a composite likelihood approach to binary spatial data abstract conventional geostatistics addresses the problem of estimation and prediction for continuous observations but in many practical applications in public health environmental remediation or ecological research the most commonly available data are in the form of counts e g number of cases or indicator variables denoting above or below threshold values also in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest such as a contaminant this article proposes a computationally simple method for estimation and prediction using binary or indicator data in space the proposed method is based on pairwise likelihood contributions and the large sample properties of the estimators are obtained in a straightforward manner we illustrate the methodology through application to indicator data related to gypsy moth defoliation in massachusetts

a nonparametric test for spatial isotropy using subsampling a common requirement for spatial modeling is the development of an appropriate correlation structure although the assumption of isotropy is often made for this structure it is not always appropriate a conventional practice when checking for isotropy is to informally assess plots of direction specific sample semi variograms although a useful diagnostic these graphical techniques are difficult to assess and open to interpretation formal alternatives to graphical diagnostics are valuable but have been applied to a limited class of models in this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models this approach which is based on the asymptotic joint normality of the sample variogram can be used to compare sample variograms in multiple directions an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic a subsampling approach and a limiting

periodicity directionality and randomness wold features for image modeling and retrieval one of the fundamental challenges in pattern recognition is choosing a set of features appropriate to a class of problems in applications such as database retrieval it is important that image features used in pattern comparison provide good measures of image perceptual similarities we present an image model with a new set of features that address the challenge of perceptual similarity the model is based on the 2d wold decomposition of homogeneous random fields the three resulting mutually orthogonal subfields have perceptual properties which can be described as periodicity directionality and randomness approximating what are indicated to be the three most important dimensions of human texture perception the method presented improves upon earlier wold based models in its tolerance to a variety of local inhomogeneities which arise in natural textures and its invariance under image transformation such as rotation an image retrieval algorithm based on the new texture model is presented different types of image features are aggregated for similarity comparison by using a bayesian probabilistic approach the effectiveness of the wold model at retrieving perceptually similar natural textures is demonstrated in comparison to that of two other well known pattern recognition methods the wold model appears to offer a perceptually more satisfying measure of pattern similarity while exceeding the performance of these other methods by traditional pattern recognition criteria examples of natural scene wold texture modeling are also presented

minimax entropy principle and its application to texture modeling this article proposes a general theory and methodology called the minimax entropy principle for building statistical models for images or signals in a variety of applications this principle consists of two parts the first is the maximum entropy principle for feature binding or fusion for a given set of observed feature statistics a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them the second part is the minimum entropy principle for feature selection among all plausible sets of feature statistics we choose the set whose maximum entropy distribution has the minimum entropy computational and inferential issues in both parts are addressed in particular a feature pursuit procedure is proposed for approximately selecting the optimal set of features the minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics and an information criterion for feature pursuit is derived the minimax entropy principle is applied to texture modeling where a novel markov random field mrf model called frame filter random field and minimax entropy is derived and encouraging results are obtained in experiments on a variety of texture images the relationship between our theory and the mechanisms of neural computation is also discussed

hajlasz gradients are upper gradients abstract let x d be a metric measure space with a borel regular measure in this article we prove that if u l loc 1 x and g is a hajlasz gradient of u then there exists u such that u u almost everywhere and 4g is a p weak upper gradient of u this result avoids a priori assumption on the quasi continuity of u used in shanmugalingam 2000 19 we also introduce the notion of local hajlasz gradients and investigate the relations between the local hajlasz gradient and the upper gradient

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

gradient estimates for heat kernels and harmonic functions abstract let x d be a doubling metric measure space endowed with a dirichlet form e deriving from a carre du champ assume that x d e supports a scale invariant l 2 poincare inequality in this article we study the following properties of harmonic functions heat kernels and riesz transforms for p 2 i g p l p estimate for the gradient of the associated heat semigroup ii r h p l p reverse holder inequality for the gradients of harmonic functions iii r p l p boundedness of the riesz transform p iv g b e a generalised bakry emery condition we show that for p 2 i ii iii are equivalent while for p i ii iv are equivalent moreover some of these equivalences still hold under weaker conditions than the l 2 poincare inequality our result gives a characterisation of li yau s gradient estimate of heat kernels for p while for p 2 it is a substantial improvement as well as a generalisation of earlier results by auscher coulhon duong hofmann 7 and auscher coulhon 6 applications to isoperimetric inequalities and sobolev inequalities are given our results apply to riemannian and sub riemannian manifolds as well as to non smooth spaces and to degenerate elliptic parabolic equations in these settings

