cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

robust tests for treatment effects based on censored recurrent event data observed over multiple periods summary we derive semiparametric methods for estimating and testing treatment effects when censored recurrent event data are available over multiple periods these methods are based on estimating functions motivated by a working mixed poisson assumption under which conditioning can eliminate subject specific random effects robust pseudoscore test statistics are obtained via sandwich variance estimation the relative efficiency of conditional versus marginal analyses is assessed analytically under a mixed time homogeneous poisson model the robustness and empirical power of the semiparametric approach are assessed through simulation adaptations to handle recurrent events arising in crossover trials are described and these methods are applied to data from a two period crossover trial of patients with bronchial asthma

hierarchical bayesian image restoration from partially known blurs we examine the restoration problem when the point spread function psf of the degradation system is partially known for this problem the psf is assumed to be the sum of a known deterministic and an unknown random component this problem has been examined before however in most previous works the problem of estimating the parameters that define the restoration filters was not addressed in this paper two iterative algorithms that simultaneously restore the image and estimate the parameters of the restoration filter are proposed using evidence analysis ea within the hierarchical bayesian framework we show that the restoration step of the first of these algorithms is in effect almost identical to the regularized constrained total least squares rctls filter while the restoration step of the second is identical to the linear minimum mean square error lmmse filter for this problem therefore in this paper we provide a solution to the parameter estimation problem of the rctls filter we further provide an alternative approach to the expectation maximization em framework to derive a parameter estimation algorithm for the lmmse filter these iterative algorithms are derived in the discrete fourier transform dft domain therefore they are computationally efficient even for large images numerical experiments are presented that test and compare the proposed algorithms

total variation structured total least squares method for image restoration in this paper we study the total variation structured total least squares method for image restoration in the image restoration problem the point spread function is corrupted by errors in the model we study the objective function by minimizing two variables the restored image and the estimated error of the point spread function the proposed objective function consists of the data fitting term containing these two variables the magnitude of error and the total variation regularization of the restored image by making use of the structure of the objective function an efficient alternating minimization scheme is developed to solve the proposed model numerical examples are also presented to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme

the backus gilbert method and their minimum norm solution abstractthis paper has two objectives one is to review the backus gilbert bg method backus and gilbert investigate continuous inverse problems in a radially symmetric earth using an approach completely different from that of standard inversion methods if m is an earth property of interest the bg method provides average values of m over some radial intervals if an interval w is relatively short and centered near a particular radius r0 the bg average will be a local average of m near r0 with a resolving length of w backus and gilbert also introduce the concept of trade off between resolution and error which is essential in inverse theory regardless of the inversion method in spite of its importance inverse theory texts neither describe the bg method in full nor show how to apply it in all its generality because the three papers that introduce the bg method are mathematically difficult this paper provides background material and a detailed derivation of the method as well as two completely wor

estimation of a common effect parameter from sparse follow up data breslow 1981 biometrika 68 73 84 has shown that the mantel haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications for cohort studies however estimation of a common risk ratio or risk difference can be of greater interest under a binomial sparse data model the mantel haenszel risk ratio and risk difference estimators are consistent in sparse stratifications while the maximum likelihood and weighted least squares estimators are biased under poisson sparse data models the mantel haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent while the weighted least squares estimators are again biased similarly of the common rate difference estimators the weighted least squares estimators are biased while the estimator employing mantel haenszel weights is consistent in sparse data variance estimators that are consistent in both sparse data and large strata can be derived for all the mantel haenszel estimators

bayesian restoration using a new nonstationary edge preserving image prior in this paper we propose a class of image restoration algorithms based on the bayesian approach and a new hierarchical spatially adaptive image prior the proposed prior has the following two desirable features first it models the local image discontinuities in different directions with a model which is continuous valued thus it preserves edges and generalizes the on off binary line process idea used in previous image priors within the context of markov random fields mrfs second it is gaussian in nature and provides estimates that are easy to compute using this new hierarchical prior two restoration algorithms are derived the first is based on the maximum a posteriori principle and the second on the bayesian methodology numerical experiments are presented that compare the proposed algorithms among themselves and with previous stationary and non stationary mrf based with line process algorithms these experiments demonstrate the advantages of the proposed prior

