fast and accurate binary response mixed model analysis via expectation propagation expectation propagation is a general prescription for approximation of integrals in statistical inference problems its literature is mainly concerned with bayesian inference scenarios however ex

anti aliased three dimensional cone beam reconstruction of low contrast objects with algebraic methods examines the use of the algebraic reconstruction technique art and related techniques to reconstruct 3 d objects from a relatively sparse set of cone beam projections although art has been widely used for cone beam reconstruction of high contrast objects e g in computed angiography the work presented here explores the more challenging low contrast case which represents a little investigated scenario for art preliminary experiments indicate that for cone angles greater than 20 spl deg traditional art produces reconstructions with strong aliasing artifacts these artifacts are in addition to the usual off midplane inaccuracies of cone beam tomography with planar orbits the authors find that the source of these artifacts is the nonuniform reconstruction grid sampling and correction by the cone beam rays during the art projection backprojection procedure a new method to compute the weights of the reconstruction matrix is devised which replaces the usual constant size interpolation filter by one whose size and amplitude is dependent on the source voxel distance this enables the generation of reconstructions free of cone beam aliasing artifacts at only little extra cost an alternative analysis reveals that simultaneous art sart also produces reconstructions without aliasing artifacts however at greater computational cost finally the authors thoroughly investigate the influence of various art parameters such as volume initialization relaxation coefficient spl lambda correction scheme number of iterations and noise in the projection data on reconstruction quality the authors find that art typically requires only 3 iterations to render satisfactory reconstruction results

the same class of stationary solutions to some multidimensional kinetic systems with extensive background density abstract in this study we investigate the existence and uniqueness of the same class of stationary solutions for some kinetic systems comprising the vlasov poisson fokker planck system vlasov poisson boltzmann system and vlasov maxwell boltzmann system in arbitrary space dimensions n n 3 essentially the problem can be reduced to solving the problem of a second order elliptic equation with exponential nonlinearity this result had been proved in three spatial dimensions but the extension to a higher dimensional setting makes the existence proof nontrivial in particular it necessary to highlight that the requirement regarding the background density function is relaxed compared with previous studies in the case of three spatial dimensions

asymptotic behaviour and self similarity for the three dimensional vlasov poisson fokker planck system abstract the aim of this work is to study the asymptotic behaviour of global in time solutions of the vlasov poisson fokker planck system in three dimensions we consider both cases with gravitational and electrostatic interaction but disregard friction it is proved that the distribution of particles tends for large time to the fundamental solution of the linear operator in l 1 norm which means that the effect of the interaction potential vanishes comparatively at t in quantitative terms the result assures that the total nonlinear interaction force decays for large time with a decay rate of order t 3 and the potential energy behaves like o t 3 2 the asymptotic result is independent of the repulsive or attractive character of the interaction field the main idea is to use the self similarity of the fundamental solution of the linear part of the equation and the regularity of the fokker planck operator in order to study the large time distribution of particles

on the trend to global equilibrium in spatially inhomogeneous entropy dissipating systems the linear fokker planck equation we study the long time behavior of kinetic equations in which transport and spatial confinement in an exterior potential or in a box are associated with a degenerate collision operator acting only in the velocity variable we expose a general method based on logarithmic sobolev inequalities and the entropy to overcome the well known problem due to the degeneracy in the position variable of the existence of infinitely many local equilibria this method requires that the solution be somewhat smooth in this paper we apply it to the linear fokker planck equation and prove decay to equilibrium faster than o t 1 for all 0 2001 john wiley sons inc

relative entropies for kinetic equations in bounded domains irreversibility stationary solutions uniqueness the relative entropy method describes the irreversibility of the vlasov poisson and vlasov boltzmann poisson systems in bounded domains with incoming boundary conditions uniform in time estimates are deduced from the entropy in some cases these estimates are sufficient to prove the convergence of the solution to a unique stationary solution as time goes to infinity the method is also used to analyse other types of boundary conditions such as mass and energy preserving diffuse reflection boundary conditions and to prove the uniqueness of stationary solutions for some special collision terms

