limitations on universality in the continuous spin ising model the authors give by explicit counterexample numerical evidence that critical exponent universality fails for the two dimensional continuous spin ising model this result is contrary to what has previously been assumed

an algorithm for coarsening unstructured meshes we develop and analyze a procedure for creating a hierarchical basis of continuous piecewise linear polynomials on an arbitrary unstructured nonuniform triangular mesh using these hierarchical basis functions we are able to define and analyze corresponding iterative methods for solving the linear systems arising from finite element discretizations of elliptic partial differential equations we show that such iterative methods perform as well as those developed for the usual case of structured locally refined meshes in particular we show that the generalized condition numbers for such iterative methods are of order j 2 where j is the number of hierarchical basis levels

statistical geometry in quantum mechanics a statistical model m is a family of probability distributions characterised by a set of continuous parameters known as the parameter space this possesses natural geometrical properties induced by the embedding of the family of probability distributions into the space of all square integrable functions more precisely by consideration of the square root density function we can regard m as a submanifold of the unit sphere s in a real hilbert space h therefore h embodies the state space of the probability distributions and the geometry of the given statistical model can be described in terms of the embedding of m in s the geometry in question is characterised by a natural riemannian metric the fisher rao metric thus allowing us to formulate the principles of classical statistical inference in a natural geometric setting in particular we focus attention on the variance lower bounds for statistical estimation and establish generalisations of the classical cramer rao and bhattacharyya inequalities described in terms of the geometry of the underlying real hilbert space as a comprehensive illustration of the utility of the geometric framework the statistical model m is then specialised to the case of a submanifold of the state space of a quantum mechanical system this is pursued by introducing a compatible complex structure on the underlying real hilbert space which allows the operations of ordinary quantum mechanics to be reinterpreted in the language of real hilbert space geometry the application of generalised variance bounds in the case of quantum statistical estimation leads to a set of higher order corrections to the heisenberg uncertainty relations for canonically conjugate observables

block diagonal and constraint preconditioners for nonsymmetric indefinite linear systems part i theory we study block diagonal preconditioners and an efficient variant of constraint preconditioners for general two by two block linear systems with zero 2 2 block we derive block diagonal preconditioners from a splitting of the 1 1 block of the matrix from the resulting preconditioned system we derive a smaller so called related system that yields the solution of the original problem solving the related system corresponds to an efficient implementation of constraint preconditioning we analyze the properties of both classes of preconditioned matrices in particular their spectra using analytical results we show that the related system matrix has the more favorable spectrum which in many applications translates into faster convergence for krylov subspace methods we show that fast convergence depends mainly on the quality of the splitting a topic for which a substantial body of theory exists our analysis also provides a number of new relations between block diagonal preconditioners and constraint preconditioners for constrained problems solving the related system produces iterates that satisfy the constraints exactly just as for systems with a constraint preconditioner finally for the lagrange multiplier formulation of a constrained optimization problem we show how scaling nonlinear constraints can dramatically improve the convergence for linear systems in a newton iteration our theoretical results are confirmed by numerical experiments on a constrained optimization problem we consider the general nonsymmetric nonsingular case our only additional requirement is the nonsingularity of the schur complement type matrix derived from the splitting that defines the preconditioners in particular the 1 2 block need not equal the transposed 2 1 block and the 1 1 block might be indefinite or even singular this is the first paper in a two part sequence in the second paper we will study the use of our preconditioners in a variety of applications

algebraic multigrid amg experiences and comparisons algebraic multigrid methods are designed for the solution of sparse linear systems of equations using multigrid principles in contrast to standard multigrid methods amg does not take advantage of the origin of a particular system of equations at hand nor does it exploit any underlying geometrical situation fully automatically and based solely on algebraic information contained in the given matrix amg constructs a sequence of grids and corresponding operators a special amg algorithm will be presented for a wide range of problems including certain problems which do not have a continuous background this algorithm yields an iterative method which exhibits a convergence behavior typical for multigrid methods

on learning multicategory classification with sample queries consider the pattern recognition problem of learning multicategory classification from a labeled sample for instance the problem of learning character recognition where a category corresponds to an alphanumeric letter the classical theory of pattern recognition assumes labeled examples appear according to the unknown underlying pattern class conditional probability distributions where the pattern classes are picked randomly according to their a priori probabilities in this paper we pose the following question can the learning accuracy be improved if labeled examples are independently randomly drawn according to the underlying class conditional probability distributions but the pattern classes are chosen not necessarily according to their a priori probabilities we answer this in the affirmative by showing that there exists a tuning of the sub sample proportions which minimizes a loss criterion the tuning is relative to the intrinsic complexity of the bayes classifier as this complexity depends on the underlying probability distributions which are assumed to be unknown we provide an algorithm which learns the proportions in an on line manner utilizing sample querying which asymptotically minimizes the criterion in practice this algorithm may be used to boost the performance of existing learning classification algorithms by apportioning better sub sample proportions

