Edge effects and efficient parameter estimation for stationary random fields

We consider the estimation of the parameters of a stationary random field on d-dimensional lattice by minimizing the classical Whittle approximation to the Gaussian log likelihood. If the usual biased sample covariances are used, the estimate is efficient only in one dimension. To remove this edge effect, we introduce data tapers and show that the resulting modified estimate is efficient also in two and three dimensions. This avoids the use of the unbiased sample covariances which are in general not positive-definit

Bridging the ensemble Kalman and particle filters

In many applications of Monte Carlo nonlinear filtering, the propagation step is computationally expensive, and hence the sample size is limited. With small sample sizes, the update step becomes crucial. Particle filtering suffers from the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids this, at the expense of treating non-Gaussian features of the forecast distribution incorrectly. Here we introduce a procedure that makes a continuous transition indexed by γ∈[0,1] between the ensemble and the particle filter update. We propose automatic choices of the parameter γ such that the update stays as close as possible to the particle filter update subject to avoiding degeneracy. In various examples, we show that this procedure leads to updates that are able to handle non-Gaussian features of the forecast sample even in high-dimensional situation

Generalized cross-covariances and their estimation

Generalized cross-covariances describe the linear relationships between spatial variables observed at different locations. They are invariant under translation of the locations for any intrinsic processes, they determine the cokriging predictors without additional assumptions and they are unique up to linear functions. If the model is stationary, that is if the variograms are bounded, they correspond to the stationary cross-covariances. Under some symmetry condition they are equal to minus the usual cross-variogram. We present a method to estimate these generalized cross-covariances from data observed at arbitrary sampling locations. In particular we do not require that all variables are observed at the same points. For fitting a linear coregionalization model we combine this new method with a standard algorithm which ensures positive definite coregionalization matrices. We study the behavior of the method both by computing variances exactly and by simulating from various model

Karotten von der Saat bis zum Teller - Einfluss von Sorte Standort, Jahr und Anbauweise auf den Mineralstoffgehalt

Wie wertvoll sind Karotten für unsere Ernährung? Die Fachwelt ist sich einig, dass der tägliche Konsum von Früchten und Gemüse erhöht werden soll. Es gibt jedoch Presseberichte, die den ernährungsphysiologischen Wert von heutigem Gemüse hinterfragen. Die Rolle der Karotte als Mineralstoffquelle wird durchleuchtet

Bayesian multi-model projection of climate: bias assumptions and interannual variability

Current climate change projections are based on comprehensive multi-model ensembles of global and regional climate simulations. Application of this information to impact studies requires a combined probabilistic estimate taking into account the different models and their performance under current climatic conditions. Here we present a Bayesian statistical model for the distribution of seasonal mean surface temperatures for control and scenario periods. The model combines observational data for the control period with the output of regional climate models (RCMs) driven by different global climate models (GCMs). The proposed Bayesian methodology addresses seasonal mean temperatures and considers both changes in mean temperature and interannual variability. In addition, unlike previous studies, our methodology explicitly considers model biases that are allowed to be time-dependent (i.e. change between control and scenario period). More specifically, the model considers additive and multiplicative model biases for each RCM and introduces two plausible assumptions ("constant bias” and "constant relationship”) about extrapolating the biases from the control to the scenario period. The resulting identifiability problem is resolved by using informative priors for the bias changes. A sensitivity analysis illustrates the role of the informative prior. As an example, we present results for Alpine winter and summer temperatures for control (1961-1990) and scenario periods (2071-2100) under the SRES A2 greenhouse gas scenario. For winter, both bias assumptions yield a comparable mean warming of 3.5-3.6°C. For summer, the two different assumptions have a strong influence on the probabilistic prediction of mean warming, which amounts to 5.4°C and 3.4°C for the "constant bias” and "constant relation” assumptions, respectively. Analysis shows that the underlying reason for this large uncertainty is due to the overestimation of summer interannual variability in all models considered. Our results show the necessity to consider potential bias changes when projecting climate under an emission scenario. Further work is needed to determine how bias information can be exploited for this tas

Karotten von der Saat bis zum Teller - Einfluss von Sorte, Standort, Jahr, Anbauweise und Lagerung auf den Carotingehalt

Karotten sind ergiebige Quellen an a- und ß-Carotin und weiterer sekundärer Pflanzenstoffe (SPS). Es ist bekannt, dass viele SPS auch für Geschmack, Aroma und Farbe eine Rolle spielen. Der Einfluss von Vorernte- und Nacherntefaktoren auf den Gehalt an SPS gewinnt deshalb zunehmend an Bedeutung. Für die Entwicklung eines Qualitätssicherungskonzepts sind die Kenntnisse über die Auswirkung dieser Faktoren unumgänglich

Using the Bootstrap to test for symmetry under unknown dependence

This paper considers tests for symmetry of the one-dimensional marginal distribution of fractionally integrated processes. The tests are implemented by using an autoregressive sieve bootstrap approximation to the null sampling distribution of the relevant test statistics. The sieve bootstrap allows inference on symmetry to be carried out without knowledge of either the memory parameter of the data or of the appropriate norming factor for the test statistic and its asymptotic distribution. The small-sample properties of the proposed method are examined by means of Monte Carlo experiments, and applications to real-world data are also presented

Super-resolution in map-making based on a physical instrument model and regularized inversion. Application to SPIRE/Herschel

We investigate super-resolution methods for image reconstruction from data provided by a family of scanning instruments like the Herschel observatory. To do this, we constructed a model of the instrument that faithfully reflects the physical reality, accurately taking the acquisition process into account to explain the data in a reliable manner. The inversion, ie the image reconstruction process, is based on a linear approach resulting from a quadratic regularized criterion and numerical optimization tools. The application concerns the reconstruction of maps for the SPIRE instrument of the Herschel observatory. The numerical evaluation uses simulated and real data to compare the standard tool (coaddition) and the proposed method. The inversion approach is capable to restore spatial frequencies over a bandwidth four times that possible with coaddition and thus to correctly show details invisible on standard maps. The approach is also applied to real data with significant improvement in spatial resolution.Comment: Astronomy & Astrophysic