on the trend to global equilibrium for spatially inhomogeneous kinetic systems the boltzmann equation as part of our study of convergence to equilibrium for spatially inhomogeneous kinetic equations started in 21 we derive estimates on the rate of convergence to equilibrium for solutions of the boltzmann equation like o t our results hold conditionally to some strong but natural estimates of smoothness decay at large velocities and strict positivity which at the moment have only been established in certain particular cases among the most important steps in our proof are 1 quantitative variants of boltzmann s h theorem as proven in 52 60 based on symmetry features hypercontractivity and information theoretical tools 2 a new quantitative version of the instability of the hydrodynamic description for non small knudsen number 3 some functional inequalities with geometrical content in particular the korn type inequality which we established in 22 and 4 the study of a system of coupled differential inequalities of second order by a treatment inspired from 21 we also briefly point out the particular role of conformal velocity fields when they are allowed by the geometry of the problem

cauchy problem for the vlasov poisson boltzmann system the dynamics of dilute electrons can be modelled by the fundamental vlasov poisson boltzmann system which describes mutual interactions of the electrons through collisions in the self consistent electric field in this paper it is shown that any smooth perturbation of a given global maxwellian leads to a unique global in time classical solution when either the mean free path is small or the background charge density is large moreover the solution converges to the global maxwellian when time tends to infinity the analysis combines the techniques used in the study of conservation laws with the decomposition of the boltzmann equation introduced in 17 19 by obtaining new entropy estimates for this physical model

the weighted distance scheme a globally optimizing projection ordering method for art the order in which the projections are applied in the algebraic reconstruction technique art has a great effect on speed of convergence accuracy and the amount of noise like artifacts in the reconstructed image in this paper a new projection ordering scheme for art is presented the weighted distance scheme wds it heuristically optimizes the angular distance of a newly selected projection with respect to an extended sequence of previously applied projections this sequence of influential projections may incorporate the complete set of all previously applied projections or any limited time interval subset thereof the selection algorithm results in uniform sampling of the projection access space minimizing correlation in the projection sequence this produces more accurate images with less noise like artifacts than previously suggested projection ordering schemes

a variational maximization maximization algorithm for generalized linear mixed models with crossed random effects we present a variational maximization maximization algorithm for approximate maximum likelihood estimation of generalized linear mixed models with crossed random effects e g item response models with random items random raters or random occasion specific effects the method is based on a factorized variational approximation of the latent variable distribution given observed variables which creates a lower bound of the log marginal likelihood the lower bound is maximized with respect to the factorized distributions as well as model parameters with the proposed algorithm a high dimensional intractable integration is translated into a two dimensional integration problem we incorporate an adaptive gauss hermite quadrature method in conjunction with the variational method in order to increase computational efficiency numerical studies show that under the small sample size conditions that are considered the proposed algorithm outperforms the laplace approximation

the vlasov maxwell boltzmann system near maxwellians perhaps the most fundamental model for dynamics of dilute charged particles is described by the vlasov maxwell boltzmann system in which particles interact with themselves through collisions and with their self consistent electromagnetic field despite its importance no global in time solutions weak or strong have been constructed so far it is shown in this article that any initially smooth periodic small perturbation of a given global maxwellian which preserves the same mass total momentum and reduced total energy 22 leads to a unique global in time classical solution for such a master system the construction is based on a recent nonlinear energy method with a new a priori estimate for the dissipation the linear collision operator l not its time integration is positive definite for any solutionf t x v with small amplitude to the vlasov maxwell boltzmann system 8 and 12 as a by product such an estimate also yields an exponential decay for the simpler vlasov poisson boltzmann system 24

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

existence of stationary solutions to the vlasov poisson boltzmann system abstract in this paper we study the existence of stationary solutions to the vlasov poisson boltzmann system when the background density function tends to a positive constant with a very mild decay rate as x in fact the stationary vlasov poisson boltzmann system can be written into an elliptic equation with exponential nonlinearity under the assumption on the decay rate being ln e x for some 0 it is shown that this elliptic equation has a unique solution this result generalizes the previous work r glassey j schaeffer y zheng steady states of the vlasov poisson fokker planck system j math anal appl 202 1996 1058 1075 where the decay rate 1 x 1 2 is assumed