monte carlo calculations of the conformal charge the conformal charge is an important quantity which characterizes the nature of the two dimensional phase transition we report a first attempt to use a new numerical method to calculate the conformal charge in this paper we apply our method to the 2 dimensional 4 continuous spin ising model by varying the parameters in the hamiltonian one can change continuously from the known gaussian limit to the ising limit it is well known that the critical points for these two systems are not in the same universality class we study this behavior for the gaussian model the single well 4 model the border model and the double well 4 model for a large lattice our results while giving a good general picture are not so far sufficient to differentiate whether the non gaussian cases studied belong to the ising model universality class or not further studies of other lattice sizes should serve to improve greatly our conclusions

adjusted qmle for the spatial autoregressive parameter abstract one simple and often very effective way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter we apply this general principle to the quasi maximum likelihood estimator qmle of the autoregressive parameter in a spatial autoregression the resulting estimator for has better finite sample properties compared to the qmle for especially in the presence of a large number of covariates it can also solve the incidental parameter problem that arises for example in social interaction models with network fixed effects however spatial autoregressions present specific challenges for this type of adjustment because recentering the profile score may cause the adjusted estimate to be outside the usual parameter space for conditions for this to happen are given and implications are discussed for inference we propose confidence intervals based on a lugannani rice approximation to the distribution of the adjusted qmle of based on our simulations the coverage properties of these intervals are excellent even in models with a large number of covariates

adjusted estimates and wald statistics for the ar 1 model with constant abstract adjusted profile likelihood of cox and reid 1993 journal of the royal statistical society b 55 467 471 for the autoregressive coefficient of the ar 1 model with constant yields an estimator which can be more accurate than the maximum likelihood estimator in small samples whether the process is stationary or a random walk and in the latter case also asymptotically a related estimator is asymptotically distributed compactly and symmetrically around zero under a random walk but is not consistent in general the adjusted wald statistic can follow the asymptotic standard normal distribution much better than the non adjusted under stationarity or a drifted random walk

mean square consistency of the variance estimator in steady state simulation output analysis in steady state simulation output analysis mean square consistency of the process variance estimator is important for a number of reasons one way to construct an asymptotically valid confidence interval around a sample mean is via construction of a consistent estimator of the process variance and a central limit theorem also if an estimator is consistent in the mean square sense a mean square error analysis is theoretically justified finally batch size selection is an open research problem in steady state output analysis and a mean square error analysis approach has been proposed in the literature to be valid the process variance estimators constructed must be consistent in the mean square sense in this paper we prove mean square consistency of the process variance estimator for the methods of batch means overlapping batch means standardized time series area and spaced batch means by rigorously computing the rate of decay of the variance of the process variance estimators asymptotic results for third and higher centered moments of the batch means and area variance estimators are also given along with central limit theorems

simulation of stopped diffusions in this work we study standard euler updates for simulating stopped diffusions as an immediate application we discuss the computation of first exit times of diffusions from a domain we focus on one dimensional situations and show how the ideas for the simulation of killed diffusions can be adapted to this problem in particular we give a fully implementable algorithm to compute the first exit time from an interval numerically the brownian motion case is treated in detail and extensions to general diffusions are given special emphasis is given to numerical experiments for every ansatz we include numerical experiments confirming the conjectured accuracy of our methods our algorithm is of order one in a weak sense comparisons with other algorithms are shown results that are superior to those obtained with other methods are presented when approximating a first hitting time distribution the results obtained with our algorithm are much better than those achieved with other methods

bpx type preconditioners for second and fourth order elliptic problems on the sphere we develop two bramble pasciak xu type preconditioners for second resp fourth order elliptic problems on the surface of the two sphere to discretize the second order problem we construct c 0 linear elements on the sphere and for the fourth order problem we construct c 1 finite elements of powell sabin type on the sphere the main reason these bpx preconditioners work depends on this particular choice of basis we prove optimality and provide numerical examples furthermore we numerically compare the bpx preconditioners with the suboptimal hierarchical basis preconditioners

single observation unbiased priors this paper studies a class of default priors which we call single observation unbiased priors soup a prior for a parameter is a soup if the corresponding posterior mean of the parameter based on a single observation is an unbiased estimator of the parameter we prove that under mild regularity conditions a default prior for a convolution parameter is noninformative in the sense of yielding a posterior inference invariant under amalgamation only if it is a soup therefore when amalgamation invariance is desirable as in our motivating example of performing imputation for census undercount soup is the only possible coherent noninformative prior for bayesian predictions that will be utilized under aggregation the use of soup also mutually calibrates bayesian and frequentist inferences for aggregates of convolution parameters across many small areas we describe approaches that identify soups in many common models in particular a constructive duality method that identifies soups in pairs of distribution families we introduce o completeness a necessary and sufficient condition for a prior distribution to be uniquely characterized by the corresponding posterior mean uniqueness of the soup is determined by the o completeness of the dual family o completeness of a natural exponential family is implied by its completeness hence the diaconis ylvisaker characterization of the conjugate prior for natural exponential families via linear posterior expectation is a direct consequence of the completeness of such families for most of the examples we have examined the inverse of the variance function is the soup for the mean parameter of the corresponding family suggesting that hartigan s results on asymptotic unbiasedness can be generalized to some families with discrete parameters we also discuss a possible extension of berger s result on the inadmissibility of unbiased estimators as the nonexistence of soup can be a first step in establishing such inadmissibility

