inconsistent estimation and asymptotically equal interpolations in model based geostatistics it is shown that in model based geostatistics not all parameters in the matern class can be estimated consistently if data are observed in an increasing density in a fixed domain regardless of the estimation methods used nevertheless one quantity can be estimated consistently by the maximum likelihood method and this quantity is more important to spatial interpolation the results are established by using the properties of equivalence and orthogonality of probability measures some sufficient conditions are provided for both gaussian and non gaussian equivalent measures and necessary conditions are provided for gaussian equivalent measures two simulation studies are presented that show that the fixed domain asymptotic properties can explain some finite sample behavior of both interpolation and estimation when the sample size is moderately large

estimation of nonstationary spatial covariance structure summary we introduce a method for estimating nonstationary spatial covariance structure from space time data and apply the method to an analysis of sydney wind patterns our method constructs a process honouring a given spatial covariance matrix at observing stations and uses one or more stationary processes to describe conditional behaviour given observing site values the stationary processes give a localised description of the spatial covariance structure the method is computationally attractive and can be extended to the assessment of covariance for multivariate processes the technique is illustrated for data describing the east west component of sydney winds for this example our own methods are contrasted with a geometrically appealing though computationally intensive technique which describes spatial correlation via an isotropic process and a deformation of the geographical space

generalized kahler manifolds commuting complex structures and split tangent bundles we study generalized kahler manifolds for which the corresponding complex structures commute and classify completely the compact four dimensional ones

spatio temporal covariance and cross covariance functions of the great circle distance on a sphere abstractin this article we propose stationary covariance functions for processes that evolve temporally over a sphere as well as cross covariance functions for multivariate random fields defined over a sphere for such processes the great circle distance is the natural metric that should be used to describe spatial dependence given the mathematical difficulties for the construction of covariance functions for processes defined over spheres cross time approximations of the state of nature have been proposed in the literature by using the euclidean based on map projections and the chordal distances we present several methods of construction based on the great circle distance and provide closed form expressions for both spatio temporal and multivariate cases a simulation study assesses the discrepancy between the great circle distance chordal distance and euclidean distance based on a map projection both in terms of estimation and prediction in a space time and a bivariate spatial setting where t

invariant and homogeneous bundles on g γ abstract let be a cocompact lattice in a connected complex lie group g given an invariant holomorphic vector bundle e on g we show that there is a trivial holomorphic subbundle f e such that any holomorphic section of e factors through holomorphic sections of f given two homomorphisms 1 and 2 from to a complex linear algebraic lie group h with relatively compact image we prove that any holomorphic isomorphism between the associated holomorphic principal h bundles e h 1 and e h 2 is automatically g equivariant

unobstructed k deformations of generalized complex structures and bi hermitian structures abstract we introduce k deformations of generalized complex structures on a compact kahler manifold m x j with an effective anti canonical divisor and show that obstructions to k deformations of generalized complex structures on m always vanish applying unobstructed k deformations and the stability theorem for generalized kahler structures we construct deformations of bi hermitian structures in the form j j t h t on a compact kahler surface with a non zero holomorphic poisson structure then we prove that a compact kahler surface s admits a non trivial bi hermitian structure with the torsion condition and the same orientation if and only if s has a non zero holomorphic poisson structure we also obtain bi hermitian structures j j h on del pezzo surfaces degenerate del pezzo surfaces and some ruled surfaces for which the complex structure j is not equivalent to j under diffeomorphisms

generalized kahler manifolds and off shell supersymmetry we solve the long standing problem of finding an off shell supersymmetric formulation for a general n 2 2 nonlinear two dimensional sigma model geometrically the problem is equivalent to proving the existence of special coordinates these correspond to particular superfields that allow for a superspace description we construct and explain the geometric significance of the generalized kahler potential for any generalized kahler manifold this potential is the superspace lagrangian

modeling tangential vector fields on a sphere abstractphysical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences these naturally occurring vector fields are often subject to physical constraints such as being curl free or divergence free we start with constructing parametric models for curl free and divergence free vector fields that are tangential to the unit sphere through applying the surface gradient or the surface curl operator to a scalar random potential field on the unit sphere using the helmholtz hodge decomposition we then construct a class of simple but flexible parametric models for general tangential vector fields which are represented as a sum of a curl free and a divergence free components we propose a likelihood based parameter estimation procedure and show that fast computation is possible even for large data sets when the observations are on a regular latitude longitude grid characteristics and practical utility of the proposed methodology are illustrated th

instantons poisson structures and generalized kahler geometry using the idea of a generalized kahler structure we construct bihermitian metrics on cp2 and cp1 cp1 and show that any such structure on a compact 4 manifold m defines one on the moduli space of anti self dual connections on a fixed principal bundle over m we highlight the role of holomorphic poisson structures in all these constructions

