a novel multiscale nonlinear thresholding method for ultrasonic speckle suppressing this paper presents a novel speckle suppression method for medical b scan ultrasonic images an original image is first separated into two parts with an adaptive filter these two parts are then transformed into a multiscale wavelet domain and the wavelet coefficients are processed by a soft thresholding method which is a variation of donoho s 1995 soft thresholding method the processed coefficients for each part are then transformed back into the space domain finally the denoised image is obtained as the sum of the two processed parts a computer simulated image and an in vitro b scan image of a pig heart have been used to test the performance of this new method this technique effectively reduces the speckle noise while preserving the resolvable details it performs well in comparison to the multiscale thresholding technique without adaptive preprocessing and two other speckle suppression methods

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

the logarithmic sobolev inequality for discrete spin systems on a lattice for finite range lattice gases with a finite spin space it is shown that the dobrushin shlosman mixing condition is equivalent to the existence of a logarithmic sobolev inequality for the associated unique gibbs state in addition implications of these considerations for the ergodic properties of the corresponding glauber dynamics are examined

adaptive noise smoothing filter for images with signal dependent noise in this paper we consider the restoration of images with signal dependent noise the filter is noise smoothing and adapts to local changes in image statistics based on a nonstationary mean nonstationary variance nmnv image model for images degraded by a class of uncorrelated signal dependent noise without blur the adaptive noise smoothing filter becomes a point processor and is similar to lee s local statistics algorithm 16 the filter is able to adapt itself to the nonstationary local image statistics in the presence of different types of signal dependent noise for multiplicative noise the adaptive noise smoothing filter is a systematic derivation of lee s algorithm with some extensions that allow different estimators for the local image variance the advantage of the derivation is its easy extension to deal with various types of signal dependent noise film grain and poisson signal dependent restoration problems are also considered as examples all the nonstationary image statistical parameters needed for the filter can be estimated from the noisy image and no a priori information about the original image is required

coercive inequalities for gibbs measures abstract we prove the generalized nash and logarithmic nash inequalities for gibbs measures with dirichlet form associated to the kawasaki dynamics

poincare and transportation inequalities for gibbs measures under the dobrushin uniqueness condition in in this paper we establish an explicit and sharp estimate of the spectral gap poincare inequality and the transportation inequality for gibbs measures under the dobrushin uniqueness condition moreover we give a generalization of the liggett s m e theorem for interacting particle systems

robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

nonlinear diffusion in laplacian pyramid domain for ultrasonic speckle reduction a new speckle reduction method i e laplacian pyramid based nonlinear diffusion lpnd is proposed for medical ultrasound imaging with this method speckle is removed by nonlinear diffusion filtering of bandpass ultrasound images in laplacian pyramid domain for nonlinear diffusion in each pyramid layer a gradient threshold is automatically determined by a variation of median absolute deviation mad estimator the performance of the proposed lpnd method has been compared with that of other speckle reduction methods including the recently proposed speckle reducing anisotropic diffusion srad and nonlinear coherent diffusion ncd in simulation and phantom studies an average gain of 1 55 db and 1 34 db in contrast to noise ratio was obtained compared to srad and ncd respectively the visual comparison of despeckled in vivo ultrasound images from liver and carotid artery shows that the proposed lpnd method could effectively preserve edges and detailed structures while thoroughly suppressing speckle these preliminary results indicate that the proposed speckle reduction method could improve image quality and the visibility of small structures and fine details in medical ultrasound imaging

logarithmic sobolev inequalities for mollified compactly supported measures abstract we show that the convolution of a compactly supported measure on r with a gaussian measure satisfies a logarithmic sobolev inequality lsi we use this result to give a new proof of a classical result in random matrix theory that states that under certain hypotheses the empirical law of eigenvalues of a sequence of random real symmetric matrices converges weakly in probability to its mean we then examine the optimal constants in the lsis for the convolved measures in terms of the variance of the convolving gaussian we conclude with partial results on the extension of our main theorem to higher dimensions

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

on parametric bootstrap methods for small area prediction summary the particularly wide range of applications of small area prediction e g in policy making decisions has meant that this topic has received substantial attention in recent years the problems of estimating mean squared predictive error of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers although existing methodology is still restricted to a narrow range of models to overcome this difficulty we develop new bootstrap based methods which are applicable in very general settings for constructing bias corrected estimators of mean squared error and for computing prediction regions unlike existing techniques which are based largely on taylor expansions our bias corrected mean squared error estimators do not require analytical calculation they also have the property that they are non negative our prediction intervals have a high degree of coverage accuracy o n 3 where n is the number of areas if double bootstrap methods are employed the techniques do not depend on the form of the small area estimator and are applicable to general two level small area models where the variables at either level can be discrete or continuous and in particular can be non normal most importantly the new methods are simple and easy to apply