a multiresolution approach to iterative reconstruction algorithms in x ray computed tomography in computed tomography the application of iterative reconstruction methods in practical situations is impeded by their high computational demands especially in high resolution x ray computed tomography where reconstruction volumes contain a high number of volume elements several giga voxels this computational burden prevents their actual breakthrough besides the large amount of calculations iterative algorithms require the entire volume to be kept in memory during reconstruction which quickly becomes cumbersome for large data sets to overcome this obstacle we present a novel multiresolution reconstruction which greatly reduces the required amount of memory without significantly affecting the reconstructed image quality it is shown that combined with an efficient implementation on a graphical processing unit the multiresolution approach enables the application of iterative algorithms in the reconstruction of large volumes at an acceptable speed using only limited resources

interactive image segmentation via adaptive weighted distances an interactive algorithm for soft segmentation of natural images is presented in this paper the user first roughly scribbles different regions of interest and from them the whole image is automatically segmented this soft segmentation is obtained via fast linear complexity computation of weighted distances to the user provided scribbles the adaptive weights are obtained from a series of gabor filters and are automatically computed according to the ability of each single filter to discriminate between the selected regions of interest we present the underlying framework and examples showing the capability of the algorithm to segment diverse images

asymptotic behavior of an initial boundary value problem for the vlasov poisson fokker planck system the asymptotic behavior for the vlasov poisson fokker planck system in bounded domains is analyzed in this paper boundary conditions defined by a scattering kernel are considered it is proven that the distribution of particles tends for large time to a maxwellian determined by the solution of the poisson boltzmann equation with dirichlet boundary condition in the proof of the main result the conservation law of mass and the balance of energy and entropy identities are rigorously derived an important argument in the proof is to use a lyapunov type functional related to these physical quantities

a sample reuse method for accurate parametric empirical bayes confidence intervals abstract parametric empirical bayes methods of point estimation for a vector of unknown parameters date to the landmark paper of james and stein 1961 the usual approach is to use the mean of the estimated posterior distribution of each parameter where the estimation of the prior parameters hyperparameters is accomplished through the marginal distribution of the data while point estimates computed this way usually perform well interval estimates based on the estimated posterior called naive eb intervals are not they fail to account for the variability in the estimation of the hyperparameters generally resulting in sub nominal coverage probability in the eb sense defined in morris 1983a in this paper we extend the work of carlin and gelfand 1989 who proposed a conditional bias correction method for developing eb intervals which corrects the deficiencies in the naive intervals we show how bias correction can be implemented in general via a type iii parametric bootstrap procedure a sample reuse method first employed by laird and louis 1987

the vlasov poisson boltzmann system in the whole space the hard potential case abstract this paper is concerned with the cauchy problem on the vlasov poisson boltzmann system for hard potentials in the whole space when the initial data is a small perturbation of a global maxwellian a satisfactory global existence theory of classical solutions to this problem together with the corresponding temporal decay estimates on the global solutions is established our analysis is based on time decay properties of solutions and a new time velocity weight function which is designed to control the large velocity growth in the nonlinear term for the case of non hard sphere interactions

steady states of the vlasov poisson fokker planck system abstract the form of steady state solutions to the vlasov poisson fokker planck system is known from the works of dressler and others in these papers an external potential is present which tends to infinity as x it is shown here that this assumption is needed to obtain nontrivial steady states this is achieved by showing that for a given nonnegative background density satisfying certain integrability conditions only the trivial solution is possible this result is sharp and exactly matches the known existence criteria of f bouchut and j dolbeault differential integral equations 8 1995 487 514 and others these steady states are solutions to a nonlinear elliptic equation with an exponential nonlinearity for a given background density which is asymptotically constant it is directly shown by elementary means that this nonlinear elliptic equation possesses a smooth and uniquely determined global solution

global hilbert expansion for the vlasov poisson boltzmann system the dynamics of an electron gas in a constant ion background can be decribed by the vlasov poisson boltzmann system at the kinetic level or by the compressible euler poisson system at the fluid level we prove that any solution of the vlasov poisson boltzmann system near a smooth local maxwellian with a small irrotational velocity converges global in time to the corresponding solution to the euler poisson system as the mean free path e goes to zero we use a recent l2 l framework in the boltzmann theory to control the higher order remainder in the hilbert expansion uniformly in e and globally in time