ito sde based generator for a class of non gaussian vector valued random fields in uncertainty quantification this paper is concerned with the derivation of a generic sampling technique for a class of non gaussian vector valued random fields such an issue typically arises in uncertainty quantification for complex systems where the input coefficients associated with the elliptic operators must be identified by solving statistical inverse problems specifically we consider the case of non gaussian random fields with values in some arbitrary bounded or semi bounded subsets of r n the approach involves two main features the first one is the construction of a family of random fields converging at a user controlled rate towards the target random field each of these auxialiary random fields can be subsequently simulated by solving a family of ito stochastic differential equations the second ingredient is the definition of an adaptive discretization algorithm the latter allows refining the integration step on the fly and prevents the scheme from diverging the proposed strategy is finally exemplified on three examples each of which serving as a benchmark either for the adaptivity procedure or for the convergence of the diffusions

powering up with space time wind forecasting the technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality high quality short term forecasts of wind speed are vital to making this a more reliable energy source gneiting et al 2006 have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information the forecasts produced by this model are accurate and subject to accuracy the predictive distribution is sharp that is highly concentrated around its center however this model is split into nonunique regimes based on the wind direction at an offsite location this paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model it is robust in many experiments such as predicting wind at other locations we compare this with the more common approach of modeling wind speeds and directions in the cartesian space and use a skew t distribution for the errors the quality of t

multivariate type g matern stochastic partial differential equation random fields for many applications with multivariate data random field models capturing departures from gaussianity within realizations are appropriate for this reason we formulate a new class of multivariate non gaussian models based on systems of stochastic partial differential equations with additive type g noise whose marginal covariance functions are of matern type we consider four increasingly flexible constructions of the noise where the first two are similar to existing copula based models in contrast with these the last two constructions can model non gaussian spatial data without replicates computationally efficient methods for likelihood based parameter estimation and probabilistic prediction are proposed and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications less

matern cross covariance functions for multivariate random fields we introduce a flexible parametric family of matrix valued covariance functions for multivariate spatial random fields where each constituent component is a matern process the model parameters are interpretable in terms of process variance smoothness correlation length and colocated correlation coefficients which can be positive or negative both the marginal and the cross covariance functions are of the matern type in a data example on error fields for numerical predictions of surface pressure and temperature over the north american pacific northwest we compare the bivariate matern model to the traditional linear model of coregionalization

matern class tensor valued random fields and beyond we construct classes of homogeneous random fields on a three dimensional euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of 3 times 3 orthogonal matrices the constructed classes depend on finitely many isotropic spectral densities we say that such a field belongs to either the matern or the dual matern class if all of the above densities are matern or dual matern several examples are considered

poisson structures on moduli spaces of sheaves over poisson surfaces we introduce and study the notion of poisson surface we prove that the choice of a poisson structure on a surfaces canonically determines a poisson structure on the moduli space of stable sheaves ons this result generalizes previous results obtained by mukai 14 for abelian ork3 surfaces and by tyurin 16

a valid matern class of cross covariance functions for multivariate random fields with any number of components we introduce a valid parametric family of cross covariance functions for multivariate spatial random fields where each component has a covariance function from a well celebrated matern class unlike previous attempts our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components we present the conditions on the parameter space that result in valid models with varying degrees of complexity we discuss practical implementations including reparameterizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency we perform various monte carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging the application of the proposed multivariate matern model is illustrated on two meteorological datasets temperature pressure over the pacific northwest bivariate and wind temperature pressure in oklahoma trivariate in the latter case our flexi

aberrant crypt foci and semiparametric modeling of correlated binary data motivated by the spatial modeling of aberrant crypt foci acf in colon carcinogenesis we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent gaussian spatial process that accounts for short range dependencies the mean is modeled in a general way using regression splines the mean function can be viewed as a fixed effect and is estimated with a penalty for regularization with the latent process viewed as another random effect the model becomes a generalized linear mixed model in our motivating data set and other applications the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation reml so pairwise likelihood a special case of composite likelihood is used instead we develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications including but not limited to the problem that motivated this work the splines have penalty parameters that must converge to zero asymptotically we derive theory for this along with a data driven method for selecting the penalty parameter a method that is shown in simulations to improve greatly upon standard devices such as likelihood crossvalidation finally we apply the methods to the data from our experiment acf we discover an unexpected location for peak formation of acf

multivariate max stable spatial processes summary max stable processes allow the spatial dependence of extremes to be modelled and quantified so they are widely adopted in applications for a better understanding of extremes it may be useful to study several variables simultaneously to this end we study the maxima of independent replicates of multivariate processes both in the gaussian and student t cases we define a poisson process construction and introduce multivariate versions of the smith gaussian extreme value the schlather extremal gaussian and extremal t and the brown resnick models we develop inference for the models based on composite likelihoods we present results of monte carlo simulations and an application to daily maximum wind speed and wind gust

existence of engel structures we develop a construction of engel structures on 4 manifolds based on decompositions of manifolds into round handles this allows us to show that all parallelizable 4 manifolds admit an engel structure we also show that given two engel manifolds m1 m2 satisfying a certain condition on the characteristic foliations there is an engel structure on m1 m2 s2 s2 which is closely related to the original engel structures