finite size scaling analysis of the φ 4 field theory on the square lattice monte carlo calculations are performed for the model hamiltonian i r 2 2 i u 4 gf4 i c 2 i j 2 for various values of the parametersr u c in the crossover region from the ising limit r u to the displacive limit r 0 the variable i is a scalar continuous spin variable which can lie in the range i for each lattice site i i is a priori selected proportional to the single site probability in our monte carlo algorithm the critical line is obtained in very good agreement with other previous approaches a decrease of apparent critical exponents deduced from a finite size scaling analysis is attributed to a crossover toward mean field values at the displacive limit the relation of this model to the coarse grained landau ginzburg wilson free energy functional of ising models is discussed in detail and by matching local moments 2 i 4 i to corresponding averages of subsystem blocks of ising systems with linear dimensionsl 5 tol 15 an explicit construction of this coarse grained free energy is attempted self consistency checks applied to this matching procedure show qualitatively reasonable behavior but quantitative difficulties remain indicating that higher order terms are needed for a quantitatively satisfactory description

a one dimensional analysis for the probability of error of linear classifiers for normally distributed classes computing the probability of error is an important problem in evaluating classifiers when dealing with normally distributed classes this problem becomes intricate due to the fact that there is no closed form expression for integrating the probability density function in this paper we derive lower and upper bounds for the probability of error for a linear classifier where the random vectors representing the underlying classes obey the multivariate normal distribution the expression of the error is derived in the one dimensional space independently of the dimensionality of the original problem based on the two bounds we propose an approximating expression for the error of a generic linear classifier in particular we derive the corresponding bounds and the expression for approximating the error of fisher s classifier our empirical results on synthetic data including up to two hundred dimensional featured samples show that the computations for the error are extremely fast and quite accurate it differs from the actual error in at most e 0 0184340683 the scheme has also been successfully tested on real life data sets drawn from the uci machine learning repository

the hierarchical basis multigrid method we derive and analyze the hierarchical basis multigrid method for solving discretizations of self adjoint elliptic boundary value problems using piecewise linear triangular finite elements the method is analyzed as a block symmetric gau seidel iteration with inner iterations but it is strongly related to 2 level methods to the standard multigridv cycle and to earlier jacobi like hierarchical basis methods the method is very robust and has a nearly optimal convergence rate and work estimate it is especially well suited to difficult problems with rough solutions discretized using highly nonuniform adaptively refined meshes

some remarks on a multigrid preconditioner this paper is devoted to a class of multilevel preconditioners developed in math comp 55 1990 pp 1 22 by bramble pasciak and xu and in the ph d thesis of xu at cornell university ithaca ny 1989 a simple proof is given for optimal estimation of the conditioning a derivation of matrix representations and a description of efficient implementation techniques are also given some modified preconditioners are proposed combining the hierarchical basis method numerical examples are also given that compare various preconditioners discussed in this paper

coarsening strategies for unstructured multigrid techniques with application to anisotropic problems over the years multigrid has been demonstrated as an efficient technique for solving inviscid flow problems however for viscous flows convergence rates often degrade this is generally due to the required use of stretched meshes i e the aspect ratio ar delta y delta x 1 in order to capture the boundary layer near the body usual techniques for generating a sequence of grids that produce proper convergence rates on isotropic meshes are not adequate for stretched meshes this work focuses on the solution of laplace s equation discretized through a galerkin finite element formulation on unstructured stretched triangular meshes a coarsening strategy is proposed and results are discussed

blind separation of independent sources for virtually any source probability density function the blind source separation bss problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure in the bss scenario of two noiseless real valued instantaneous linear mixtures of two sources an approximate maximum likelihood ml approach has been suggested in the literature which is only valid under certain constraints on the probability density function pdf of the sources in the present paper the expression for this ml estimator is reviewed and generalized to include virtually any source distribution an intuitive geometrical interpretation of the new estimator is also given in terms of the scatter plots of the signals involved an asymptotic performance analysis is then carried out yielding a closed form expression for the estimator asymptotic pdf simulations illustrate the behavior of the suggested estimator and show the accuracy of the asymptotic analysis in addition an extension of the method to the general bss scenario of more than two sources and two sensors is successfully implemented

diagnosis and impacts of non gaussianity of innovations in data assimilation most of the atmospheric and oceanic data assimilation da schemes rely on the best linear unbiased estimator blue which is sub optimal if errors of assimilated data are non gaussian thus calling for a full bayesian data assimilation this paper contributes to the study of the non gaussianity of errors in the observational space possible sources of non gaussianity range from the inherent statistical skewness and positiveness of some physical observables e g moisture chemical species the nonlinearity both of the data assimilation models and of the observation operators among others deviations from gaussianity can be justified from a priori hypotheses or inferred from statistical diagnostics of innovations observation minus background leading to consistency relationships between the error statistics from samples of observations and backgrounds as well as their specified error variances we evaluate some measures of the innovation non gaussianity such as the skewness kurtosis and negentropy under the assumption of additive errors and by relating statistical moments from both data errors and innovations we identify potential sources of the innovation non gaussianity these sources range from 1 univariate error non gaussianity 2 nonlinear correlations between errors 3 spatio temporal variability of error variances heteroscedasticity and 4 multiplicative noise observational and background errors are often assumed independent this leads to variance dependent bounds for the skewness and the kurtosis of errors from innovation statistics we assess the potential da impact of some scenarios of non gaussian errors this impact is measured through the mean square difference between the blue and the minimum variance unbiased estimator mvue obtained with univariate observations and background estimates in order to accomplish this we compute maximum entropy probability density functions pdfs of the errors constrained by the first four order moments these pdfs are then used to compute the bayesian posterior pdf and the mvue the referred impact is studied for a large range of statistical moments being higher for skewed innovations and growing in average with the skewness of data errors specially if the skewnesses have the same sign an application has been performed to the quality accepted ecmwf innovations of brightness temperatures of a set of high resolution infrared sounder hirs channels in this context the mvue has led in some extreme cases to a potential reduction of 20 60 of the posterior error variance as compared to the blue specially for extreme values of the innovations