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

cutoff for the ising model on the lattice introduced in 1963 glauber dynamics is one of the most practiced and extensively studied methods for sampling the ising model on lattices it is well known that at high temperatures the time it takes this chain to mix in l 1 on a system of size n is o logn whether in this regime there is cutoff i e a sharp transition in the l 1 convergence to equilibrium is a fundamental open problem if so as conjectured by peres it would imply that mixing occurs abruptly at c o 1 logn for some fixed c 0 thus providing a rigorous stopping rule for this mcmc sampler however obtaining the precise asymptotics of the mixing and proving cutoff can be extremely challenging even for fairly simple markov chains already for the one dimensional ising model showing cutoff is a longstanding open problem

uniqueness and global markov property for euclidean fields the case of general polynomial interactions we give a general method for proving uniqueness and global markov property for euclidean quantum fields the method is based on uniform continuity of local specifications proved by using potential theoretical tools and exploitation of a suitable fkg order structure we apply this method to give a proof of uniqueness and global markov property for the gibbs states and to study extremality of gibbs states also in the case of non uniqueness in particular we prove extremality for 2 4 also in the case of non uniqueness and global markov property for weak coupling 2 4 which solves a long standing problem uniqueness and extremality holds also at any point of differentiability of the pressure with respect to the external magnetic field

dispersion matrix in balanced mixed anova models the inverse of the dispersion matrix plays an important role in mixed model analysis searle and henderson j amer statist assoc 74 1979 465 showed that for a general balanced mixed anova model such an inverse can be expression in the same form as the dispersion matrix i e a linear combination of kronecker products however the coefficients of such a linear combination are given in a way that it is not easy to see what each coefficient is in this paper we give explicit expressions for these coefficients an application of the result is considered

comparing noisy patches for image denoising a double noise similarity model this paper presents a concept of noise similarity ns which can be used to refine the comparison of noisy patch and enhance the denoising power of the nonlocal means nlm filter the fact behind this concept is that the similarity of noisy patch should depend on not only the underlying signal noise free patches but also the noise based on the concept of noise similarity we derived a double ns dns model which converts the denoising problem into the problem of reducing two kinds of noise one is the superimposed additive noise the other is the deviation error defined as another kind of noise denoting the difference between similar pixels on their true intensities the former corresponds to noise suppression while the latter corresponds to the restoration of image details to evaluate the effectiveness of the dns model we proposed an iterative version of the nlm filter where the two noise similarities can work collaboratively in the framework of maximum a posterior finally the experimental results demonstrate that the proposed approach can provide competitive performance when compared with other state of the art nlm filters

approach to equilibrium of glauber dynamics in the one phase region i the attractive case various finite volume mixing conditions in classical statistical mechanics are reviewed and critically analyzed in particular somefinite size conditions are discussed together with their implications for the gibbs measures and for the approach to equilibrium of glauber dynamics inarbitrarily large volumes it is shown that dobrushin shlosman s theory ofcomplete analyticity and its dynamical counterpart due to stroock and zegarlinski cannot be applied in general to the whole one phase region since it requires mixing properties for regions ofarbitrary shape an alternative approach based on previous ideas of oliveri and picco is developed which allows to establish results on rapid approach to equilibrium deeply inside the one phase region in particular in the ferromagnetic case we considerably improve some previous results by holley and aizenman and holley our results are optimal in the sene that for example they show for the first time fast convergence of the dynamicsfor any temperature above the critical one for thed dimensional ising model with or without an external field in part ii we extensively consider the general case not necessarily attractive and we develop a new method based on renormalizations group ideas and on an assumption of strong mixing in a finite cube to prove hypercontractivity of the markov semigroup of the glauber dynamics

rayleigh maximum likelihood filtering for speckle reduction of ultrasound images speckle is a multiplicative noise that degrades ultrasound images recent advancements in ultrasound instrumentation and portable ultrasound devices necessitate the need for more robust despeckling techniques for both routine clinical practice and teleconsultation methods previously proposed for speckle reduction suffer from two major limitations 1 noise attenuation is not sufficient especially in the smooth and background areas 2 existing methods do not sufficiently preserve or enhance edges they only inhibit smoothing near edges in this paper we propose a novel technique that is capable of reducing the speckle more effectively than previous methods and jointly enhancing the edge information rather than just inhibiting smoothing the proposed method utilizes the rayleigh distribution to model the speckle and adopts the robust maximum likelihood estimation approach the resulting estimator is statistically analyzed through first and second moment derivations a tuning parameter that naturally evolves in the estimation equation is analyzed and an adaptive method utilizing the instantaneous coefficient of variation is proposed to adjust this parameter to further tailor performance a weighted version of the proposed estimator is introduced to exploit varying statistics of input samples finally the proposed method is evaluated and compared to well accepted methods through simulations utilizing synthetic and real ultrasound data

estimation in covariance components models abstract estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes the estimation of fixed and random effects when the variances and covariances are known is presented in bayesian terms point estimates of the unknown variances and covariances are computed using the em algorithm for maximum likelihood estimation from incomplete data the techniques are illustrated with data on law schools field mice and professional football teams

speckle reducing anisotropic diffusion this paper provides the derivation of speckle reducing anisotropic diffusion srad a diffusion method tailored to ultrasonic and radar imaging applications srad is the edge sensitive diffusion for speckled images in the same way that conventional anisotropic diffusion is the edge sensitive diffusion for images corrupted with additive noise we first show that the lee and frost filters can be cast as partial differential equations and then we derive srad by allowing edge sensitive anisotropic diffusion within this context just as the lee 1980 1981 1986 and frost 1982 filters utilize the coefficient of variation in adaptive filtering srad exploits the instantaneous coefficient of variation which is shown to be a function of the local gradient magnitude and laplacian operators we validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery we also demonstrate the algorithm performance with real sar data the performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes in the presence of speckle noise speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation variance reduction and edge localization