least squares variogram fitting by spatial subsampling summary least squares methods are popular for fitting valid variogram models to spatial data the paper proposes a new least squares method based on spatial subsampling for variogram model fitting we show that the method proposed is statistically efficient among a class of least squares methods including the generalized least squares method further it is computationally much simpler than the generalized least squares method the method produces valid variogram estimators under very mild regularity conditions on the underlying random field and may be applied with different choices of the generic variogram estimator without analytical calculation an extension of the method proposed to a class of spatial regression models is illustrated with a real data example results from a simulation study on finite sample properties of the method are also reported

joint composite estimating functions in spatiotemporal models summary modelling of spatiotemporal processes has received considerable attention in recent statistical research however owing to the high dimensionality of the data the joint modelling of spatial and temporal processes presents a great computational challenge in both likelihood based and bayesian approaches we propose a joint composite estimating function approach to estimating spatiotemporal covariance structures this substantially reduces the computational complexity and is more efficient than existing composite likelihood methods the novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial temporal and spatiotemporal cross pairs which results in overidentified estimating functions thus we form a joint inference function in a spirit that is similar to hansen s generalized method of moments we show that under practical scenarios the estimator proposed is consistent and asymptotically normal simulation studies prove that our method performs well in finite samples finally we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates pm10 in the north eastern usa over a 32 month period

batch size effects in the analysis of simulation output batching is a commonly used method for calculating confidence intervals on the mean of a sequence of correlated observations arising from a simulation experiment several recent papers have considered the effect of using batch sizes too small to satisfy assumptions of normality and or independence and the resulting incorrect probabilities of the confidence interval covering the mean this paper quantifies the effects of using batch sizes larger than necessary to satisfy normality and independence assumptions these effects include 1 correct probability of covering the mean 2 an increase in expected half length 3 an increase in the standard deviation and coefficient of variation of the half length and 4 an increase in the probability of covering points not equal to the mean for any sample size and independent and normal batch means the results are 1 the effects of less than 10 batches are large and the effects of more than 30 batches small and 2 additional batches have lesser effects on

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

on optimal spatial subsample size for variance estimation we consider the problem of determining the optimal block or subsample size for a spatial subsampling method for spatial processes observed on regular grids we derive expansions for the mean square error of the subsampling variance estimator which yields an expression for the theoretically optimal block size the optimal block size is shown to depend in an intricate way on the geometry of the spatial sampling region as well as characteristics of the underlying random field final expressions for the optimal block size make use of some nontrivial estimates of lattice point counts in shifts of convex sets optimal block sizes are computed for sampling regions of a number of commonly encountered shapes numerical studies are performed to compare subsampling methods as well as procedures for estimating the theoretically best block size

analytic bethe ansatz and functional equations associated with any simple root systems of the lie superalgebra sl r 1 s 1 abstract the lie superalgebra sl r 1 s 1 admits several inequivalent choices of simple root systems we have carried out analytic bethe ansatz for any simple root systems of sl r 1 s 1 we present transfer matrix eigenvalue formulae in dressed vacuum form which are expressed as the young supertableaux with some semistandard like conditions these formulae have determinant expressions which can be viewed as quantum analogue of jacobi trudi and giambelli formulae for sl r 1 s 1 we also propose a class of transfer matrix functional relations which is specialization of hirota bilinear difference equation using the particle hole transformation relations among the bethe ansatz equations for various kinds of simple root systems are discussed