fast implementations of algebraic methods for three dimensional reconstruction from cone beam data the prime motivation of this work is to devise techniques that make the algebraic reconstruction technique art and related methods more efficient for routine clinical use while not compromising their accuracy since most of the computational effort of art is spent for projection backprojection operations the authors first seek to optimize the projection algorithm existing projection algorithms are surveyed and it is found that these algorithms either lack accuracy or speed or are not suitable for cone beam reconstruction the authors hence devise a new and more accurate extension to the splatting algorithm a well known voxel driven projection method they also describe a new three dimensional 3 d ray driven projector that is considerably faster than the voxel driven projector and at the same time more accurate and perfectly suited for the demands of cone beam the authors then devise caching schemes for both art and simultaneous art sart which minimize the number of redundant computations for projection and backprojection and at the same time are very memory conscious they find that with caching the cost for an art projection backprojection operation can be reduced to the equivalent cost of 1 12 projections they also find that sart due to its image based volume correction scheme is considerably harder to accelerate with caching implementations of the algorithms yield runtime ratios t sub sart t sub art between 1 5 and 1 15 depending on the amount of caching used

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

global existence of classical solutions to the vlasov poisson boltzmann system the time evolution of the distribution function for the charged particles in a dilute gas is governed by the vlasov poisson boltzmann system when the force is self induced and its potential function satisfies the poisson equation in this paper we give a satisfactory global existence theory of classical solutions to this system when the initial data is a small perturbation of a global maxwellian moreover the convergence rate in time to the global maxwellian is also obtained through the energy method the proof is based on the theory of compressible navier stokes equations with forcing and the decomposition of the solutions to the boltzmann equation with respect to the local maxwellian introduced in 23 and elaborated in 31

expectation propagation in the large data limit summary expectation propagation ep is a widely successful algorithm for variational inference ep is an iterative algorithm used to approximate complicated distributions typically to find a gaussian approximation of posterior distributions in many applications of this type ep performs extremely well surprisingly despite its widespread use there are very few theoretical guarantees on gaussian ep and it is quite poorly understood to analyse ep we first introduce a variant of ep averaged ep which operates on a smaller parameter space we then consider averaged ep and ep in the limit of infinite data where the overall contribution of each likelihood term is small and where posteriors are almost gaussian in this limit we prove that the iterations of both averaged ep and ep are simple they behave like iterations of newton s algorithm for finding the mode of a function we use this limit behaviour to prove that ep is asymptotically exact and to obtain other insights into the dynamic behaviour of ep e g that it may diverge under poor initialization exactly like newton s method ep is a simple algorithm to state but a difficult one to study our results should facilitate further research into the theoretical properties of this important method

existence and uniqueness of a global smooth solution for the vlasov poisson fokker planck system in three dimensions abstract studying precisely the regularity of the force field created by the solution of the linear vlasov fokker planck equation we prove existence and uniqueness of a smooth solution to the vlasov poisson fokker planck system in three dimensions the attractive and repulsive cases are treated the method involves an analysis of the effect of the fokker planck kernel without any force field on non linear expressions coming from the vlasov term

algebraic reconstruction in ct from limited views the author presents an algebraic reconstruction technique art as a viable alternative in computerized tomography ct from limited views recently algorithms of iterative reconstruction reprojection irr based on the method of convolution backprojection have been proposed for application in limited view ct reprojection was used in an iterative fashion alternating with backprojection as a means of estimating projection values within the sector of missing views in algebraic methods of reconstruction for ct only those projections corresponding to known data are required reprojection along missing views would merely serve to introduce redundant equations computer simulation studies are presented which demonstrate significantly improved reconstructed images achieved by an art algorithm as compared to irr methods

estimability and likelihood inference for generalized linear mixed models using data cloning maximum likelihood estimation for generalized linear mixed models glmm an important class of statistical models with substantial applications in epidemiology medical statistics and many other fields poses significant computational difficulties in this article we use data cloning a simple computational method that exploits advances in bayesian computation in particular the markov chain monte carlo method to obtain maximum likelihood estimators of the parameters in these models this method also leads to a simple estimator of the asymptotic variance of the maximum likelihood estimators determining estimability of the parameters in a mixed model is in general a very difficult problem data cloning provides a simple graphical test to not only check if the full set of parameters is estimable but also and perhaps more importantly if a specified function of the parameters is estimable one of the goals of mixed models is to predict random effects we suggest a frequentist method to obtain predict