on the exponentiality of stochastic linear systems under the max plus algebra considers stochastic linear systems under the max plus algebra for such a system the states are governed by the recursive equation x sub n a sub n spl otimes x sub n 1 spl oplus u sub n with the initial condition condition x sub 0 x sub 0 by transforming the linear system under the max plus algebra into a sublinear system under the usual algebra we establish various exponential upper bounds for the tail distributions of the states x sub n under the independently identically distributed i i d assumption on a sub n u sub n sub 1 n spl ges 1 and a couple of regularity conditions on a sub 1 u sub 1 and the initial condition x sub 0 these upper bounds are related to the spectral radius or the perron frobenius eigenvalue of the nonnegative matrix in which each element is the moment generating function of the corresponding element in the state feedback matrix a sub 1 in particular we have kingman s upper bound for gi gi 1 queue when the system is one dimensional we also show that some of these upper bounds can be achieved if a sub 1 is lower triangular these bounds are applied to some commonly used systems to derive new results or strengthen known results

signal recovery by best feasible approximation the objective of set theoretical signal recovery is to find a feasible signal in the form of a point in the intersection of s of sets modeling the information available about the problem for problems in which the true signal is known to lie near a reference signal r the solution should not be any feasible point but one which best approximates r i e a projection of r onto s such a solution cannot be obtained by the feasibility algorithms currently in use e g the method of projections onto convex sets pocs and its offsprings methods for projecting a point onto the intersection of closed and convex sets in a hilbert space are introduced and applied to signal recovery by best feasible approximation of a reference signal these algorithms are closely related to the above projection methods to which they add little computational complexity

inference on the rate ratio of recurrent events for the matched pairs design as statistical methods for testing the null hypothesis of no difference between two groups for the matched pairs design the paired t test wilcoxon signed rank sum test and mcnemar test are well known however there is no simple test for the comparison of incidence rate of recurrent events this paper proposes a simple statistical method and a sample size formula for the comparison of counts of recurrent events over a specified period of observation under the matched pairs design where the subject specific incidence of recurrent events is assumed to follow a time homogeneous poisson process as a special case the proposed method is found to be virtually equivalent in form to mantel haenszel method for a common rate ratio among the set of stratified tables based on person time data the proposed methods are illustrated with the within arm comparison of data from a clinical trial of 59 epileptics with baseline count data

bounds on the speedup and efficiency of partial synchronization in parallel processing systems in this paper we derive bounds on the speedup and efficiency of applications that schedule tasks on a set of parallel processors we assume that the application runs an algorithm that consists of n iterations and before starting its i 1st iteration a processor must wait for data i e synchronize calculated in the i th iteration by a subset of the other processors of the system processing times and interconnections between iterations are modeled by random variables with possibly deterministic distributions scientific applications consisting of iterations of recursive equations are examples of such applications that can be modeled within this formulation we consider the efficiency of applications and show that although efficiency decreases with an increase in the number of processors it has a nonzero limit when the number of processors increases to infinity we obtain a lower bound for the efficiency by solving an equation that depends on the distribution of task service times and the expected number of tasks needed to be synchronized we also show that the lower bound is approached if the topology of the processor graph is ldquo spread out a notion we define in the paper

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

restoration of randomly blurred images by the wiener filter the restoration of images distorted by systems with noisy point spread functions and additive detective noise is considered the criterion considered for the restoration is based on the wiener technique the proposed wiener based filter is iterative in nature the overall computation of this modified wiener filter can be carried out in the frequency domain using the fast fourier transform and circulant matrix approximation experimental results show that the modified wiener filter outperforms its linear counterpart neglecting the impulse response noise the modified wiener filter also gives better restoration results than the backus gilbert technique the wiener based filter is found to be computationally robust and inexpensive

deblurring random blur we introduce a modified backus gilbert technique for restoring an image that has been distorted by a linear system whose impulse response function is itself random and in the presence of detection noise the restoration is based on a weighted superposition of a small number of shifted versions of the distorted image optimum weights are determined to minimize a measure of the average width of the impulse response functions of the overall system and the noise variance