nonparametric estimation of the moments of a general statistic computed from spatial data abstract a statistic s is computed on spatially indexed data x i i d where d is a finite subset of the integer lattice z2 we propose a simple nonparametric method for estimating the moments e g variance skewness of s d using only the observed data at hand the method uses replicates of s computed on smaller subsets of d no explicit knowledge of the underlying spatial dependence mechanism is needed and the marginal distribution of x i may also be unknown the shape of d can be quite irregular and s is allowed to be a general statistic the proposed estimator is shown to be consistent and asymptotically normal under mild conditions on s d and mixing conditions on the strength of spatial dependence as a numerical example the estimator is used in assessing the geographic clumping of cancer deaths in the united states

on nonparametric variance estimation for second order statistics of inhomogeneous spatial point processes with a known parametric intensity form we introduce new variance estimation procedures for second order statistics that are computed from a single realization of intensity reweighted stationary spatial point processes the statistics are defined either on a subset b of the observation window or on the whole window for the former we use subblocks that have the same size and shape as b as replicates of b in order to estimate the target variance for the latter we develop a subsampling estimator for a key component in the target variance and estimate its other components by method of moment methods under some suitable conditions we prove that the proposed variance estimators are consistent for the target variances in both cases simulations and an application to a real data example are used to demonstrate the usefulness of the proposed methods this article has supplementary material online

the poincare inequality is an open ended condition let p 1 and let x d be a complete metric measure space with borel and doubling that admits a 1 p poincare inequality then there exists e 0 such that x d admits a 1 q poincare inequality for every q p e quantitatively

semiparametric normal transformation models for spatially correlated survival data there is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiologic studies in this article we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data this class of models assumes that survival outcomes marginally follow a cox proportional hazard model with unspecified baseline hazard and their joint distribution is obtained by transforming survival outcomes to normal random variables whose joint distribution is assumed to be multivariate normal with a spatial correlation structure a key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields we study the relationship of the spatial correlation structure of the transformed no

a weighted estimating equation approach for inhomogeneous spatial point processes we introduce a new estimation method for parametric intensity function models of inhomogeneous spatial point processes based on weighted estimating equations the weights can incorporate information on both inhomogeneity and dependence of the process simulations show that significant efficiency gains can be achieved for non poisson processes compared to the poisson maximum likelihood estimator an application to tropical forest data illustrates the use of the proposed method

analytic bethe ansatz related to a one parameter family of finite dimensional representations of the lie superalgebra as is well known the type 1 lie superalgebra admits a one parameter family of finite dimensional irreducible representations we have carried out an analytic bethe ansatz related to this family of representations we present formulae which are deformations of previously proposed determinant formulae labelled by a young superdiagram these formulae will provide a transfer matrix eigenvalue in a dressed vacuum form related to the solutions of a graded yang baxter equation which depend not only on the spectral parameter but also on a non additive continuous parameter a class of transfer matrix functional relations among these formulae is briefly mentioned

symmetry and compact embeddings for critical exponents in metric measure spaces abstract we obtain a compact sobolev embedding for h invariant functions in compact metric measure spaces where h is a subgroup of the measure preserving bijections in riemannian manifolds h is a subgroup of the volume preserving diffeomorphisms a compact embedding for the critical exponents follows the results can be viewed as an extension of sobolev embeddings of functions invariant under isometries in compact manifolds

moment estimation for statistics from marked point processes in spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations in other words the data form a realization of a marked point process in this paper we formulate subsampling estimators of the moments of general statistics computed from marked point process data and we establish their l 2 consistency the variance estimator in particular can be used for the construction of confidence intervals for estimated parameters a practical data based method for choosing a subsampling parameter is given and illustrated on a data set finite sample simulation examples are also presented

assessment of texture stationarity using the asymptotic behavior of the empirical mean and variance given textured images considered as realizations of 2 d stochastic processes a framework is proposed to evaluate the stationarity of their mean and variance existing strategies focus on the asymptotic behavior of the empirical mean and variance respectively em and ev known for some types of nondeterministic processes in this paper the theoretical asymptotic behaviors of the em and ev are studied for large classes of second order stationary ergodic processes in the sense of the wold decomposition scheme including harmonic and evanescent processes minimal rates of convergence for the em and the ev are derived for these processes they are used as criteria for assessing the stationarity of textures the experimental estimation of the rate of convergence is achieved using a nonparametric block sub sampling method our framework is evaluated on synthetic processes with stationary or nonstationary mean and variance and on real textures it is shown that anomalies in the asymptotic behavior of the empirical estimators allow detecting nonstationarities of the mean and variance of the processes in an objective way

