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

testing the order of a model using locally conic parametrization population mixtures and stationary arma processes in this paper we address the problem of testing hypotheses using the likelihood ratio test statistic in nonidentifiable models with application to model selection in situations where the parametrization for the larger model leads to nonidentifiability in the smaller model we give two major applications the case where the number of populations has to be tested in a mixture and the case of stationary arma p q processes where the order p q has to be tested we give the asymptotic distribution for the likelihood ratio test statistic when testing the order of the model in the case of order selection for armas the asymptotic distribution is invariant with respect to the parameters generating the process a locally conic parametrization is a key tool in deriving the limiting distributions it allows one to discover the deep similarity between the two problems

an advanced and adaptive mathematical function for an efficient anisotropic image filtering image de noising and enhancement are becoming increasingly widespread anisotropic diffusion is one of the greatest techniques that are used to remove noise of the image while keeping the important information unvaried nevertheless it suffers from many drawbacks such as the image blurring this work is concerned with a new anisotropic diffusion approach founded on an innovative mathematical function for noise reducing and edge preserving the entire contribution can be observed from the experimental results which have shown that the new proposed anisotropic scheme is not only able to remove the noise efficiently but also to preserve the content in the denoised image

derivation of hartree s theory for generic mean field bose systems in this paper we provide a novel strategy to prove the validity of hartree s theory for the ground state energy of bosonic quantum systems in the mean field regime for the well known case of trapped bose gases this can be shown using the strong quantum de finetti theorem which gives the structure of infinite hierarchies of k particles density matrices here we deal with the case where some particles are allowed to escape to infinity leading to a lack of compactness our approach is based on two ingredients 1 a weak version of the quantum de finetti theorem and 2 geometric techniques for many body systems our strategy does not rely on any special property of the interaction between the particles in particular our results cover those of benguria lieb and lieb yau for respectively bosonic atoms and boson stars

hypothesis testing under mixture models application to genetic linkage analysis summary in this paper we propose a new class of statistics to test a simple hypothesis against a family of alternatives characterized by a mixture model unlike the likelihood ratio statistic whose large sample distribution is still unknown in this situation these new statistics have a simple asymptotic distribution to which to refer under the null hypothesis simulation results suggest that it has adequate power in detecting the alternatives its application to genetic linkage analysis in the presence of the genetic heterogeneity that motivated this work is emphasized

theoretical explanation of observed decreasing failure rate pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate more refined analysis showed that the failure distribution for each airplane separately was exponential but with a different failure rate using the theorem that a mixture of distributions each having a non increasing failure rate e g a mixture of exponential distributions itself has a non increasing failure rate the apparent decreasing failure rate of the pooled air conditioning life distribution was satisfactorily explained the present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters

testing for a finite mixture model with two components summary we consider a finite mixture model with k components and a kernel distribution from a general one parameter family the problem of testing the hypothesis k 2 versus k 3 is studied there has been no general statistical testing procedure for this problem we propose a modified likelihood ratio statistic where under the null and the alternative hypotheses the estimates of the parameters are obtained from a modified likelihood function it is shown that estimators of the support points are consistent the asymptotic null distribution of the modified likelihood ratio test proposed is derived and found to be relatively simple and easily applied simulation studies for the asymptotic modified likelihood ratio test based on finite mixture models with normal binomial and poisson kernels suggest that the test proposed performs well simulation studies are also conducted for a bootstrap method with normal kernels an example involving foetal movement data from a medical study illustrates the testing procedure

a perturbed mean field model of an interacting boson gas and the large deviation principle this is a study of the equilibrium thermodynamics of a mean field model of an interacting boson gas perturbed by a term quadratic in the occupation numbers of the free gas energy levels we prove the existence of the pressure in the thermodynamic limit we obtain also a variational formula for the pressure this enables us to compare the effect of a smooth quadratic perturbation with that of a singular one the huang yang luttinger model the proof uses a large deviation result for the occupation measure of the free boson gas which is of independent interest

