the covariance matrix is asymptotically bounded away from zero. Several practical implications are discussed as well.

math.ST↗

arXiv2014

Hierarchical modelling of faecal egg counts to assess anthelmintic efficacy

Counting the number of parasite eggs in faecal samples is a widely used diagnostic method to evaluate parasite burden. Typically a sub-sample of the diluted faeces is examined for eggs. The resulting egg counts are multiplied by a specific correction factor to estimate the mean parasite burden. To detect anthelmintic resistance, the mean parasite burden from treated and untreated animals are compared. However, this standard method has some limitations. In particular, the analysis of repeated samples may produce quite variable results as the sampling variability due to the counting technique is ignored. We propose a hierarchical model that takes this sampling variability as well as between-animal variation into account. Bayesian inference is done via Markov chain Monte Carlo sampling. The performance of the hierarchical model is illustrated by a re-analysis of faecal egg count data from a Swedish study assessing the anthelmintic resistance of nematode parasite in sheep. A simulation study shows that the hierarchical model provides better classification of anthelmintic resistance compared to the standard method.

stat.AP↗

arXiv2013

Intelligent Compaction and Quality Assurance of Roller Measurement Values utilizing Backfitting and Multiresolution Scale Space Analysis

Modern earthwork compaction rollers collect location and compaction information as they traverse a compaction site. These roller measurement values present a challenging spatio-temporal statistical problem that requires careful implementation of a proper stochastic model and estimation procedure. Heersink and Furrer (2013) proposed a sequential, spatial mixed-effects model and a sequential, spatial backfitting routine for estimation of the modeling terms for such data. The estimated fields produced from this backfitting procedure are analyzed using a multiresolution scale space analysis developed by Holmstrom et al. (2011). This image analysis is proposed as a viable solution to improved intelligent compaction and quality assurance of the compaction process.

stat.AP↗

arXiv2013

Conjugate distributions in hierarchical Bayesian ANOVA for computational efficiency and assessments of both practical and statistical significance

Assessing variability according to distinct factors in data is a fundamental technique of statistics. The method commonly regarded to as analysis of variance (ANOVA) is, however, typically confined to the case where all levels of a factor are present in the data (i.e. the population of factor levels has been exhausted). Random and mixed effects models are used for more elaborate cases, but require distinct nomenclature, concepts and theory, as well as distinct inferential procedures. Following a hierarchical Bayesian approach, a comprehensive ANOVA framework is shown, which unifies the above statistical models, emphasizes practical rather than statistical significance, addresses issues of parameter identifiability for random effects, and provides straightforward computational procedures for inferential steps. Although this is done in a rigorous manner the contents herein can be seen as ideological in supporting a shift in the approach taken towards analysis of variance.

stat.ME↗

arXiv2013

Spatial Backfitting of Roller Measurement Values from a Florida Test Bed

Modern earthwork compaction rollers collect location and compaction information as they traverse a compaction site. These data are indirectly observed through non-linear measurement operators, inherently multivariate with complex correlation structures, and collected in huge quantities. The nature of such data was investigated at a large, atypically compacted test bed in Florida, USA. Exploratory analysis of this data through detrending and empirical semivariogram estimation is performed. A second analysis using a sequential, spatial backfitting algorithm is used to investigate the importance of driving direction of the roller.

stat.AP↗

arXiv2012

MMANOVA: A general multilevel framework for multivariate analysis of variance

Classical analysis of variance requires that model terms be labeled as fixed or random and typically culminate by comparing variability from each batch (factor) to variability from errors; without a standard methodology to assess the magnitude of a batch's variability, to compare variability between batches, nor to consider the uncertainty in this assessment. In this paper we support recent work, placing ANOVA into a general multilevel framework, then refine this through batch level model specifications, and develop it further by extension to the multivariate case. Adopting a Bayesian multilevel model parametrization, with improper batch level prior densities, we derive a method that facilitates comparison across all sources of variability. Whereas classical multivariate ANOVA often utilizes a single covariance criterion, e.g. determinant for Wilks' lambda distribution, the method allows arbitrary covariance criteria to be employed. The proposed method also addresses computation. By introducing implicit batch level constraints, which yield improper priors, the full posterior is efficiently factored, thus alleviating computational demands. For a large class of models, the partitioning mitigates, or even obviates the need for methods such as MCMC. The method is illustrated with simulated examples and an application focusing on climate projections with global climate models.

stat.ME↗

arXiv2011

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.

stat.AP↗