model selection through a statistical analysis of the global minimum of a weighted nonlinear least squares cost function this paper presents a model selection algorithm for the identification of parametric models that are linear in the measurements it is based on the mean and variance expressions of the global minimum of a weighted nonlinear least squares cost function the method requires the knowledge of the noise covariance matrix but does not assume that the true model belongs to the model set unlike the traditional order estimation methods available in literature the presented technique allows to detect undermodeling the theory is illustrated by simulations on signal modeling and system identification problems and by one real measurement example

a simple method for the adjustment of profile likelihoods summary we propose a simple adjustment for profile likelihoods the aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods such as bias inconsistency and overoptimistic variance estimates the adjustment is applied to the profile loglikelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function for cases in which explicit calculation of the adjustments is difficult we give two methods to simplify their computation an automatic simulation method that requires as input only the profile loglikelihood and its first few derivatives first order asymptotic expressions some examples are provided and a comparison is made with the conditional profile log likelihood of cox and reid

non parametric unconditional quantile estimation for efficiency analysis with an application to federal reserve check processing operations abstract this paper examines the technical efficiency of us federal reserve check processing offices over 1980 2003 we extend results from park et al park b simar l weiner c 2000 fdh efficiency scores from a stochastic point of view econometric theory 16 855 877 and daouia and simar daouia a simar l 2007 nonparametric efficiency analysis a multivariate conditional quantile approach journal of econometrics 140 375 400 to develop an unconditional hyperbolic quantile estimator of efficiency our new estimator is fully non parametric and robust with respect to outliers when used to estimate distance to quantiles lying close to the full frontier it is strongly consistent and converges at rate root n thus avoiding the curse of dimensionality that plagues data envelopment analysis dea estimators our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices

bootstrapping in controlled calibration experiments we consider the determination of an unknown quantity for example the concentration of a particular chemical in a given sample or samples using controlled calibration here several samples are prepared with concentrations chosen to cover a required range and these are used to establish the relationship between concentration and the measured response to an assay method this relationship is then used to estimate the concentration in the unknown samples from their measured responses confidence intervals for the estimated concentrations can usually be calculated by inverting a prediction interval but in some situations this method becomes intractable we explore the use of the bootstrap as an alternative in linear nonlinear and multivariate controlled calibration using both simulation and real datasets from the field of immunoassay we also discuss the alternatives afforded by replication of the design points the bootstrap is found to be comparable to the standard method in simple situations and is ea

technical communique estimation of the risk for an unstable behaviour of feedback systems in the presence of nonlinear distortions a criterion to verify experimentally the stability of a nonlinear system captured in a feedback loop is proposed the basic idea is to split the output power in coherent linearly related to the input and noncoherent power the remaining power a nonlinear power gain measuring the sensitivity of the noncoherent output power to input variations is introduced using the small gain theorem it is possible to check the local stability of the feedback for the actual class of excitation signals the risk is estimated that the feedback system would become unstable for another realization of the experiment using extreme value statistics

energy landscape analysis of the two dimensional nearest neighbor φ4 model the stationary points of the potential energy function of the a 4 model on a two dimensional square lattice with nearest neighbor interactions are studied by means of two numerical methods a numerical homotopy continuation method and a globally convergent newton raphson method we analyze the properties of the stationary points in particular with respect to a number of quantities that have been conjectured to display signatures of the thermodynamic phase transition of the model although no such signatures are found for the nearest neighbor a 4 model our study illustrates the strengths and weaknesses of the numerical methods employed

regression to the mean for nonnormal populations summary regression to the mean is the term used to describe the effect by which individuals selected on the basis of an initial measurement which is particularly high or low compared with other members of the population have upon remeasurement values nearer to the population mean for the normal distribution simple expressions for estimates of the magnitude of this effect are available many biological variables however are not normally distributed estimates for regression to the mean for nonnormal data are given based on edgeworth series and saddlepoint approximations

simulation of static critical phenomena in nonideal fluids with the lattice boltzmann method a fluctuating nonideal fluid at its critical point is simulated with the lattice boltzmann method it is demonstrated that the method employing a ginzburg landau free energy functional correctly reproduces the static critical behavior associated with the ising universality class a finite size scaling analysis is applied to determine the critical exponents related to the order parameter compressibility and specific heat a particular focus is put on finite size effects and issues related to the global conservation of the order parameter