invariance implies gibbsian some new results we investigate stationary distributions of stochastic gradient systems in riemannian manifolds and prove that under certain assumptions such distributions are symmetric these results are extended to countable products of finite dimensional manifolds and applied to gibbs distributions in the case where the single spin spaces are riemannian manifolds in particular we obtain a new result concerning the question whether all invariant measures are gibbsian actually we consider a more general object weak elliptic equations for measures which on the one hand yields the results obtained stronger than the above mentioned statements and on the other hand enables us to give simpler proofs of more general than previously known facts applications to concrete models of lattice systems over d with not necessarily compact spin space are presented also in the case d 3 under certain assumptions of decay of interaction

evaluation of four probability distribution models for speckle in clinical cardiac ultrasound images segmenting cardiac ultrasound images requires a model for the statistics of speckle in the images although the statistics of speckle are well understood for the raw transducer signal the statistics of speckle in the image are not this paper evaluates simple empirical models for first order statistics for the distribution of gray levels in speckle the models are created by analyzing over 100 images obtained from commercial ultrasound machines in clinical settings the data in the images suggests a unimodal scalable family of distributions as a plausible model four families of distributions gamma weibull normal and log normal are compared with the data using goodness of fit and misclassification tests attention is devoted to the analysis of artifacts in images and to the choice of goodness of fit and misclassification tests the distribution of parameters of one of the models is investigated and priors for the distribution are suggested

small area estimation when auxiliary information is measured with error summary small area estimation methods typically combine direct estimates from a survey with pre dictions from a model in order to obtain estimates of population quantities with reduced mean squared error when the auxiliary information used in the model is measured with error using a small area estimator such as the fay herriot estimator while ignoring measurement error may be worse than simply using the direct estimator we propose a new small area estimator that accounts for sampling variability in the auxiliary information and derive its properties in particular show ing that it is approximately unbiased the estimator is applied to predict quantities measured in the u s national health and nutrition examination survey with auxiliary information from the u s national health interview survey

robust empirical bayes estimation of means from stratified samples abstract this article considers simultaneous estimation of means from several strata where each stratum contains a finite number of elements for example quite often estimates of annual incomes unemployment rates and so forth must be made simultaneously for many areas our results find application in small area estimation where very few samples are available from an individual area and an estimate of a certain area mean or simultaneous estimates of several area means can be improved by incorporating information from similar neighboring areas ghosh and meeden 1986 considered empirical bayes estimation of the finite population mean assuming a normal superpopulation model their estimators generalize automatically when one estimates a vector of stratum means this article relaxes the normality assumption and assumes instead that the posterior expectation of any stratum mean is a linear function of the sample observations this is the so called posterior linearity property as described in ericson 1

small area estimation with uncertain random effects random effects models play an important role in model based small area estimation random effects account for any lack of fit of a regression model for the population means of small areas on a set of explanatory variables in a recent article datta hall and mandal showed that if the random effects can be dispensed with via a suitable test then the model parameters and the small area means may be estimated with substantially higher accuracy the work of datta hall and mandal is most useful when the number of small areas m is moderately large for large m the null hypothesis of no random effects will likely be rejected rejection of the null hypothesis is usually caused by a few large residuals signifying a departure of the direct estimator from the synthetic regression estimator as a flexible alternative to the fay herriot random effects model and the approach in datta hall and mandal in this article we consider a mixture model for random effects it is reasonably expected that small areas wit

goodness of fit tests for mixed model diagnostics a simple goodness of fit test is proposed for checking distributional assumptions involved in a mixed linear model an estimated critical value of the test statistic is derived and is shown to be asymptotically correct under mild conditions as a special case the test may be applied to linear regression models to formally check distribution of the errors finite sample performance of the proposed test is examined and compared with that of a previously proposed test by simulations

novel bayesian multiscale method for speckle removal in medical ultrasound images a novel speckle suppression method for medical ultrasound images is presented first the logarithmic transform of the original image is analyzed into the multiscale wavelet domain the authors show that the subband decompositions of ultrasound images have significantly non gaussian statistics that are best described by families of heavy tailed distributions such as the alpha stable then the authors design a bayesian estimator that exploits these statistics they use the alpha stable model to develop a blind noise removal processor that performs a nonlinear operation on the data finally the authors compare their technique with current state of the art soft and hard thresholding methods applied on actual ultrasound medical images and they quantify the achieved performance improvement

detection of significant disease risks using a spatial conditional autoregressive model summary the conditional autoregressive car model is widely used to describe the geographical distribution of a specific disease risk in lattice mapping successful developments based on frequentist and bayesian procedures have been extensively applied to obtain two stage disease risk predictions at the subregional level bayesian procedures are preferred for making inferences as the posterior standard errors se of the two stage prediction account for the variability in the variance component estimates however some recent work based on frequentist procedures and the use of bootstrap adjustments for the se has been undertaken in this article we investigate the suitability of an analytical adjustment for disease risk inference that provides accurate interval predictions by using the penalized quasilikelihood pql technique to obtain model parameter estimates the method is a first order approximation of the naive se based on a taylor expansion and is interpreted as a conditional measure of variability providing conditional calibrated prediction intervals given the data we conduct a simulation study to demonstrate how the method can be used to estimate the specific subregion risk by interval we evaluate the proposed methodology by analyzing the commonly used example data set of lip cancer incidence in the 56 counties of scotland for the period 1975 1980 this evaluation reveals a close similarity between the solutions provided by the method proposed here and those of its fully bayesian counterpart