simulation output analysis using standardized time series the method of standardized time series sts was proposed by schruben as an approach for constructing asymptotic confidence intervals for the steady state mean from a single simulation run the sts method cancels out the variance constant while other methods attempt to consistently estimate the variance constant our goal in this paper is to generalize the sts method and to study some of its basic properties starting from a functional central limit theorem fclt for the sample mean of the simulated process a class of mappings of c 0 1 to is identified each of which leads to a sts confidence interval one of these mappings leads to the batch means method a lower bound is obtained for the expected length of the asymptotic as the run size becomes large sts confidence intervals this lower bound is not attained but can be approached arbitrarily closely by sts confidence intervals methods that consistently estimate the variance constant do realize this lower bound the variance of the length of a sts confidence interval is of larger order in the run length than is that for the regenerative method

a test of stationarity for textured images this article proposes a test of stationarity for random fields on a regular lattice motivated by a problem arising from texture analysis our approach is founded on the locally stationary two dimensional wavelet ls2w process model for lattice processes that has previously been used for standard texture analysis tasks such as texture discrimination and classification we propose two variants of our stationarity test both of which can be performed on a single realization a feature of particular practical importance within texture analysis we illustrate our approach with pilled fabric data demonstrating that the test is capable of identifying visually subtle changes in stationarity supplementary material for this article is available online

a nonparametric assessment of properties of space time covariance functions we propose a unified framework for testing various assumptions commonly made for covariance functions of stationary spatio temporal random fields the methodology is based on the asymptotic normality of space time covariance estimators we focus on tests for full symmetry and separability in this article but our framework naturally covers testing for isotropy and taylor s hypothesis our test successfully detects the asymmetric and nonseparable features in two sets of wind speed data we perform simulation experiments to evaluate our test and conclude that our method is reliable and powerful for assessing common assumptions on space time covariance functions

weighted empirical adaptive variance estimators for correlated data regression estimating equations based on marginal generalized linear models are useful for regression modelling of correlated data but inference and testing require reliable estimates of standard errors we introduce a class of variance estimators based on the weighted empirical variance of the estimating functions and show that an adaptive choice of weights allows reliable estimation both asymptotically and by simulation in finite samples connections with previous bootstrap and jackknife methods are explored the effect of reliable variance estimation is illustrated in data on health effects of air pollution in king county washington

estimating space and space time covariance functions for large data sets a weighted composite likelihood approach in this article we propose two methods for estimating space and space time covariance functions from a gaussian random field based on the composite likelihood idea the first method relies on the maximization of a weighted version of the composite likelihood function while the second one is based on the solution of a weighted composite score equation this last scheme is quite general and could be applied to any kind of composite likelihood an information criterion for model selection based on the first estimation method is also introduced the methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency the effectiveness of the methods is illustrated through examples simulation experiments and by analyzing a dataset on ozone measurements

prediction of spatial cumulative distribution functions using subsampling abstract the spatial cumulative distribution function scdf is a random function that provides a statistical summary of a random field over a spatial domain of interest in this article we develop a spatial subsampling method for predicting an scdf based on observations made on a hexagonal grid similar to the one used in the environmental monitoring and assessment program of the u s environmental protection agency we show that under quite general conditions the proposed subsampling method provides accurate data based approximations to the sampling distributions of various functionals of the scdf predictor in particular it produces estimators of different population characteristics such as the quantiles and weighted mean integrated squared errors of the empirical predictor as an illustration we apply the subsampling method to construct large sample prediction bands for the scdf of an ecological index for foliage condition of red maple trees in the state of maine

analytic bethe ansatz and t system in c2 1 vertex models eigenvalues of the commuting family of transfer matrices are expected to obey the t system a set of functional relations proposed recently here we obtain the solution to the t system for c2 1 vertex models they are compatible with the analytic bethe ansatz and yang baxterize the classical characters

assessing isotropy for spatial point processes summary a common assumption while analyzing spatial point processes is direction invariance i e isotropy in this article we propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second order intensity function we derive an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample second order intensity function and use this to construct a test statistic with a 2 limiting distribution we demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set where our approach confirms suspected directional effects in the spatial distribution of the desert plant species