expansion of moments of bernstein polynomials abstract in this paper we give expansions of moments and absolute moments of the bernstein polynomials the results are applied to derive a new expansion of the bernstein polynomials in increasing powers of 1 n and a voronovskaya type theorem

monte carlo analysis of the extended ashkin teller model abstract monte carlo simulations are used to analyse the behavior of the extended ashkin teller model in two dimensions from the ratio of the square of the second moment of the order parameter to its fourth moment the critical surface in three dimensional parameter space is calculated in regions where the ising transitions are expected the continuity of the order parameter at the critical surface is verified by a finite size scaling analysis for both ferromagnetic and antiferromagnetic parts of the phase diagram

generating dithering noise for maximum likelihood estimation from quantized data the quantization theorem i qt i implies that the likelihood function can be reconstructed from quantized sensor observations given that appropriate dithering noise is added before quantization we present constructive algorithms to generate such dithering noise the application to maximum likelihood estimation mle is studied in particular in short dithering has the same role for amplitude quantization as an anti alias filter has for sampling in that it enables perfect reconstruction of the dithered but unquantized signal s likelihood function without dithering the likelihood function suffers from a kind of aliasing expressed as a counterpart to poisson s summation formula which makes the exact mle intractable to compute with dithering it is demonstrated that standard mle algorithms can be re used on a smoothed likelihood function of the original signal and statistically efficiency is obtained the implication of dithering to the cramer rao lower bound crlb is studied and illustrative examples are provided

a study of a coarse grained free energy functional for the three dimensional ising model the joint distribution function of the nearest neighbour cell magnetisation of the three dimensional ising model has been studied by monte carlo methods this function has a double peaked structure for t tc and can be represented by a coarse grained functional of two cell variables the authors have determined the dependence of this functional on the coarse graining cell size for several temperatures below tc in particular they have calculated the dependence of the spinodal curve on the scaled coarse graining size

amg e based on element agglomeration this paper contains the main ideas for an amge algebraic multigrid for finite elements method based on element agglomeration in the method coarse grid elements are formed by agglomerating fine grid elements compatible interpolation operators are constructed which yield coarse grid basis functions with a minimal energy property heuristics based on interpolation quality measures are used to guide the agglomeration procedure the performance of the resulting method is demonstrated in two level numerical experiments

the analysis of ring recovery data using random effects we show how random terms describing both yearly variation and overdispersion can easily be incorporated into models for mark recovery data through the use of bayesian methods for recovery data on lapwings we show that the incorporation of the random terms greatly improves the goodness of fit omitting the random terms can lead to overestimation of the significance of weather on survival and overoptimistic prediction intervals in simulations of future population behavior random effects models provide a natural way of modeling overdispersion which is more satisfactory than the standard classical approach of scaling up all standard errors by a uniform inflation factor we compare models by means of bayesian p values and the deviance information criterion dic

error bounds for numerical inversion of a probability characteristic function given the characteristic function of a continuous real random variable it is possible to construct a finite fourier series that approximates the density over any specified finite interval this series converges in mean square if the density decays faster than x 1 and the characteristic function decays faster than t 1 2 it converges in minimax if the density decays faster than x 1 and the characteristic function decays faster than t 1 it is also possible to construct a finite fourier series for the distribution function that has arbitrarily small maximum error over any finite interval provided that the characteristic function decays as t beta for some beta 0 and that either the distribution or the density decays to 0 or 1 as appropriate as x alpha for some alpha 1 these conditions are weak enough to include most continuous distributions of practical interest explicit error bounds can be obtained directly from the characteristic function without prior knowledge of either the distribution or density making these series useful for numerical inversion

on the method of logarithmic cumulants for parametric probability density function estimation parameter estimation of probability density functions is one of the major steps in the area of statistical image and signal processing in this paper we explore several properties and limitations of the recently proposed method of logarithmic cumulants molc parameter estimation approach which is an alternative to the classical maximum likelihood ml and method of moments mom approaches we derive the general sufficient condition for a strong consistency of the molc estimates which represents an important asymptotic property of any statistical estimator this result enables the demonstration of the strong consistency of molc estimates for a selection of widely used distribution families originating from but not restricted to synthetic aperture radar image processing we then derive the analytical conditions of applicability of molc to samples for the distribution families in our selection finally we conduct various synthetic and real data experiments to assess the comparative properties applicability and small sample performance of molc notably for the generalized gamma and k families of distributions supervised image classification experiments are considered for medical ultrasound and remote sensing sar imagery the obtained results suggest that molc is a feasible and computationally fast yet not universally applicable alternative to mom molc becomes especially useful when the direct ml approach turns out to be unfeasible