optimal spatial adaptation for patch based image denoising a novel adaptive and patch based approach is proposed for image denoising and representation the method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel our contribution is to associate with each pixel the weighted sum of data points within an adaptive neighborhood in a manner that it balances the accuracy of approximation and the stochastic error at each spatial position this method is general and can be applied under the assumption that there exists repetitive patterns in a local neighborhood of a point by introducing spatial adaptivity we extend the work earlier described by buades et al which can be considered as an extension of bilateral filtering to image patches finally we propose a nearly parameter free algorithm for image denoising the method is applied to both artificially corrupted white gaussian noise and real images and the performance is very close to and in some cases even surpasses that of the already published denoising methods

on equivalence of spin and field pictures of lattice systems we investigate the spin and field systems on a lattice connected by the kac siegert transform it is shown that the structures of corresponding theories are equivalent in the sense of isomorphy of space of gibbs states and order parameters using the idea of equivalence of spin and field pictures we exhibit a class of lattice systems possessing infinitely uncountably many ground states the systems of this type with infinite range slow decaying interactions are expected to have a spin glass phase transition

spectral gap and logarithmic sobolev inequality for kawasaki and glauber dynamics we prove that the spectral gap of the kawasaki dynamics shrink at the rate of 1 l2 for cubes of sizel provided that some mixing conditions are satisfied we also prove that the logarithmic sobolev inequality for the glauber dynamics in standard cubes holds uniformly in the size of the cube if the dobrushin shlosman mixing condition holds for standard cubes

isoperimetry for gibbs measures we show that a strong mixing condition implies a bakry bobkov ledoux inequality for a probability measure on infinite dimensional space

small area inference for binary variables in the national health interview survey abstract the national health interview survey is designed to produce precise estimates of finite population parameters for the entire united states but not for small geographical areas or subpopulations our investigation concerns estimates of proportions such as the probability of at least one visit to a doctor within the past 12 months to include all sources of variation in the model we carry out a bayesian hierarchical analysis for the desired finite population quantities first for each cluster county a separate logistic regression relates the individual s probability of a doctor visit to his or her characteristics second a multivariate linear regression links cluster regression parameters to covariates measured at the cluster level we describe the numerical methods needed to obtain the desired posterior moments then we compare estimates produced using the exact numerical method with approximations finally we compare the hierarchical bayes estimates to empirical bayes estimates and to stand

small area estimation based on natural exponential family quadratic variance function models and survey weights summary we propose pseudo empirical best linear unbiased estimators of small area means based on natural exponential family quadratic variance function models when the basic data consist of survey weighted estimators of these means area specific covariates and certain summary measures involving the weights we also provide explicit approximate mean squared errors of these estimators in the spirit of prasad rao 1990 and these estimators can be readily evaluated a simulation study is undertaken to evaluate the performance of the proposed inferential procedure we estimate also the proportion of poor children in the 5 17 years age group for the different counties in one of the states in the united states

hypercontractivity in noncommutative lpspaces we introduce and study a setup for hypercontractivity in the interpolating family of noncommutative lpspaces associated to a locally normal state on an inductive limitc algebra

hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic ising models abstract we describe some results relating the spectral gap and logarithmic sobolev constants we work initially in the context of symmetric diffusions on a finite dimensional manifold and later apply our results to the analysis of certain infinite systems of mildly interacting diffusions

speckle reduction and contrast enhancement of echocardiograms via multiscale nonlinear processing this paper presents an algorithm for speckle reduction and contrast enhancement of echocardiographic images within a framework of multiscale wavelet analysis the authors apply wavelet shrinkage techniques to eliminate noise while preserving the sharpness of salient features in addition nonlinear processing of feature energy is carried out to enhance contrast within local structures and along object boundaries the authors show that the algorithm is capable of not only reducing speckle but also enhancing features of diagnostic importance such as myocardial walls in two dimensional echocardiograms obtained from the parasternal short axis view shrinkage of wavelet coefficients via soft thresholding within finer levels of scale is carried out on coefficients of logarithmically transformed echocardiograms enhancement of echocardiographic features is accomplished via nonlinear stretching followed by hard thresholding of wavelet coefficients within selected midrange spatial frequency levels of analysis the authors formulate the denoising and enhancement problem introduce a class of dyadic wavelets and describe their implementation of a dyadic wavelet transform their approach for speckle reduction and contrast enhancement was shown to be less affected by pseudo gibbs phenomena the authors show experimentally that this technique produced superior results both qualitatively and quantitatively when compared to results obtained from existing denoising methods alone a study using a database of clinical echocardiographic images suggests that such denoising and enhancement may improve the overall consistency of expert observers to manually defined borders