the yang yang thermodynamic formalism and large deviations the partition function for a one dimensional system of bosons with repulsive delta function interaction is investigated we prove that if the bethe ansatz eigenfunctions form a complete set then the grand canonical pressure is given by the yang yang formula the proof uses a probabilistic formalism to express the partition function as an expectation with respect to a probability measure on a banach space of measures the asymptotic behaviour of the expectation in the thermodynamic limit is determined by the large deviation principle this method is applicable in situations in which the hamiltonian can be diagonalised using the bethe ansatz

anisotropic diffusion with generalized diffusion coefficient function for defect detection in low contrast surface images in this paper an anisotropic diffusion model with a generalized diffusion coefficient function is presented for defect detection in low contrast surface images and especially aims at material surfaces found in liquid crystal display lcd manufacturing a defect embedded in a low contrast surface image is extremely difficult to detect because the intensity difference between the unevenly illuminated background and the defective region is hardly observable and no clear edges are present between the defect and its surroundings the proposed anisotropic diffusion model provides a generalized diffusion mechanism that can flexibly change the curve of the diffusion coefficient function it adaptively carries out a smoothing process for faultless areas and performs a sharpening process for defect areas in an image an entropy criterion is proposed as the performance measure of the diffused image and then a stochastic evolutionary computation algorithm particle swarm optimization pso is applied to automatically determine the best parameter values of the generalized diffusion coefficient function experimental results have shown that the proposed method can effectively and efficiently detect small defects in various low contrast surface images

image recovery using the anisotropic diffusion equation a new approach for image recovery using the anisotropic diffusion equation is developed which is based on the first derivative of the signal in time embedded in family of images with different scales the diffusion coefficient is determined as a function of the gradient of the signal convolved with a symmetric exponential filter a new discrete realization is developed for the simultaneous removal of noise and preservation of edges

testing the order of a finite mixture the order is an important parameter in applications of finite mixture models yet designing a valid and easy to use statistical test for the order is challenging to date most results on hypothesis tests have focused on homogeneity a special case where the null model has order 1 in this work we designed an em test for the general problem of testing the null hypothesis of order m0 versus an alternative hypothesis of order larger than m0 for any positive integer m0 the null limiting distribution of the em test is a mixture of 2 distributions the weights in this mixture limiting distribution can be conveniently computed compared with related results the new result is obtained under much less strict requirements on the component distribution and the parameter space extensive simulation studies show that the limiting distributions closely match the finite sample distributions of the em test when m0 2 the new em test has more accurate type i errors and matches the power of the modified likelihood

when is the student t statistic asymptotically standard normal let x x i i in mathbb n be independent identically distributed random variables it is shown that the student t statistic based upon the sample x i i 1 n is asymptotically n 0 1 if and only if x is in the domain of attraction of the normal law it is also shown that for any x if the self normalized sums u n sum i 1 n x i sum i 1 n x i 2 1 2 n in mathbb n are stochastically bounded then they are uniformly subgaussian that is sup n mathbb e exp lambda u n 2 infty for some lambda 0

asymptotics for likelihood ratio tests under loss of identifiability this paper describes the large sample properties of the likelihood ratio test statistic lrts when the parameters characterizing the true null distribution are not unique it is well known that the classical asymptotic theory for the likelihood ratio test does not apply to such problems and the lrts may not have the typical chi squared type limiting distribution this paper establishes a general quadratic approximation of the log likelihood ratio function in a hellinger neighborhood of the true density which is valid with or without loss of identifiability of the true distribution under suitable conditions the asymptotic null distribution of the lrts under loss of identifiability can be obtained by maximizing the quadratic form these results extend the work of chernoff and le cam in particular applications to testing the number of mixture components in finite mixture models are discussed