comparison of approximate methods for handling hyperparameters i examine two approximate methods for computational implementation of bayesian hierarchical models that is models that include unknown hyperparameters such as regularization constants and noise levels in the evidence framework the model parameters are integrated over and the resulting evidence is maximized over the hyperparameters the optimized hyperparameters are used to define a gaussian approximation to the posterior distribution in the alternative map method the true posterior probability is found by integrating over the hyperparameters the true posterior is then maximized over the model parameters and a gaussian approximation is made the similarities of the two approaches and their relative merits are discussed and comparisons are made with the ideal hierarchical bayesian solution in moderately ill posed problems integration over hyperparameters yields a probability distribution with a skew peak which causes signifi cant biases to arise in the map method in contrast the evidence fram

image features invariant with respect to blur abstract the paper is devoted to the feature based description of blurred images acquired by a linear shift invariant imaging system the proposed features are invariant with respect to blur this means with respect to the system point spread function are based on image moments and are calculated directly from the blurred image this way we are able to describe the original image without the psf identification and image restoration in many applications such as in image recognition from a database our approach is much more effective than the traditional blind restoration one the derivation of the blur invariants is the major theoretical result of the paper several experiments are presented to illustrate the efficiency of the invariants for blurred image description stability of the invariants with respect to additive random noise and boundary effect is also discussed and is shown to be sufficiently high

bayesian and regularization methods for hyperparameter estimation in image restoration in this paper we propose the application of the hierarchical bayesian paradigm to the image restoration problem we derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori map analysis within the hierarchical bayesian paradigm we show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the map approach for the image restoration problem we furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters or their ratio defined as the regularization parameter finally the proposed algorithms are tested experimentally

regularized constrained total least squares image restoration in this paper the problem of restoring an image distorted by a linear space invariant lsi point spread function psf that is not exactly known is formulated as the solution of a perturbed set of linear equations the regularized constrained total least squares rctls method is used to solve this set of equations using the diagonalization properties of the discrete fourier transform dft for circulant matrices the rctls estimate is computed in the dft domain this significantly reduces the computational cost of this approach and makes its implementation possible even for large images an error analysis of the rctls estimate based on the mean squared error mse criterion is performed to verify its superiority over the constrained total least squares ctls estimate numerical experiments for different errors in the psf are performed to test the rctls estimator objective and visual comparisons are presented with the linear minimum mean squared error lmmse and the regularized least squares rls estimator our experiments show that the rctls estimator reduces significantly ringing artifacts around edges as compared to the two other approaches

set theoretic signal restoration using an error in variables criterion the restoration of a signal degraded by a stochastic impulse response is formulated as a problem with uncertainties in both the measurements and the impulse response the method of total least squares and variants thereof are effective techniques for solving this class of problems however unlike set theoretic estimation schemes these methods do not allow the incorporation of other a priori information in the estimate in this correspondence two new sets motivated by total least squares are introduced for set theoretic estimation the convexity of these sets is established and the projection operators onto these sets are given through simulations the advantages of the new technique over conventional and older set theoretic schemes for restoration are demonstrated

the solution of nonlinear inverse problems and the levenberg marquardt method although the levenberg marquardt damped least squares method is an extremely powerful tool for the iterative solution of nonlinear problems its theoretical basis has not been described adequately in the literature this is unfortunate because levenberg and marquardt approached the solution of nonlinear problems in different ways and presented results that go far beyond the simple equation that characterizes the method the idea of damping the solution was introduced by levenberg who also showed that it is possible to do that while at the same time reducing the value of a function that must be minimized iteratively this result is not obvious although it is taken for granted moreover levenberg derived a solution more general than the one currently used marquardt started with the current equation and showed that it interpolates between the ordinary least squares method and the steepest descent method in this tutorial the two papers are combined into a unified presentation which will help the reader gain a better understanding of what happens when solving nonlinear problems because the damped least squares and steepest descent methods are intimately related the latter is also discussed in particular in its relation to the gradient when the inversion parameters have the same dimensions and units the direction of steepest descent is equal to the direction of minus the gradient in other cases it is necessary to introduce a metric i e a definition of distance in the parameter space to establish a relation between the two directions although neither levenberg nor marquardt discussed these matters their results imply the introduction of a metric some of the concepts presented here are illustrated with the inversion of synthetic gravity data corresponding to a buried sphere of unknown radius and depth finally the work done by early researchers that rediscovered the damped least squares method is put into a historical context

methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation the application of regularization to ill conditioned problems necessitates the choice of a regularization parameter which trades fidelity to the data with smoothness of the solution the value of the regularization parameter depends on the variance of the noise in the data the problem of choosing the regularization parameter and estimating the noise variance in image restoration is examined an error analysis based on an objective mean square error mse criterion is used to motivate regularization two approaches for choosing the regularization parameter and estimating the noise variance are proposed the proposed and existing methods are compared and their relationship to linear minimum mean square error filtering is examined experiments are presented that verify the theoretical results

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

feasible images and practical stopping rules for iterative algorithms in emission tomography the discussion of the causes of image deterioration in the maximum likelihood estimator mle method of tomographic image reconstruction initiated with the publication of a stopping rule for that iterative process e veklerov and j llacer 1987 is continued the concept of a feasible image is introduced which is a result of a reconstruction that if it were a radiation field could have generated the initial projection data by the poisson process that governs radioactive decay from the premise that the result of a reconstruction should be feasible the shape and characteristics of the region of feasibility in projection space are examined with a new rule reconstructions from real data can be tested for feasibility results of the tests and reconstructed images for the hoffman brain phantom are shown a comparative examination of the current methods of dealing with mle image deterioration is included

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

approximate analysis of fork join synchronization in parallel queues an approximation technique called scaling approximation is introduced and applied to the analysis of homogeneous fork join queuing systems consisting of k or 2 servers the development of the scaling approximation technique is guided by both experimental and theoretical considerations the approximation is based on the observation that there exist upper and lower bounds on the mean response time that grow at the same rate as a function of k simple closed form approximate expressions for the mean response time are derived and compared to simulation results the relative error in the approximation is less than 5 for k

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

some mathematical considerations in dealing with the inverse problem many problems of mathematical physics can be formulated in terms of the operator equation ax y where a is an integro differential operator given a and x the solution for y is usually straightforward however the inverse problem which consists of the solution for x when given a and y is much more difficult the following questions relative to the inverse problem are explored 1 does specification of the operator a determine the set y for which a solution x is possible 2 does the inverse problem always have a unique solution 3 do small perturbations of the forcing function y always result in small perturbations of the solution 4 what are some of the considerations that enter into the choice of a solution technique for a specific problem the concept of an ill posed problem versus that of a well posed problem is discussed specifically the manner by which an ill posed problem may be regularized to a well posed problem is presented the concepts are illustrated by several examples

stable plane wave decomposition and spherical wave reconstruction applications to converted s mode separation and trace interpolation plane wave decomposition of the vertical displacement component of a spherical wave field corresponding to a compressional point source is solved as a set of inverse problems the solution method utilizes the power and stability of backus and gilbert smallest and flattest model construction techniques and achieves computational efficiency through the use of analytical solutions to the involved integrals the theory and algorithms developed in this work allow stable and efficient reconstruction of spherical wave fields from a relatively sparse set of their plane wave components comparison of the algorithms with discrete integration of the hankel transform shows very little or no advantage for the transformation from the time distance t x domain to the intercept time angle of emergence tau gamma domain if the seismograms are equisampled spatially however when the observed seismograms are not equally spaced or the transformation tau gamma to t x is performed the proposed schemes are superior to the discrete integration of the hankel transform applicability of the algorithms to reflection seismology is demonstrated by means of the solution of the problem of trace interpolation and also that of the separation of converted s modes from other modes presented in common source gathers in both cases the application of the algorithms to a set of synthetic reflection seismograms yields satisfactory results

restoration of randomly blurred images via the maximum a posteriori criterion the maximum a posteriori map estimation technique is applied to the problem of restoring images distorted by noisy point spread functions and additive noise the resulting map estimator is nonlinear and is obtained by numerically maximizing a conditional probability density function the energy nonnegativity constraint is incorporated in the optimization process although the deblurring results are slightly inferior to those obtained by applying the wiener criterion the advantage of the map estimator lies in its significant suppression of noise