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n sphere a logarithmic sobolev inequality with respect to the probability measure a 1 x2 12 dx on 1 1 is proved for all 12 from this inequality sharp hypercontractive estimates are derived for the heat semigroups for ultraspherical polynomials and on the n sphere

design and sample size considerations for valuation studies of multi attribute utility instruments the eq 5d a widely used multiattribute utility instrument is commonly used in health economic evaluations where the goal is to decide on which treatments to reimburse like other instruments value sets of the eq 5d are constructed using valuation studies typically valuing a subset of the health states and using predicted values from a regression model for the unvalued health states in current practice the prediction errors associated with the value sets are substantial the goal of this work is 2 fold first derive a formula of the mean squared error mse of a value set assuming that the value set is estimated using a linear mixed model with either an independent or a gaussian spatial correlation on the model misspecification error second explore the effect of the number of health states directly valued the number of participants and the correlation structure on the mse keeping the total number of participants and the total number of valuations fixed valuing all 242 health states of the eq 5d 3l was found to reduce the mse considerably compared with the common practice of valuing only 42 health states furthermore an independent correlation structure with 3773 participants valuing 42 health states produced the mse that can be achieved with less than 600 participants valuing all 242 health states under a gaussian spatial correlation structure based on the comparison of the mse values of some of the well known designs our suggestion is to value more health states and to use a model with spatially correlated misspecification errors

empirical bayes estimation in finite population sampling abstract empirical bayes methods are becoming increasingly popular in statistics robbins 1955 introduced the method in the context of nonparametric estimation of a completely unspecified prior distribution subsequently the method has been explored very successfully in a series of articles by efron and morris 1973 1975 1977 in a parametric framework in the efron morris setup a family of parametric distributions is used as possible priors but only when one or more of the parameters of the family of prior distributions is estimated from the data morris 1983 listed a number of areas where empirical bayes methods are used one of the main features of empirical bayes analysis is to borrow strength from the ensemble that is use information from similar sources in constructing estimators and predictors in addition to the most directly available source of information there are some situations in finite population sampling where such methods might be suitable for instance in many repetitive surve

correlation at low temperature i exponential decay abstract the present paper generalizes the analysis in ann h poincare 1 2000 59 math j ams 8 1997 123 of the correlations for a lattice system of real valued spins at low temperature the gibbs measure is assumed to be generated by a fairly general hamiltonian function with pair interaction the novelty as compared to 2 20 is that the single site self energies of the spins are not required to have only a single local minimum and no other extrema our derivation of exponential decay of correlations goes through the spectral analysis of a deformed laplacian closely related to the witten laplacian studied in 2 20 we prove that this laplacian has a spectral gap above zero and argue that this implies exponential decay of the correlations

mean squared error estimation in transformed fay herriot models summary the problem of accurately estimating the mean squared error of small area estimators within a fay herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable for bias corrected empirical best linear unbiased predictor small area point estimators mean squared error formulae and estimators are provided with biases of smaller order than the reciprocal of the number of small areas the performance of these mean squared error estimators is illustrated by a simulation study and a real data example relating to the county level estimation of child poverty rates in the us census bureau s on going small area income and poverty estimation project

on the design consistency property of hierarchical bayes estimators in finite population sampling we obtain a limit of a hierarchical bayes estimator of a finite population mean when the sample size is large the limit is in the sense of ordinary calculus where the sample observations are treated as fixed quantities our result suggests a simple way to correct the hierarchical bayes estimator to achieve design consistency a well known property in the traditional randomization approach to finite population sampling we also suggest three different measures of uncertainty of our proposed estimator

the logarithmic sobolev inequality for continuous spin systems on a lattice abstract in this article we give cf theorem 1 6 a sufficient condition on a local specification for the associated gibbs state to satisfy a logarithmic sobolev inequality in the final section cf theorem 3 10 we relate our condition to the type of mixing condition introduced by dobrushin and shlosman in connection with their work on complete analyticity

postreconstruction nonlocal means filtering of whole body pet with an anatomical prior positron emission tomography pet images usually suffer from poor signal to noise ratio snr due to the high level of noise and low spatial resolution which adversely affect its performance for lesion detection and quantification the complementary information present in high resolution anatomical images from multi modality imaging systems could potentially be used to improve the ability to detect and or quantify lesions however previous methods that use anatomical priors usually require matched organ lesion boundaries in this study we investigated the use of anatomical information to suppress noise in pet images while preserving both quantitative accuracy and the amplitude of prominent signals that do not have corresponding boundaries on computerized tomography ct the proposed approach was realized through a postreconstruction filter based on the nonlocal means nlm filter which reduces noise by computing the weighted average of voxels based on the similarity measurement between patches of voxels within the image anatomical knowledge obtained from ct was incorporated to constrain the similarity measurement within a subset of voxels in contrast to other methods that use anatomical priors the actual number of neighboring voxels and weights used for smoothing were determined from a robust measurement on pet images within the subset thus the proposed approach can be robust to signal mismatches between pet and ct a 3 d search scheme was also investigated for the volumetric pet ct data the proposed anatomically guided median nonlocal means filter amnlm was first evaluated using a computer phantom and a physical phantom to simulate realistic but challenging situations where small lesions are located in homogeneous regions which can be detected on pet but not on ct the proposed method was further assessed with a clinical study of a patient with lung lesions the performance of the proposed method was compared to gaussian edge preserving bilateral and nlm filters as well as median nonlocal means mnlm filtering without an anatomical prior the proposed amnlm method yielded improved lesion contrast and snr compared with other methods even with imperfect anatomical knowledge such as missing lesion boundaries and mismatched organ boundaries