orthogonality and completeness of the bethe ansatz eigenstates of the nonlinear schroedinger model a rigorous proof is given of the orthogonality and the completeness of the bethe ansatz eigenstates of then body hamiltonian of the nonlinear schroedinger model on a finite interval the completeness proof is based on ideas of c n yang and c p yang but their continuity argument at infinite coupling is replaced by operator monotonicity at zero coupling the orthogonality proof uses the algebraic bethe ansatz method or inverse scattering method applied to a lattice approximation introduced by izergin and korepin the latter model is defined in terms of monodromy matrices without writing down an explicit hamiltonian it is shown that the eigenfunctions of the transfer matrices for this model converge to the bethe ansatz eigenstates of the nonlinear schroedinger model

non finite fisher information and homogeneity an em approach summary even simple examples of finite mixture models can fail to fulfil the regularity conditions that are routinely assumed in standard parametric inference problems many methods have been investigated for testing for homogeneity in finite mixture models for example but all rely on regularity conditions including the finiteness of the fisher information and the space of the mixing parameter being a compact subset of some euclidean space very simple examples where such assumptions fail include mixtures of two geometric distributions and two exponential distributions and more generally mixture models in scale distribution families to overcome these difficulties we propose and study an em test statistic which has a simple limiting distribution for examples in this paper simulations show that the em test has accurate type i errors and is more efficient than existing methods when they are applicable a real example is also included

a modified likelihood ratio test for homogeneity in finite mixture models summary testing for homogeneity in finite mixture models has been investigated by many researchers the asymptotic null distribution of the likelihood ratio test lrt is very complex and difficult to use in practice we propose a modified lrt for homogeneity in finite mixture models with a general parametric kernel distribution family the modified lrt has a x2 type of null limiting distribution and is asymptotically most powerful under local alternatives simulations show that it performs better than competing tests they also reveal that the limiting distribution with some adjustment can satisfactorily approximate the quantiles of the test statistic even for moderate sample sizes

continuous spin mean field models limiting kernels and gibbs properties of local transforms we extend the notion of gibbsianness for mean field systems to the setup of general possibly continuous local state spaces we investigate the gibbs properties of systems arising from an initial mean field gibbs measure by application of given local transition kernels this generalizes previous case studies made for spins taking finitely many values to the first step in the direction to a general theory containing the following parts 1 a formula for the limiting conditional probability distributions of the transformed system it holds both in the gibbs and in the non gibbs regime and invokes a minimization problem for a constrained rate function 2 a criterion for gibbsianness of the transformed system for initial lipschitz hamiltonians involving concentration properties of the transition kernels and 3 a continuity estimate for the single site conditional distributions of the transformed system while 2 and 3 have provable lattice counterparts the characterization of 1 is stronger in m

adaptive smoothing via contextual and local discontinuities a novel adaptive smoothing approach is proposed for noise removal and feature preservation where two distinct measures are simultaneously adopted to detect discontinuities in an image inhomogeneity underlying an image is employed as a multiscale measure to detect contextual discontinuities for feature preservation and control of the smoothing speed while local spatial gradient is used for detection of variable local discontinuities during smoothing unlike previous adaptive smoothing approaches two discontinuity measures are combined in our algorithm for synergy in preserving nontrivial features which leads to a constrained anisotropic diffusion process that inhomogeneity offers intrinsic constraints for selective smoothing thanks to the use of intrinsic constraints our smoothing scheme is insensitive to termination times and the resultant images in a wide range of iterations are applicable to achieve nearly identical results for various early vision tasks our algorithm is formally analyzed and related to anisotropic diffusion comparative results indicate that our algorithm yields favorable smoothing results and its application in extraction of hydrographic objects demonstrates its usefulness as a tool for early vision