resampling methods for spatial regression models under a class of stochastic designs in this paper we consider the problem of bootstrapping a class of spatial regression models when the sampling sites are generated by a possibly nonuniform stochastic design and are irregularly spaced it is shown that the natural extension of the existing block bootstrap methods for grid spatial data does not work for irregularly spaced spatial data under nonuniform stochastic designs a variant of the blocking mechanism is proposed it is shown that the proposed block bootstrap method provides a valid approximation to the distribution of a class of m estimators of the spatial regression parameters finite sample properties of the method are investigated through a moderately large simulation study and a real data example is given to illustrate the methodology

point and interval estimation of variogram models using spatial empirical likelihood we present a spatial blockwise empirical likelihood method for estimating variogram model parameters in the analysis of spatial data on a grid the method produces point estimators that require no spatial variance estimates to compute unlike least squares methods for variogram fitting but are as efficient as the best least squares estimator in large samples our approach also produces confidence regions for the variogram without requiring knowledge of the full joint distribution of the spatial data in addition the empirical likelihood formulation extends to spatial regression problems and allows simultaneous inference on both spatial trend and variogram parameters we examine the asymptotic behavior of the estimator analytically and investigate its behavior in finite samples through simulation studies

variance estimation for statistics computed from spatial lattice data summary a statistic s is computed on spatially indexed data x i e d where d is a finite subset of the integer lattice 22 we propose a method for estimating the variance and other moments of s by using only the data the set d may be irregularly shaped the statistic s may be arbitrarily complicated and no distributional assumptions marginal or joint are necessary the method uses the statistic computed on overlapping subshapes of d as replicates of s the estimator is simply the sample variance of the standardized replicates we demonstrate c2 consistency of the estimator under mild conditions on s and the strength of spatial dependence a rate of convergence is also given giving guidance into the appropriate choice of subshape size and the estimator is illustrated in two data examples

a thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns when modeling inhomogeneous spatial point patterns it is of interest to fit a parametric model for the first order intensity function foif of the process in terms of some measured covariates estimates for the regression coefficients say can be obtained by maximizing a poisson maximum likelihood criterion little work has been done on the asymptotic distribution of except in some special cases in this article we show that is asymptotically normal for a general class of mixing processes to estimate the variance of we propose a novel thinned block bootstrap procedure that assumes that the point process is second order reweighted stationary to apply this procedure only the foif and not any high order terms of the process needs to be estimated we establish the consistency of the resulting variance estimator and demonstrate its efficacy through simulations and an application to a real data example

on subsampling estimators with unknown rate of convergence abstract politis and romano have put forth a general subsampling methodology for the construction of large sample confidence regions for a general unknown parameter associated with the probability distribution generating the stationary sequence x 1 x n the subsampling methodology hinges on approximating the large sample distribution of a statistic t n t n x 1 x n that is consistent for at some known rate n although subsampling has been shown to yield confidence regions for of asymptotically correct coverage under very weak assumptions the applicability of the methodology as it has been presented so far is limited if the rate of convergence n happens to be unknown or intractable in a particular setting in this article we show how it is possible to circumvent this limitation by a using the subsampling methodology to derive a consistent estimator of the rate n and b using the estimated rate to construct asymptotically correct confidence regions for based on subsampling

asymptotic normality for a general statistic from a stationary sequence on obtient un ensemble de conditions necessaires et suffisantes pour la normalite asymptotique conjointe de t n et une valeur de sous serie t m m n

bias corrected variance estimation and hypothesis testing for spatial point and marked point processes using subsampling summary we introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes for variance estimation our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval we show that they can achieve better rates in mean squared error than the usual subsampling variance estimator in particular for n n observation windows the optimal rate of n 2 can be achieved if the data have a finite dependence range for hypothesis testing we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics we assess the numerical performance of the proposed methods through simulation and apply them to analyze a tropical forest data set