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

how the unbounded drift shapes the dirichlet semigroups behaviour of non gaussian gibbs measures abstract we investigate the dirichlet operator semigroups of non gaussian gibbs measures on linear spin lattice systems we prove that dirichlet semigroups preserve spaces of l 2 differentiable functions we show how the non linearity and unboundedness of drift term in dirichlet operator affects the structure of the spaces involved

logarithmic sobolev inequality for lattice gases with mixing conditions let mu lambda l lambda gc denote the grand canonical gibbs measure of a lattice gas in a cube of sizel with the chemical potential and a fixed boundary condition let mu lambda l n c be the corresponding canonical measure defined by conditioning mu lambda l lambda gc on sigma x in lambda eta x n consider the lattice gas dynamics for which each particle performs random walk with rates depending on near by particles the rates are chosen such that for everyn andl fixed mu lambda l n c is a reversible measure suppose that the dobrushin shlosman mixing conditions holds for mu l lambda gc forall chemical potentials we prove that smallint f log fd mu lambda l n c leqq const l 2 d sqrt f for any probability densityf with respect to mu lambda l n c here the constant is independent ofn orl andd denotes the dirichlet form of the dynamics the dependence onl is optimal

log sobolev inequalities for infinite one dimensional lattice systems it is shown that a unique gibbs measure of infinite spin system with short range interaction on one dimensional lattice satisfies log sobolev inequality

sumca simple unified monte carlo assisted approach to second order unbiased mean squared prediction error estimation we propose a simple unified monte carlo assisted approach called sumca to second order unbiased estimation of the mean squared prediction error mspe of a small area predictor the mspe estimator proposed is easy to derive has a simple expression and applies to a broad range of predictors that include the traditional empirical best linear unbiased predictor empirical best predictor and post model selection empirical best linear unbiased predictor and empirical best predictor as special cases furthermore the leading term of the mspe estimator proposed is guaranteed positive the lower order term corresponds to a bias correction which can be evaluated via a monte carlo method the computational burden for the monte carlo evaluation is much less compared with other monte carlo based methods that have been used for producing second order unbiased mspe estimators such as the double bootstrap and monte carlo jackknife the sumca estimator also has a nice stability feature theoretical and empirical results demonstrate properties and advantages of the sumca estimator

mean squared error of empirical predictor the term empirical predictor refers to a two stage predictor of a linear combination of fixed and random effects in the first stage a predictor is obtained but it involves unknown parameters thus in the second stage the unknown parameters are replaced by their estimators in this paper we consider mean squared errors mse of empirical predictors under a general setup where ml or reml estimators are used for the second stage we obtain second order approximation to the mse as well as an estimator of the mse correct to the same order the general results are applied to mixed linear models to obtain a second order approximation to the mse of the empirical best linear unbiased predictor eblup of a linear mixed effect and an estimator of the mse of eblup whose bias is correct to second order the general mixed linear model includes the mixed anova model and the longitudinal model as special cases

small area estimates for cross classifications we develop a class of log linear structural models that is suited to estimation of small area cross classified counts based on survey data this allows us to account for various association structures within the data and includes as a special case the restricted log linear model underlying structure preserving estimation the effect of survey design can be incorporated into estimation through the specification of an unbiased direct estimator and its associated covariance structure we illustrate our approach by applying it to estimation of small area labour force characteristics in norway

dobrushin uniqueness theorem and logarithmic sobolev inequalities we formulate a condition on a local specification e on a countable product space m m being a riemannian manifold or a discrete set 1 1 assuring that the corresponding set of gibbs measures consists of a unique measure satisfying a logarithmic sobolev inequality

delta method and bootstrap in linear mixed models to estimate a proportion when no event is observed application to intralesional resection in bone tumor surgery resecting bone tumors requires good cutting accuracy to reduce the occurrence of local recurrence this issue is considerably reduced with a navigated technology the estimation of extreme proportions is challenging especially with small or moderate sample sizes when no success is observed the commonly used binomial proportion confidence interval is not suitable while the rule of three provides a simple solution unfortunately these approaches are unable to differentiate between different unobserved events different delta methods and bootstrap procedures are compared in univariate and linear mixed models with simulations and real data by assuming the normality the delta method on the z score and parametric bootstrap provide similar results but the delta method requires the estimation of the covariance matrix of the estimates in mixed models the observed fisher information matrix with unbounded variance components should be preferred the parametric bootstrap easier to apply outperforms the delta method for larger sample sizes but it may be time costly copyright 2016 john wiley sons ltd

a very simple proof of the lsi for high temperature spin systems abstract we present a very simple proof that the o n model satisfies a uniform logarithmic sobolev inequality lsi if the difference between the largest and the smallest eigenvalue of the coupling matrix is less than n this condition applies in particular to the sk spin glass model at inverse temperature 1 4 it is the first result of rapid relaxation for the sk model and requires significant cancellations between the ferromagnetic and anti ferromagnetic spin couplings that cannot be obtained by existing methods to prove log sobolev inequalities the proof also applies to more general bounded and unbounded spin systems it uses a single step of zero range renormalisation and bakry emery theory for the renormalised measure

ultrasound image despeckling using stochastic distance based bm3d ultrasound image despeckling is an important research field since it can improve the interpretability of one of the main categories of medical imaging many techniques have been tried over the years for ultrasound despeckling and more recently a great deal of attention has been focused on patch based methods such as non local means and block matching collaborative filtering bm3d a common idea in these recent methods is the measure of distance between patches originally proposed as the euclidean distance for filtering additive white gaussian noise in this paper we derive new stochastic distances for the fisher tippett distribution based on well known statistical divergences and use them as patch distance measures in a modified version of the bm3d algorithm for despeckling log compressed ultrasound images state of the art results in filtering simulated synthetic and real ultrasound images confirm the potential of the proposed approach