nonlinear regularized reaction diffusion filters for denoising of images with textures denoising is always a challenging problem in natural imaging and geophysical data processing in this paper we consider the denoising of texture images using a nonlinear reaction diffusion equation and directional wavelet frames in our model a curvelet shrinkage is used for regularization of the diffusion process to preserve important features in the diffusion smoothing and a wave atom shrinkage is used as the reaction in order to preserve and enhance interesting oriented textures we derive a digital reaction diffusion filter that lives on graphs and show convergence of the corresponding iteration process experimental results and comparisons show very good performance of the proposed model for texture preserving denoising

testing homogeneity in a mixture distribution via the l2 distance between competing models ascertaining the number of components in a mixture distribution is an interesting and challenging problem for statisticians chen chen and kalbfleisch recently proposed a modified likelihood ratio test mlrt which is distribution free and locally most powerful asymptotically in this article we present a new method for testing whether a finite mixture distribution is homogeneous our method the d test is based on the l2 distance between a fitted homogeneous model and a fitted heterogeneous model for mixture components from standard parametric families the d test statistic has a closed form expression in terms of parameter estimators whereas likelihood ratio type test statistics do not the latter test statistics are nontrivial functions of both the parameter estimators and the full dataset the convergence rates of the d test statistic under a null hypothesis of homogeneity and an alternative hypothesis of heterogeneity are established the d test is shown to be competitive with the mlrt when th

testing the number of components in normal mixture regression models testing the number of components in finite normal mixture models is a long standing challenge because of its nonregularity this article studies likelihood based testing of the number of components in normal mixture regression models with heteroscedastic components we construct a likelihood based test of the null hypothesis of m0 components against the alternative hypothesis of m0 1 components for any m0 the null asymptotic distribution of the proposed modified em test statistic is the maximum of m0 random variables that can be easily simulated the simulations show that the proposed test has very good finite sample size and power properties supplementary materials for this article are available online

combined curvelet shrinkage and nonlinear anisotropic diffusion in this paper a diffusion based curvelet shrinkage is proposed for discontinuity preserving denoising using a combination of a new tight frame of curvelets with a nonlinear diffusion scheme in order to suppress the pseudo gibbs and curvelet like artifacts the conventional shrinkage results are further processed by a projected total variation diffusion in which only the insignificant curvelet coefficients or high frequency part of the signal are changed by use of a constrained projection numerical experiments from piecewise smooth to textured images show good performances of the proposed method to recover the shape of edges and important detailed components in comparison to some existing methods

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

plmet a novel pseudolikelihood based em test for homogeneity in generalilzed exponential tilt mixture models motivated by analyses of dna methylation data we propose a semiparametric mixture model namely the generalized exponential tilt mixture model to account for heterogeneity between differentially methylated and non differentially methylated subjects in the cancer group and capture the differences in higher order moments e g mean and variance between subjects in cancer and normal groups a pairwise pseudolikelihood is constructed to eliminate the unknown nuisance function to circumvent boundary and non identifiability problems as in parametric mixture models we modify the pseudolikelihood by adding a penalty function in addition the test with simple asymptotic distribution has computational advantages compared with permutation based test for high dimensional genetic or epigenetic data we propose a pseudolikelihood based expectation maximization test and show the proposed test follows a simple chi squared limiting distribution simulation studies show that the proposed test controls type i errors well and has better power compared to several current tests in particular the proposed test outperforms the commonly used tests under all simulation settings considered especially when there are variance differences between two groups the proposed test is applied to a real data set to identify differentially methylated sites between ovarian cancer subjects and normal subjects

tests for genetic linkage and homogeneity this report concerns likelihood ratio tests in a heterogeneous model for linkage where the recombination fraction has a binomial mixture distribution with an unknown proportion of unlinked families we consider families of unequal sizes with known or unknown phase data in both cases the limit distributions of the linkage test statistics are a mixture of a mass at and of a x2 1 distribution in equal proportions and homogeneity test statistics tend to the supremum of gaussian processes the critical values of the homogeneity tests are simulated and the power functions of the linkage and homogeneity tests are compared in a simulation study