vanishing theorems on l k strong kahler manifolds with torsion abstract we derive sufficient conditions for the vanishing of plurigenera p m j m 0 on compact l k strong l k 0 kahler manifolds with torsion in particular we show that the plurigenera of closed l k strong manifolds k n 1 for which hol s u n vanish where is the hermitian connection with skew symmetric torsion as a consequence all generalized k gauduchon manifolds for which hol s u n do not admit holomorphic n 0 forms furthermore we show that all conformally balanced l k strong kahler manifolds with torsion k n 1 are kahler we also give several examples of l k strong kahler and calabi yau manifolds with torsion

studies in the history of probability and statistics xlix on the matern correlation family summary handcock stein 1993 introduced the matern family of spatial correlations into statistics as a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field we document the varied history of this family which includes contributions by eminent physical scientists and statisticians

generalized pseudo kahler structures in this paper we consider pseudo bihermitian structures pairs of complex structures compatible with a pseudo riemannian metric we establish relations of these structures with generalized pseudo kahler geometry and holomorphic poisson structures similar to that in the positive definite case we provide a list of compact complex surfaces which could admit pseudo bihermitian structures and give examples of such structures on some of them we also consider a naturally defined null plane distribution on a generalized pseudo kahler 4 manifold and show that under a mild restriction it determines an engel structure

cross covariance functions for multivariate random fields based on latent dimensions summary the problem of constructing valid parametric cross covariance functions is challenging we propose a simple methodology based on latent dimensions and existing covariance models for univariate random fields to develop flexible interpretable and computationally feasible classes of cross covariance functions in closed form we focus on spatio temporal cross covariance functions that can be nonseparable asymmetric and can have different covariance structures for instance different smoothness parameters in each component we discuss estimation of these models and perform a small simulation study to demonstrate our approach we illustrate our methodology on a trivariate spatio temporal pollution dataset from california and demonstrate that our cross covariance performs better than other competing models

spatially varying cross correlation coefficients in the presence of nugget effects summary we derive sufficient conditions for the cross correlation coefficient of a multivariate spatial process to vary with location when the spatial model is augmented with nugget effects the derived class is valid for anychoiceofcovariancefunctions andyieldssubstantialflexibilitybetweenmultipleprocesses thekeyis to identify the cross correlation coefficient matrix with a contraction matrix which can be either diagonal implying a parsimonious formulation or a fully general contraction matrix yielding greater flexibility but added model complexity we illustrate the approach with a bivariate minimum and maximum temperature dataset in colorado allowing the two variables to be positively correlated at low elevations and nearly independent at high elevations while still yielding a positive definite covariance matrix

bihermitian surfaces with odd first betti number compact bihermitian surfaces are considered that is compact oriented conformal four manifolds admitting two distinct compatible complex structures it is shown that if the first betti number is odd then with respect to either complex structure such a manifold belongs to class vii of the enriques kodaira classification moreover it must be either a special hopf or an inoue surface in the strongly bihermitian case or obtained by blowing up a minimal class vii surface with curves in the non strongly bihermitian case

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

multivariate spatial covariance models a conditional approach multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain multivariate spatial covariance models need to be built with care since any covariance matrix that is derived from such a model must be nonnegative definite in this article we develop a conditional approach for spatial model construction whose validity conditions are easy to check we start with bivariate spatial covariance models and go on to demonstrate the approach s connection to multivariate models defined by networks of spatial variables in some circumstances such as modelling respiratory illness conditional on air pollution the direction of conditional dependence is clear when it is not the two directional models can be compared more generally the graph structure of the network reduces the number of possible models to compare model selection then amounts to finding possible causative links in the network we demonstrate our conditional approach on surface temperature and pressure data where the role of the two variables is seen to be asymmetric

generalized kahler geometry generalized kahler geometry is the natural analogue of kahler geometry in the context of generalized complex geometry just as we may require a complex structure to be compatible with a riemannian metric in a way which gives rise to a symplectic form we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure we prove that generalized kahler geometry is equivalent to the bi hermitian geometry on the target of a 2 dimensional sigma model with 2 2 supersymmetry we also prove the existence of natural holomorphic courant algebroids for each of the underlying complex structures and that these split into a sum of transverse holomorphic dirac structures finally we explore the analogy between pre quantum line bundles and gerbes in the context of generalized kahler geometry

aggregation cokriging for highly multivariate spatial data 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 reanalysis type high resolution historical temperature fields

probabilistic forecasts calibration and sharpness summary probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions we propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive distributions subject to calibration calibration refers to the statistical consistency between the distributional forecasts and the observations and is a joint property of the predictions and the events that materialize sharpness refers to the concentration of the predictive distributions and is a property of the forecasts only a simple theoretical framework allows us to distinguish between probabilistic calibration exceedance calibration and marginal calibration we propose and study tools for checking calibration and sharpness among them the probability integral transform histogram marginal calibration plots the sharpness diagram and proper scoring rules the diagnostic approach is illustrated by an assessment and ranking of probabilistic forecasts of wind speed at the stateline wind energy centre in the us pacific northwest in combination with cross validation or in the time series context our proposal provides very general nonparametric alternatives to the use of information criteria for model diagnostics and model selection