uniqueness and the global markov property for euclidean fields the case of general exponential interaction the uniqueness and the global markov property for the regular gibbs measure corresponding to the interaction u lambda varphi lambda int limits lambda d 2 x int d varrho alpha e alpha varphi 0 x for 0 d a probability measure with support in 2 sqrt pi 2 sqrt pi is proved

comparisons of alternative predictors under the balanced one way random model abstract prediction of an arbitrary linear combination of the random effects of a balanced one way random model is investigated alternative two stage predictors are compared on the basis of their conditional on the random effects and unconditional bias and mean squared errors when the true value of the ratio of expected mean squares is known there exists a best linear unbiased predictor blup when the true value is unknown a two stage predictor obtained from the blup by replacing the true value with an estimated value can be used when the ratio of expected mean squares is estimated by maximum likelihood bayesian methods or various related methods a two stage predictor is obtained whose properties compare favorably with for example those of the least squares predictor and the positive part james stein predictor

uniform and l 2 convergence in one dimensional stochastic ising models we study the rate of convergence to equilibrium of one dimensional stochastic ising models with finite range interactions we donot assume that the interactions are ferromagnetic or that the flip rates are attractive the infinitesimal generators of these processes all have gaps between zero and the rest of their spectra we prove that if one of these processes is observed by means of local observables then the convergence is seen to be exponentially fast with an exponent that is any number less than the spectral gap moreover this exponential convergence is uniform in the initial configuration

critical ising on the square lattice mixes in polynomial time the ising model is widely regarded as the most studied model of spin systems in statistical physics the focus of this paper is its dynamic stochastic version the glauber dynamics introduced in 1963 and by now the most popular means of sampling the ising measure intensive study throughout the last three decades has yielded a rigorous understanding of the spectral gap of the dynamics on mathbb z 2 everywhere except at criticality while the critical behavior of the ising model has long been the focus for physicists mathematicians have only recently developed an understanding of its critical geometry with the advent of sle cle and new tools to study conformally invariant systems

local adaptivity to variable smoothness for exemplar based image regularization and representation a novel adaptive and exemplar based approach is proposed for image restoration denoising and representation the method is based on a pointwise selection of similar image patches of fixed size in the variable neighborhood of each pixel the main idea is to associate with each pixel the weighted sum of data points within an adaptive neighborhood we use small image patches e g 7 7 or 9 9 patches to compute these weights since they are able to capture local geometric patterns and texels seen in images in this paper we mainly focus on the problem of adaptive neighborhood selection in a manner that balances the accuracy of approximation and the stochastic error at each spatial position the proposed pointwise estimator is then iterative and automatically adapts to the degree of underlying smoothness with minimal a priori assumptions on the function to be recovered the method is applied to artificially corrupted real images and the performance is very close and in some cases even surpasses to that of the already published denoising methods the proposed algorithm is demonstrated on real images corrupted by non gaussian noise and is used for applications in bio imaging

approach to equilibrium of glauber dynamics in the one phase region ii the general case we develop a new method based on renormalization group ideas block decimation procedure to prove under an assumption of strong mixing in a finite cube 0 a logarithmic sobolev inequality for the gibbs state of a discrete spin system as a consequence we derive the hypercontractivity of the markov semigroup of the associated glauber dynamics and the exponential convergence to equilibrium in the uniform norm in all volumes multiples of the cube 0

benchmarked empirical bayes methods in multiplicative area level models with risk evaluation the paper develops empirical bayes and benchmarked empirical bayes estimators of positive small area means under multiplicative models a simple example will be estimation of per capita income for small areas it is now well understood that small area estimation needs explicit or at least implicit use of models one potential difficulty with model based estimators is that the overall estimator for a larger geographical area based on weighted sum of the model based estimators is not necessarily identical to the corresponding direct estimator such as the overall sample mean one way to fix such a problem is the so called benchmarking approach which modifies the model based estimators to match the aggregate direct estimator benchmarked hierarchical and empirical bayes estimators have proved to be particularly useful in this regard however while estimating positive small area parameters the conventional squared error or weighted squared loss subject to the usual benchmark constraint does not necessarily produce positive estimators hence it is necessary to seek other meaningful losses to alleviate this problem in this paper we consider the transformed fay herriot model as a multiplicative model for estimating positive small area means and suggest a weighted kullbackleibler divergence as a loss function we have found out that the resulting bayes estimator is the posterior mean and that the corresponding benchmarked bayes and empirical bayes estimators retain the positivity constraint the prediction errors of the suggested empirical bayes estimators are investigated asymptotically and their second order unbiased estimators are provided in addition bootstrapped estimators of these prediction errors are also provided the

some bayesian and non bayesian procedures for the analysis of comparative experiments and for small area estimation computational aspects frequentist properties and relationships abstract the estimation of a treatment contrast from experimental data and the estimation of a small area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two part mixed linear model in this article a bayesian approach to point and interval prediction is presented and its computational requirements are examined differences between the bayesian approach and the traditional classical approach are discussed in general terms and in addition in terms of two examples taken from the literature 1 the comparison of drug formulations in a bioavailability trial westlake and 2 the estimation of corn crop areas using satellite data battese harter and fuller some deficiencies in the classical approach are pointed out and the bayesian approach is considered from a frequentist perspective it is shown via a monte carlo study that for certain noninformative choices of the prior distribution the frequentist prop