testing mutual independence between two discrete valued spatial processes a correction to pearson chi squared a common feature of data collected in environmental and earth sciences is that they typically exhibit spatial autocorrelation violating the assumption of independent observations can have dramatic effects on inferences derived from standard statistical methods in this article we examine the consequences of spatial autocorrelation on pearson s chi squared test of mutual independence between two categorical responses with a general number of classes correspondingly we suggest a simple modification to the standard test statistic that allows for spatial autocorrelation our modified statistic is based on a first order correction factor and thus provides only an approximate test however we show by monte carlo simulation that this approximation results in satisfactory inferences in several situations of practical interest the usefulness of the method is displayed through an application to categorical data arising in the study of the relationship between the distribution pattern of plant species and woodland age in a forest in northern belgium

window subsampling of estimating functions with application to regression models abstract we propose a subsampling method for estimating the asymptotic standard error of a statistic n that is the solution to an estimating equation 1 n n j 1 uj y j xj 0 where the data yj may be temporally or spatially correlated and the estimating function may depend on covariates xj a key statistic that we consider in detail is a generalized linear model regression coefficient computed under the assumption of independence the availability of a consistent variance estimator allows semiparametric regression approaches for clustered and longitudinal data to be used with time series and spatial data the methods that we develop extend the subsampling ideas of carlstein sherman and garcia soidan and hall to estimating functions our approach provides an attractive alternative to the jackknife method of lele particularly for large datasets because we do not require parameter reestimation

a unified texture model based on a 2 d wold like decomposition a unified texture model that is applicable to a wide variety of texture types found in natural images is presented this model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters the texture field is assumed to be a realization of a regular homogeneous random field which is characterized in general by a mixed spectral distribution the texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component the deterministic component is further orthogonally decomposed into a harmonic component and a generalized evanescent component both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component the model is very efficient in terms of the number of parameters required to faithfully represent textures reconstructed textures are practically indistinguishable from the originals

quasiconformal maps in metric spaces with controlled geometry this paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry the principal message is that such a theory is both relevant and viable the first main issue is the problem of definition which we next describe quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount this requirement makes sense in every metric space given a homeomorphism f from a metric space x to a metric space y then for x x and r 0 set

decay of correlations under dobrushin s uniqueness condition and its applications an estimate on the correlation of functionals of gibbs fields satisfying dobrushin s uniqueness condition is given as a consequence a result of gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole dobrushin uniqueness region applications to the central limit theorem and the second derivative of the pressure are also given

analyzing spatially distributed binary data using independent block estimating equations summary we estimate the relation between binary responses and corresponding covariate vectors both observed over a large spatial lattice we assume a hierarchical generalized linear model with probit link function partition the lattice into blocks and adopt the working assumption of independence between the blocks to obtain an easily solved estimating equation standard errors are obtained using the sandwich estimator together with window subsampling sherman 1996 journal of the royal statistical society series b 58 509 523 we apply this to a large data set describing long term vegetation growth together with two other approximate likelihood approaches pairwise composite likelihood cl and estimation under a working assumption of independence the independence and cl methods give similar point estimates and standard errors while the independent block approach gives considerably smaller standard errors as well as more easily interpretable point estimates we present numerical evidence suggesting this increased efficiency may hold more generally

constrained monte carlo maximum likelihood for dependent data maximum likelihood estimates mles in autologistic models and other exponential family models for dependent data can be calculated with markov chain monte carlo methods the metropolis algorithm or the gibbs sampler which simulate ergodic markov chains having equilibrium distributions in the model from one realization of such a markov chain a monte carlo approximant to the whole likelihood function can be constructed the parameter value if any maximizing this function approximates the mle

invariant tests for spatial stationarity using covariance structure we propose new tests for validating the ula model based on the received array data these tests use the structure of the covariance matrix of the data to decide whether the received data is spatially stationary invariance principles are used to ensure that the test has constant significance equivalent to a cfar test when the model is indeed true by eliminating the dependence on the covariance in addition a modification of the test is proposed for verifying stationarity within a specified subspace and heuristics are presented for distinguishing propagation effects from deviation from the ula model

on the central limit theorem for stationary mixing random fields a simple proof of a central limit theorem for stationary random fields under mixing conditions is given generalizing some results obtained by more complicated methods e g bernstein s method