nonparametric analysis of recurrent events and death this article is concerned with the analysis of recurrent events in the presence of a terminal event such as death we consider the mean frequency function defined as the marginal mean of the cumulative number of recurrent events over time a simple nonparametric estimator for this quantity is presented it is shown that the estimator properly normalized converges weakly to a zero mean gaussian process with an easily estimable covariance function nonparametric statistics for comparing two mean frequency functions and for combining data on recurrent events and death are also developed the asymptotic null distributions of these statistics together with consistent variance estimators are derived the small sample properties of the proposed estimators and test statistics are examined through simulation studies an application to a cancer clinical trial is provided

methods for digital restoration of signals degraded by a stochastic impulse response several digital restoration methods are extended to the cases in which signals have suffered stochastic blurring rather than being regarded in terms of averages these degradations are treated dynamically in the derivation of restoration algorithms based on various mathematical criteria it is shown that the integration of the additional uncertainties caused by the variations of the impulse response of the stochastic degradation can be used to obtain better estimates these uncertainties can be included in the restoration scheme in a very flexible manner through the use of the projection onto convex sets pocs method conventional constrained methods are also addressed the benefits of the method are illustrated through one and two dimensional simulations

analysis of delays caused by local synchronization synchronization is often necessary in parallel computing but it can create delays whenever the receiving processor is idle waiting for the information to arrive this is especially true for barrier or global synchronization in which every processor must synchronize with every other processor nonetheless barriers are the only form of synchronization explicitly supplied in openmp and they occur whenever collective communication operations are used in mpi many applications do not actually require global synchronization local synchronization in which a processor synchronizes only with those processors from or to which information or resources are needed is often adequate however when tasks take varying amounts of time the behavior of a system under local synchronization is more difficult to analyze since processors do not start tasks at the same time we show that when the synchronization dependencies form a directed cycle and the task times are geometrically distributed with p 0 5 then as the number of processors tends to infinity the processors are working 2 sqrt 2 approx0 59 of the time under global synchronization however the time to complete each task is unbounded increasing logarithmically with the number of processors similar results apply for p neq0 5 we also present some of the combinatorial properties of the synchronization problem with geometrically distributed tasks on an undirected cycle nondeterministic synchronization is also examined where processors decide randomly at the beginning of each task which neighbors s to synchronize with we show that the expected number of task dependencies for random synchronization on an undirected cycle is the same as for deterministic synchronization on a directed cycle simulations are included to extend the analytic results they show that more heavy tailed distributions can actually create fewer delays than less heavy tailed ones if the number of processors is small for some random neighbor synchronization models the results also show the rate of convergence to the steady state for various task distributions and synchronization graphs

inversion of horizontal loop electromagnetic frequency soundings a procedure has been developed to perform automatic inversion of hlem frequency soundings by the method of backus and gilbert bg using a linearized iterative scheme a layered conductivity is constructed satisfying the available soundings to an accuracy consistent with the observational uncertainties subsequently in order to investigate the resolving power of the data and hence hopefully to determine the broad scale features which are common to all conductivity models which satisfy the data bg average conductivities are computed for the constructed model at a number of depths in examples with both synthetic data and field data these averages proved to be identical except for random error to the corresponding average conductivities computed for a number of different models satisfying the same data the additional models for this analysis were generated by maximizing or minimizing the conductivities of individual layers in the original constructed model using linear programming techniques on the

linear inverse theory and deconvolution seismic source wavelet deconvolution can be treated within the framework of the backus gilbert bg inverse theory a time shift invariant version of this theory leads to the wiener shaping filter which has enjoyed widespread use for source wavelet deconvolution in exploration seismology the model of the bg theory is the ground impulse response the bg mapping kernel is the source wavelet and the bg resolving kernel is the convolution between the source wavelet and the wiener shaping filter bg inversion involves the minimization of an optimality criterion under a set of constraints the application of the bg filter energy or noise output power constraint to wiener filter design leads to the familiar prewhitening parameter that stabilizes the filter on the one hand but degrades resolution on the other the bg unimodular constraint produces an unbiased estimate of the model or ground impulse response these constraints provide novel insights into the performance of deconvolution filters

the use of a mixture model in the analysis of count data a mixture model is presented for the analysis of data on premature ventricular contractions the analysis is shown to be straightforward and the conclusions relatively simple