an inequality for relative entropy and logarithmic sobolev inequalities in euclidean spaces for a class of density functions q x on rn we prove an inequality between relative entropy and the weighted sum of conditional relative entropies of the following form d p q const i 1n i d pi y1 yi 1 yi 1 yn qi y1 yi 1 yi 1 yn for any density function p x on rn where pi y1 yi 1 yi 1 yn and qi x1 xi 1 xi 1 xn denote the local specifications of p respectively q and i is the logarithmic sobolev constant of qi x1 xi 1 xi 1 xn thereby we derive a logarithmic sobolev inequality for a weighted gibbs sampler governed by the local specifications of q moreover the above inequality implies a classical logarithmic sobolev inequality for q as defined for gaussian distribution by gross this strengthens a result by otto and reznikoff the proof is based on ideas developed by otto and villani in their paper on the connection between talagrand s transportation cost inequality and logarithmic sobolev inequality

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

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

oriented speckle reducing anisotropic diffusion ultrasound imaging systems provide the clinician with noninvasive low cost and real time images that can help them in diagnosis planning and therapy however although the human eye is able to derive the meaningful information from these images automatic processing is very difficult due to noise and artifacts present in the image the speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images we analyze the properties of the numerical scheme associated with this filter using a semi explicit scheme we then extend the filter to a matrix anisotropic diffusion allowing different levels of filtering across the image contours and in the principal curvature directions we also show a relation between the local directional variance of the image intensity and the local geometry of the image which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix finally different filtering techniques are compared on a 2 d synthetic image with two different levels of multiplicative noise and on a 3 d synthetic image of a y junction and the new filter is applied on a 3 d real ultrasound image of the liver

anisotropic diffusion filter with memory based on speckle statistics for ultrasound images ultrasound us imaging exhibits considerable difficulties for medical visual inspection and for development of automatic analysis methods due to speckle which negatively affects the perception of tissue boundaries and the performance of automatic segmentation methods with the aim of alleviating the effect of speckle many filtering techniques are usually considered as a preprocessing step prior to automatic analysis methods or visual inspection most of the state of the art filters try to reduce the speckle effect without considering its relevance for the characterization of tissue nature however the speckle phenomenon is the inherent response of echo signals in tissues and can provide important features for clinical purposes this loss of information is even magnified due to the iterative process of some speckle filters e g diffusion filters which tend to produce over filtering because of the progressive loss of relevant information for diagnostic purposes during the diffusion process in this paper we propose an anisotropic diffusion filter with a probabilistic driven memory mechanism to overcome the over filtering problem by following a tissue selective philosophy in particular we formulate the memory mechanism as a delay differential equation for the diffusion tensor whose behavior depends on the statistics of the tissues by accelerating the diffusion process in meaningless regions and including the memory effect in regions where relevant details should be preserved results both in synthetic and real us images support the inclusion of the probabilistic memory mechanism for maintaining clinical relevant structures which are removed by the state of the art filters

nonlocal means based speckle filtering for ultrasound images in image processing restoration is expected to improve the qualitative inspection of the image and the performance of quantitative image analysis techniques in this paper an adaptation of the nonlocal nl means filter is proposed for speckle reduction in ultrasound us images originally developed for additive white gaussian noise we propose to use a bayesian framework to derive a nl means filter adapted to a relevant ultrasound noise model quantitative results on synthetic data show the performances of the proposed method compared to well established and state of the art methods results on real images demonstrate that the proposed method is able to preserve accurately edges and structural details of the image

combining census dual system and evaluation study data to estimate population shares abstract the 1990 census and post enumeration survey produced census and dual system estimates dse of population by domain together with an estimated sampling covariance matrix of the dse estimates of the bias of the dse were derived from various pes evaluation programs of the three sources the unadjusted census is the least variable but is believed to be the most biased the dse is less biased but more variable and the bias estimates may be regarded as unbiased but are the most variable this article addresses methods for combining the census the dse and bias estimates obtained from the evaluation programs to produce accurate estimates of population shares as measured by weighted squared or absolute error loss functions applied to estimated population shares of domains several procedures are reviewed that choose between the census and the dse using the bias evaluation data or that average the two with weights that are constant across domains a multivariate hierarchical bayes model is propose

cutoff for general spin systems with arbitrary boundary conditions the cutoff phenomenon describes a sharp transition in the convergence of a markov chain to equilibrium in recent work the authors established cutoff and its location for the stochastic ising model on the d dimensional torus n d for any d 1 the proof used the symmetric structure of the torus and monotonicity in an essential way here we enhance the framework and extend it to general geometries boundary conditions and external fields to derive a cutoff criterion that involves the growth rate of balls and the log sobolev constant of the glauber dynamics in particular we show there is cutoff for the stochastic ising model on any sequence of bounded degree graphs with subexponential growth under arbitrary external fields provided the inverse log sobolev constant is bounded for lattices with homogenous boundary such as all plus we identify the cutoff location explicitly in terms of spectral gaps of infinite volume dynamics on half plane intersections analogous results establishing cutoff are obtained for nonmonotone spin systems at high temperatures including the gas hard core model the potts model the antiferromagnetic potts model and the coloring model 2014 wiley periodicals inc