edge detection in ultrasound imagery using the instantaneous coefficient of variation the instantaneous coefficient of variation icov edge detector based on normalized gradient and laplacian operators has been proposed for edge detection in ultrasound images in this paper the edge detection and localization performance of the icov squared icovs detector are examined first a simplified version of the icovs detector the normalized gradient magnitude squared is scrutinized in order to reveal the statistical performance of edge detection and localization in speckled ultrasound imagery both the probability of detection and the probability of false alarm are evaluated for the detector edge localization is characterized by the position of the peak and the 3 db width of the detector response then the speckle edge response of the icovs as applied to a realistic edge model is studied through theoretical analysis we reveal the compensatory effects of the normalized laplacian operator in the icov edge detector for edge localization error an icov based edge detection algorithm is implemented in which the icov detector is embedded in a diffusion coefficient in an anisotropic diffusion process experiments with real ultrasound images have shown that the proposed algorithm is effective in extracting edges in the presence of speckle quantitatively the icovs provides a lower localization error and qualitatively a dramatic improvement in edge detection performance over an existing edge detection method for speckled imagery

locally weighted polynomial regression parameter choice and application to forecasts of the great salt lake 1 relationships between hydrologic variables are often nonlinear usually the functional form of such a relationship is not known a priori a multivariate nonparametric regression methodology is provided here for approximating the underlying regression function using locally weighted polynomials locally weighted polynomials consider the approximation of the target function through a taylor series expansion of the function in the neighborhood of the point of estimate cross validatory procedures for the selection of the size of the neighborhood over which this approximation should take place and for the order of the local polynomial to use are provided and shown for some simple situations the utility of this nonparametric regression approach is demonstrated through an application to nonparametric short term forecasts of the biweekly great salt lake volume blind forecasts up to 1 year in the future using the 1847 2004 time series of the great salt lake are presented

the variation of non parametric estimates in closed loop it is known that non parametric transfer function estimates in closed loop often have infinite variance we characterise the probability density function of such estimates under the assumption that the corresponding closed loop system estimate has complex normal distribution in the frequency domain the probability density function can be described as a horseshoe encircling the inverse of the controller with a global maximum on the line between the true value and the inverse of the controller the expected value of the absolute value of such estimates is finite and we propose it as a measure of variation we also derive and discuss new expressions for the variance when an exclusion zone is introduced around the singularity

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

universality in the two dimensional continuous spin model monte carlo methods have been used to analyse the critical behaviour of the d 2 border phi 4 model which according to a recent series expansion study violates expectations based upon universality the results suggest that the model does in fact fall into the ising universality class at least as regards those parameters which characterise the critical point configurations of the ordering variable

optimal search in planar subdivisions a planar subdivision is any partition of the plane into possibly unbounded polygonal regions the subdivision search problem is the following given a subdivision s with n line segments and a query point p determine which region of s contains p we present a practical algorithm for subdivision search that achieves the same optimal worst case complexity bounds as the significantly more complex algorithm of lipton and tarjan namely o log n search time with o n storage our subdivision search structure can be constructed in linear time from the subdivision representation used in many applications

a sinusoidal contrast function for the blind separation of statistically independent sources the authors propose a new solution to the blind separation of sources bss based on statistical independence in the two dimensional 2 d case we prove that under the whiteness constraint the fourth order moment based approximation of the marginal entropy me cost function yields a sinusoidal objective function therefore we can minimize it by simply estimating its phase we prove that this estimator is consistent for any source distribution in addition such results are useful for interpreting other algorithms such as the cumulant based independent component analysis cubica and the weighted approximate maximum likelihood waml or weighted estimator we based on the waml we provide a general unifying form for several previous approximations to the me contrast the bias and the variance of this estimator have been included finally simulations illustrate the good consistency convergence and accuracy of the proposed method

inference in semiparametric dynamic models for binary longitudinal data this article deals with the analysis of a hierarchical semiparametric model for dynamic binary longitudinal responses the main complicating components of the model are an unknown covariate function and serial correlation in the errors existing estimation methods for models with these features are of o n3 where n is the total number of observations in the sample therefore nonparametric estimation is largely infeasible when the sample size is large as in typical in the longitudinal setting here we propose a new o n markov chain monte carlo based algorithm for estimation of the nonparametric function when the errors are correlated thus contributing to the growing literature on semiparametric and nonparametric mixed effects models for binary data in addition we address the problem of model choice to enable the formal comparison of our semiparametric model with competing parametric and semiparametric specifications the performance of the methods is illustrated with detailed studies involving simul

conditional power with fisher s least significant difference procedure summary conditional power calculations are very useful for assessing the likelihood of an ultimately statistically significant result given the current data we show how to calculate conditional power in a multi armed trial using the classic fisher least significant difference lsd procedure we obtain upper bounds on the probabilities of type 1 and type 2 errors analogous to those in two armed trials and show that these bounds are equalities under continuous monitoring

a note on jorgensen s iteratively defined statistics summary the newton raphson and fisher scoring iteratively reweighted least squares methods are two fundamental tools for computing parameter estimators and deletion diagnostics jorgensen 1993 proposed a modified method to compute deletion diagnostics in this paper we study the relationship between jorgensen s newton raphson and fisher scoring one step deletion estimators by using the observed and expected fisher information matrices in addition we extend jorgensen s true leverage and approximate leverage from binary regression models to general model settings

finite element approximations to surfaces of prescribed variable mean curvature we give an algorithm for finding finite element approximations to surfaces of prescribed variable mean curvature which span a given boundary curve we work in the parametric setting and prove optimal estimates in the h 1 norm the estimates are verified computationally

finding an unknown number of multivariate outliers we use the forward search to provide robust mahalanobis distances to detect the presence of outliers in a sample of multivariate normal data theoretical results on order statistics and on estimation in truncated samples provide the distribution of our test statistic we also introduce several new robust distances with associated distributional results comparisons of our procedure with tests using other robust mahalanobis distances show the good size and high power of our procedure we also provide a unification of results on correction factors for estimation from truncated samples

invariant bayesian inference in regression models that is robust against the jeffreys lindley s paradox we obtain the prior and posterior probability of a nested regression model as the hausdorff integral of the prior and posterior on the parameters of an encompassing linear regression model over a lower dimensional set that represents the nested model the hausdorff integral is invariant and therefore avoids the borel kolmogorov paradox basing priors and prior probabilities of nested regression models on the prior on the parameters of an encompassing linear regression model reduces the discrepancies between classical and bayesian inference like the jeffreys lindley s paradox we illustrate the analysis with examples of linear restrictions i e a linear regression model and non linear restrictions i e a cointegration and an autoregressive moving average model on the parameters of an encompassing linear regression model

optimality of multilevel preconditioners for local mesh refinement in three dimensions in this article we establish optimality of the bramble pasciak xu bpx norm equivalence and optimality of the wavelet modified or stabilized hierarchical basis whb preconditioner in the setting of local 3d mesh refinement in the analysis of whb methods a critical first step is to establish the optimality of bpx norm equivalence for the refinement procedures under consideration while the available optimality results for the bpx norm have been constructed primarily in the setting of uniformly refined meshes a notable exception is the local 2d red green result due to dahmen and kunoth the purpose of this article is to extend this original 2d optimality result to the local 3d red green refinement procedure introduced by bornemann erdmann and kornhuber and then to use this result to extend the whb optimality results from the quasi uniform setting to local 2d and 3d red green refinement scenarios the bpx extension is reduced to establishing that locally enriched finite element subspaces allow for the construction of a scaled basis which is formally riesz stable this construction turns out to rest not only on the shape regularity of the refined elements but also critically on a number of geometrical properties we establish between neighboring simplices produced by the bornemann erdmann kornhuber bek refinement procedure it is possible to show that the number of degrees of freedom used for smoothing is bounded by a constant times the number of degrees of freedom introduced at that level of refinement indicating that a practical implementable version of the resulting bpx preconditioner for the bek refinement setting has provably optimal linear computational complexity per iteration an interesting implication of the optimality of the whb preconditioner is the a priori h1 stability of the l2 projection the existing a posteriori approaches in the literature dictate a reconstruction of the mesh if such conditions cannot be satisfied the theoretical framework employed supports arbitrary spatial dimension d geq 1 and requires no coefficient smoothness assumptions beyond those required for well posedness in h1

some new tests of the power law process the power law process plp is often used to model failure data from repairable systems and its adequacy is tested with goodness of fit tests such as the cramer von mises test no single test however can be sensitive to all possible deviations from the plp exact tests that are powerful against some departures from the plp of particular interest to practitioners are derived heuristically the computation of their p values is described and their use is illustrated with examples one test is a modified version of the laplace test for trend another a modification of greenwood s test for clustering it is shown that these tests can be derived as score tests which ensures that they are powerful for large samples

coarse grained properties of three dimensional ising systems the universal coarse grained properties of three dimensional ising systems are investigated with the aid of wilson s recursion formula 1971 the helmholtz function is obtained in the critical regions both above and below the critical point the coarse grained free energy functional believed to control spinodal decomposition is also determined the crossover from non gaussian critical to gaussian central limit behaviour in the coarse grained coordinate distribution is investigated in both high and low temperature phases

a note on adjusted profile likelihoods in non linear regression summary the problem of partial non linear regression is used to provide an example of mccullagh and tibshirani s profile likelihood adjustment for more than one parameter of interest where for one linear nuisance parameter an expression for the adjusted profile likelihood can be derived

monte carlo state space likelihoods by weighted posterior kernel density estimation maximum likelihood estimation and likelihood ratio tests for nonlinear non gaussian state space models require numerical integration for likelihood calculations several methods including monte carlo mc expectation maximization mc likelihood ratios direct mc integration and particle filter likelihoods are inefficient for the motivating problem of stage structured population dynamics models in experimental settings an mc kernel likelihood mckl method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of bayesian posteriors mckl is derived by using bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals mc error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed zooming in on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant based approximation of mode bias a simulated example show

posterior probability intervals for wavelet thresholding summary we use cumulants to derive bayesian credible intervals for wavelet regression estimates the first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions these powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale hence a suitable modification of the discrete wavelet transform allows the posterior cumulants to be found efficiently for any given data set johnson transformations then yield the credible intervals themselves simulations show that these intervals have good coverage rates even when the underlying function is inhomogeneous where standard methods fail in the case where the curve is smooth the performance of our intervals remains competitive with established nonparametric regression methods

on a random area variable arising in discrete time queues and compact directed percolation a well known discrete time single server queueing system with mean arrival rate and mean departure rate is considered from the perspective of the area a swept out by the queue occupation process during a busy period we determine the exact form of the tail of the distribution pr a x in particular we show that pr a x cx 1 4 exp dx1 2 for all 1 where and expressions for c and d are given for the critical case 1 we show that pr a x c x 1 3 with c also given a simple mapping used in the derivation establishes a connection with compact directed percolation on a square lattice as a corollary therefore we are also able to specify the large area asymptotic behaviour of this model at all points in the phase diagram this extends previous scaling results which are only valid close to the percolation threshold

algorithms for refining triangular grids suitable for adaptive and multigrid techniques two general algorithms for refining triangular computational meshes based on the bisection of triangles by the longest side are presented and discussed the algorithms can be applied globally or locally for selective refinement of any conforming triangulation and always generate a new conforming triangulation after a finite number of interactions even when locally used the algorithms also ensure that all angles in subsequent refined triangulations are greater than or equal to half the smallest angle in the original triangulation the shape regularity of all triangles is maintained and the transition between small and large triangles is smooth in a natural way proofs of the above properties are presented the second algorithm is a simpler improved version of the first which retains most of the properties of the latter the algorithms can be used either for constructing irregular computational meshes or for locally refining any given triangulation in this sense they can be adequately combined with adaptive and or multigrid techniques for solving finite element systems examples of the application of the algorithms are given and two possible generalizations are pointed out

information geometric measure for neural spikes this study introduces information geometric measures to analyze neural firing patterns by taking not only the second order but also higher order interactions among neurons into account information geometry provides useful tools and concepts for this purpose including the orthogonality of coordinate parameters and the pythagoras relation in the kullback leibler divergence based on this orthogonality we show a novel method for analyzing spike firing patterns by decomposing the interactions of neurons of various orders as a result purely pairwise triple wise and higher order interactions are singled out we also demonstrate the benefits of our proposal by using several examples

curvatures for parameter subsets in nonlinear regression on etend les mesures de nonlinearite proposees par bates et watts 1980 a un sous ensemble arbitraire des parametres dans un modele de regression non lineaire normal

a fully discrete numerical scheme for weighted mean curvature flow we analyze a fully discrete numerical scheme approximating the evolution of n dimensional graphs under anisotropic mean curvature the highly nonlinear problem is discretized by piecewise linear finite elements in space and semi implicitly in time the scheme is unconditionally stable und we obtain optimal error estimates in natural norms we also present numerical examples which confirm our theoretical results

sensitivity of mrqap tests to collinearity and autocorrelation conditions multiple regression quadratic assignment procedures mrqap tests are permutation tests for multiple linear regression model coefficients for data organized in square matrices of relatedness among n objects such a data structure is typical in social network studies where variables indicate some type of relation between a given set of actors we present a new permutation method called double semi partialing or dsp that complements the family of extant approaches to mrqap tests we assess the statistical bias type i error rate and statistical power of the set of five methods including dsp across a variety of conditions of network autocorrelation of spuriousness size of confounder effect and of skewness in the data these conditions are explored across three assumed data distributions normal gamma and negative binomial we find that the freedman lane method and the dsp method are the most robust against a wide array of these conditions we also find that all five methods perform better if the test statistic is pivotal finally we find limitations of usefulness for mrqap tests all tests degrade under simultaneous conditions of extreme skewness and high spuriousness for gamma and negative binomial distributions

local modification of meshes for adaptive and or multigrid finite element methods abstract a mesh generation approach that allows the local modification of meshes of simplices is reviewed and discussed the generation and modification of sequences of nested irregular grids as needed for multigrid algorithms in the adaptive finite element setting can also be managed in 2 dimensions the meshes constructed are guaranteed to be nondegenerate and smooth empirical evidence has shown the 3d algorithm is in practice a powerful and realiable tool for mesh refinement

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners

group comparison of eigenvalues and eigenvectors of diffusion tensors diffusion tensor imaging dti data differ from most medical images in that values at each voxel are not scalars but 3 3 symmetric positive definite matrices called diffusion tensors dts the anatomic characteristics of the tissue at each voxel are reflected by the dt eigenvalues and eigenvectors in this article we consider the problem of testing whether the means of two groups of dt images are equal at each voxel in terms of the dt s eigenvalues eigenvectors or both because eigendecompositions are highly nonlinear existing likelihood ratio statistics lrts for testing differences in eigenvalues or eigenvectors of means of gaussian symmetric matrices assume an orthogonally invariant covariance structure between the matrix entries while retaining the form of the lrts we derive new approximations to their true distributions when the covariance between the dt entries is arbitrary and possibly different between the two groups the approximate distributions are those of similar lrt statistics comput

one to one piecewise linear mappings over triangulations we call a piecewise linear mapping from a planar triangulation to the plane a convex combination mapping if the image of every interior vertex is a convex combination of the images of its neighbouring vertices such mappings satisfy a discrete maximum principle and we show that they are one to one if they map the boundary of the triangulation homeomorphically to a convex polygon this result can be viewed as a discrete version of the rado kneser choquet theorem for harmonic mappings but is also closely related to tutte s theorem on barycentric mappings of planar graphs

multilevel solvers for unstructured surface meshes parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing such parameterization approaches give rise to large and exceedingly ill conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies since the underlying meshes are very fine to begin with such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy in this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature we introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner