the problem of moments on polytopes and other bounded regions abstract the problem of moments is considered for polytopes in r d and other bounded regions specified piecewise by curves of the form c1x1 1 cdxd d c0 necessary and sufficient conditions are suggested by a simple geometric observation for some choices of c1 cd and 1 d these conditions reduce to the conditions of hausdorff for the unit interval of hildebrandt and schoenberg for the unit square and of dale for the unit simplex in r 2 whereas for other choices new conditions are required the proofs are obtained using probabilistic techniques

dynamic sampling plan in shiryayev roberts procedure for detecting a change in the drift of brownian motion in this paper a dynamic sampling plan in the shiryayev roberts procedure is considered it is shown that a two rate dynamic sampling plan is optimal in the sense that it minimizes the stationary average delay time sadt analytical results as well as numerical comparisons show that it is significantly superior to the fixed sampling plan the comparison also shows that it is as powerful as the dynamic sampling procedure of assaf and ritov the generalizations to the fast initial response and to the cusum procedure are also briefly discussed

time average control of martingale problems a linear programming formulation one studies the average cost for controlled systems given as solutions of the martingale problem for their generator the control problem is reformulated as a linear programming problem and conditions are given for the existence of an optimal solution it is further shown that the optimal control can be taken to depend only on the history of the system and that this cost remains optimal for systems with different initial distributions

a disaggregate negative binomial regression procedure for count data analysis various research areas face the methodological problems presented by nonnegative integer count data drawn from heterogeneous populations we present a disaggregate negative binomial regression procedure for analysis of count data observed for a heterogeneous sample of cross sections possibly over some fixed time periods this procedure simultaneously pools or groups cross sections while estimating a separate negative binomial regression model for each group an e m algorithm is described within a maximum likelihood framework to estimate the group proportions the group specific regression coefficients and the degree of overdispersion in event rates within each derived group the proposed procedure is illustrated with count data entailing nonnegative integer counts of purchases events for a frequently bought consumer good

conjugate mixture models for clustering multimodal data the problem of multimodal clustering arises whenever the data are gathered with several physically different sensors observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or compare them in some common space a solution may consist in considering multiple clustering tasks independently for each modality the main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent in this letter we show that multimodal clustering can be addressed within a novel framework conjugate mixture models these models exploit the explicit transformations that are often available between an unobserved parameter space objects and each of the observation spaces sensors we formulate the problem as a likelihood maximization task and derive the associated conjugate expectation maximization algorithm the convergence properties of the proposed algorithm are thoroughly investigated several local and global optimization techniques are proposed in order to increase its convergence speed two initialization strategies are proposed and compared a consistent model selection criterion is proposed the algorithm and its variants are tested and evaluated within the task of 3d localization of several speakers using both auditory and visual data

on convergence and parameter selection of the em and da em algorithms for gaussian mixtures abstract the expectation maximization em for gaussian mixtures is popular as a clustering algorithm however the em algorithm is sensitive to initial values and so ueda and nakano 4 proposed the deterministic annealing em da em algorithm to improve it in this paper we investigate theoretical behaviors of the em and da em algorithms we first derive a general jacobian matrix of the da em algorithm with respect to posterior probabilities we then propose a theoretical lower bound for initialization of the annealing parameter in the da em algorithm on the other hand some researches mentioned that the em algorithm exhibits a self annealing behavior that is the equal posterior probability with small random perturbations can avoid the em algorithm to output the mass center for gaussian mixtures however there is no theoretical analysis on this self annealing property since the da em will become the em when the annealing parameter is 1 according to the jacobian matrix of the da em we can prove the self annealing property of the em algorithm for gaussian mixtures based on these results we give not only convergence behaviors of the equal posterior probabilities and initialization lower bound of the temperature parameter of the da em but also a theoretical explanation why the em algorithm for gaussian mixtures exhibits a self annealing behavior

mixtures of empirical distributions an iterative application of the age length key it is well known that an age length key is capable of providing biased estimates of age distributions when length distributions are applied to age length keys constructed from sampling in a different year from that in which the length data were collected in separate unpublished papers fukuda and chikuni far seas fisheries research laboratory fisheries agency of japan 1974 proposed a method of iterating an age length key that corrects this problem for a length distribution collected in any year their method provides an estimate of the age distribution corresponding to this length distribution which is consistent with an age length key constructed from the estimated age distribution and previously estimated length at age distributions we show that this method is an application of the em algorithm to mixtures of empirical distributions also we give conditions for which these estimates of age distribution are unique maximum likelihood estimates the method is used to estimate age distributions of the catch of greenland turbot reinhardtius hippoglossoides by small japanese freezer trawlers in the eastern bering sea

an exact chi squared decomposition theorem for inverse gaussian variates on montre que la deviance d echelle d un echantillon normal inverse de dimension n peut etre exprimee comme la somme de n 1 variables khi deux independantes

nonlinear optimal control via occupation measures and lmi relaxations we consider the class of nonlinear optimal control problems ocps with polynomial data i e the differential equation state and control constraints and cost are all described by polynomials and more generally for ocps with smooth data in addition state constraints as well as state and or action constraints are allowed we provide a simple hierarchy of lmi linear matrix inequality relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value under some convexity assumptions the sequence converges to the optimal value of the ocp preliminary results show that good approximations are obtained with few moments

a unified framework and sparse bayesian perspective for direction of arrival estimation in the presence of array imperfections self calibration methods play an important role in reducing the negative effects of array imperfections during direction of arrival doa estimation however the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios such as low signal to noise ratio snr and limited snapshots this paper aims at formulating a unified framework and sparse bayesian perspective for array calibration and doa estimation a comprehensive model of the array output is presented first when a single type of array imperfection is considered with mutual coupling gain phase uncertainty and sensor location error treated as typical examples the spatial sparsity of the incident signals is then exploited and a bayesian method is proposed to realize array calibration and source doa estimation the array perturbation magnitudes are assumed to be small according to most application scenarios and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear cramer rao lower bounds crlbs for the array calibration and doa estimation precisions are also obtained the sparse bayesian method is finally extended to deal with the doa estimation problem when more than one type of array perturbation coexists

array shape calibration using sources in unknown locations a maximum likelihood approach sensor location uncertainty can severely degrade the performance of direction finding systems an iterative maximum likelihood method for simultaneously estimating directions of arrival doa and sensor locations is developed to alleviate this problem the case of nondisjoint sources i e sources observed in the same frequency cell and at the same time is emphasized the algorithm converges to the global maximum of the likelihood function if the initial conditions are sufficiently good numerical examples are presented illustrating the performance of the proposed technique a distinctive feature of the algorithm is its ability to locate the sensors accurately without deploying calibration sources at known locations

computing moments of the exit time distribution for markov processes by linear programming we provide a new approach to the numerical computation of moments of the exit time distribution of markov processes the method relies on a linear programming formulation of a process exiting from a bounded domain the lp formulation characterizes the evolution of the process through the moments of the induced occupation measure and naturally provides upper and lower bounds for the exact values of the moments the conditions the moments have to satisfy are derived directly from the generator of the markov process and are not based on some approximation of the process excellent software is readily available because the computations involve finite dimensional linear programs

theoretical analyses of gain and phase error calibration with optimal implementation for linear equispaced array in array signal processing high resolution direction of arrival doa estimation algorithms are known to be sensitive to system errors in practice the system should be properly calibrated before doa estimation in this paper a calibration method of gain and phase errors of linear equispaced arrays leas is considered a class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed the statistical performance analyses of the calibration algorithms due to finite data perturbations are presented expressions for average bias abias and square root of average variance srav of the calibration algorithms are derived using first order approximation these statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations the more inferior performance that may be obtained based on this conclusion the simple and optimal gain and phase error calibration algorithms for such model are obtained

explicit hard bounding functions for boundary value problems for elliptic partial differential equations abstract we obtain tight super and sub solutions or hard bounding functions for the probabilistic representation of the solution to the boundary value problem for second order elliptic partial differential equations in an explicit polynomial form unlike accurate approximate solutions by the existing discretization based methods our hard bounding polynomial functions act as pointwise 100 confidence intervals within which the solution is guaranteed to exist our methodology can deal with a wide range of boundary conditions even of fully mixed type with dirichlet neumann and robin components without increasing the complexity the quality of hard bounds can be improved by introducing piecewise polynomial functions and domain decomposition convergence of hard bounding functions is proved under technical conditions numerical results are presented throughout the paper to support our theoretical developments and to illustrate the effectiveness of our methodology

bearing estimation without calibration for randomly perturbed arrays the bearing estimation problem of linearly periodic arrays with the presence of sensor position errors is discussed conventional approaches for solving this problem generally consist of two steps calibrating sensor locations and then performing bearing estimation based on the calibrated sensor locations approaches to carrying out bearing estimation based on the toeplitz and eigenstructure reconstruction of the covariance matrix without the need for calibration are proposed the toeplitz approximation method tam and a modification of it mtam are used to reconstruct a matrix with toeplitz structure to further enhance the capabilities of the tam and mtam an iterative algorithm incorporating with the tam itam and the mtam imtam is proposed to iteratively reconstruct both the toeplitz and the desired eigenstructure from the observed covariance matrix computer simulations show that the mtam is more effective than the tam moreover the iterative methods are superior to the noniterative ones at the price of computations

sparse power angle spectrum estimation a novel method for estimating the power angle spectrum pas is presented that decomposes the true pas into a small set of basis functions the basis coefficients for this sparse representation are found by enforcing equality to the covariance or bartlett pas subject to a minimum lscr1 norm constraint the method referred to as sparse pas estimation spase can be implemented conveniently using existing linear programming lp solvers further because only a few clusters are required in the representation the method enables reduced complexity stochastic models for the channel and possibly allows reduced overhead in channel feedback schemes application of the method to simulated channels and multiple input multiple output mimo propagation data demonstrates the utility of the method

occupation measures for controlled markov processes characterization and optimality for controlled markov processes taking values in a polish space control problems with ergodic cost infinite horizon discounted cost and finite horizon cost are studied each is posed as a convex optimization problem wherein one tries to minimize a linear functional on a closed convex set of appropriately defined occupation measures for the problem these are characterized as solutions of a linear equation asssociated with the problem this characterization is used to establish the existence of optimal markov controls the dual convex optimization problem is also studied

statistical resolution limits and the complexified crame spl acute r rao bound array resolution limits and accuracy bounds on the multitude of signal parameters e g azimuth elevation doppler range cross range depth frequency chirp polarization amplitude phase etc estimated by array processing algorithms are essential tools in the evaluation of system performance the case in which the complex amplitudes of the signals are unknown is of particular practical interest a computationally efficient formulation of these bounds from the perspective of derivations and analysis is presented for the case of deterministic and unknown signal amplitudes a new derivation is given using the unknown complex signal parameters and their complex conjugates the new formula is readily applicable to obtaining either symbolic or numerical solutions to estimation bounds for a very wide class of problems encountered in adaptive sensor array processing this formula is shown to yield several of the standard crame spl acute r rao results for array processing along with new results of fundamental interest specifically a new closed form expression for the statistical resolution limit of an aperture for any asymptotically unbiased superresolution algorithm e g music esprit is provided the statistical resolution limit is defined as the source separation that equals its own crame spl acute r rao bound providing an algorithm independent bound on the resolution of any high resolution method it is shown that the statistical resolution limit of an array or coherent integration window is about 1 2 spl middot snr sup 1 4 relative to the fourier resolution limit of 2 spl pi n radians large number n of array elements that is the highest achievable resolution is proportional to the reciprocal of the fourth root of the signal to noise ratio snr in contrast to the square root snr sup 1 2 dependence of standard accuracy bounds these theoretical results are consistent with previously published bounds for specific superresolution algorithms derived by other methods it is also shown that the potential resolution improvement obtained by separating two collinear arrays synthetic ultra wideband each with a fixed aperture b wavelengths by m wavelengths assumed large is approximately m b sup 1 2 in contrast to the resolution improvement of m b for a full aperture exact closed form results for these problems with their asymptotic approximations are presented

estimation of structured gaussian mixtures the inverse em algorithm this contribution is devoted to the estimation of the parameters of multivariate gaussian mixture where the covariance matrices are constrained to have a linear structure such as toeplitz hankel or circular constraints we propose a simple modification of the expectation maximization em algorithm to take into account the structure constraints the basic modification consists of virtually updating the observed covariance matrices in a first stage then in a second stage the estimated covariances undergo the reversed updating the proposed algorithm is called the inverse em algorithm the increasing property of the likelihood through the algorithm iterations is proved the strict increasing for nonstationary points is proved as well numerical results are shown to corroborate the effectiveness of the proposed algorithm for the joint unsupervised classification and spectral estimation of stationary autoregressive time series

a novel online mutual coupling compensation algorithm for uniform and linear arrays in this paper a novel online mutual coupling compensation algorithm especially tailored to uniform and linear arrays is presented it is conceived to simultaneously compensate for mutual coupling and estimate the direction of arrivals doas of signals impinging on the array since the estimated calibration matrix can be embedded within any classical super resolution direction finding method an alternating minimization procedure based on closed form solutions is performed to estimate the mutual coupling matrix in the field of complex symmetric toeplitz matrices unlike many existing array calibration methods it requires neither the presence of calibration sources nor previous calibration information as initialization computer simulations show the effectiveness of the proposed technique and prove that the nice statistical properties of classical super resolution doa estimation algorithms can be restored despite the presence of mutual coupling

on weak approximation of stochastic differential equations through hard bounds by mathematical programming upper and lower hard bounds of the expected value on stochastic differential equations can be obtained with the help of mathematical programming and the dynkin formula without recourse to monte carlo sample paths simulation in this paper we show that feasible solutions of those optimization approaches further provide useful additional information namely feasible solutions provide upper and lower bounds for arbitrary intermediate times and or different initial states we also show that the optimization approach can be applied to stochastic differential equations with a random initial state our theoretical analyses are illustrated by numerical results on the survival probability for a square root diffusion on the moment estimation of a doleans dade stochastic exponential with jumps and on pricing of a barrier basket option under the multiasset black scholes model

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

a diffusion process and its applications to detecting a change in the drift of brownian motion abstract the purpose of the present paper is to make a quantitative comparison of the shiryayev roberts and page procedures we do this in the context of continuous time in order to use the machinery of diffusion processes to perform explicitly certain calculations which seem impossible in discrete time although the continuous time results are not especially good approximations to the corresponding quantities in discrete time they provide very useful comparative information on which to base selection of a stopping rule this paper is organized as follows the shiryayev roberts process is defined and shown to be a novel diffusion process with some surprising properties we also specify more precisely the basis for our comparison of the two procedures and give the results of some elementary calculations these developments contain an asymptotic evaluation we define a modification of our basic procedure and give an asymptotic evaluation of its average run length numerical comparisons and a discussion of their significance are contained next our conclusions are roughly these in simple situations where the two procedures can be directly compared neither seems dramatically superior to the other however the shiryayev roberts procedure is more easily adapted to complex circumstances and consequently warrants additional study

mean exit time and escape probability for dynamical systems driven by levy noises the mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non gaussian alpha stable type levy motions an efficient and accurate numerical scheme is developed and validated for computing the mean exit time and escape probability from the governing differential integral equation an asymptotic solution for the mean exit time is given when the pure jump measure in the levy motion is small from both the analytical and numerical results it is observed that the mean exit time depends strongly on the domain size and the value of alpha in the alpha stable levy jump measure the mean exit time and escape probability could become discontinuous at the boundary of the domain when the value of alpha is in 0 1

a geometrical characterization of multidimensional hausdorff polytopes with applications to exit time problems we present a formula for the corner points of the multidimensional hausdorff polytopes and show how this result can be used to improve linear programming models for computing e g moments of exit time distributions of diffusion processes specifically we compute the mean exit time of two dimensional brownian motion from the unit square as well as higher moments of the exit time of time space brownian motion i e the two dimensional process composed of a one dimensional wiener process and the time component from a rectangle the corner point formula is complemented by a convergence result which provides the analytical underpinning of the numerical method that we use

an eigenstructure method for estimating doa and sensor gain phase errors in this paper we consider the problem of direction of arrival doa estimation in the presence of sensor gain phase errors under some mild assumptions we propose a new doa estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate by combining the new doa estimation with the conventional gain phase error estimation a method is proposed to simultaneously estimate the doa and gain phase errors without joint iteration theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors however the resolution capability of the proposed method is lower than that of the method in a j weiss and b friedlander eigenstructure methods for direction finding with sensor gain and phase uncertainties circuits systems signal process vol 9 no 3 pp 271 300 1990 named as the wf method in order to improve the resolution capability and maintain phase error independence a combined strategy is developed using the proposed and wf methods the advantage of the proposed methods is that they are independent of phase errors leading to the cancellation of phase error calibration during the operation life of an array moreover the proposed methods avoid the problem of suboptimal convergence which occurs in the wf method the drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other and they are not applicable to a linear array simulation results verify the effectiveness of the proposed methods

time average control of martingale problems existence of a stationary solution one studies the average cost for controlled systems via the martingale problem for their generator the stationary distributions for these processes on the product of the state and control spaces are characterized in terms of integration of the generator and existence of a stationary solution is established the gives existence of a stationary control

on convergence properties of the em algorithm for gaussian mixtures we build up the mathematical connection between the expectation maximization em algorithm and gradient based approaches for maximum likelihood learning of finite gaussian mixtures we show that the em step in parameter space is obtained from the gradient via a projection matrix p and we provide an explicit expression for the matrix we then analyze the convergence of em in terms of special properties of p and provide new results analyzing the effect that p has on the likelihood surface based on these mathematical results we present a comparative discussion of the advantages and disadvantages of em and other algorithms for the learning of gaussian mixture models

probits of mixtures the tolerances of individuals insects parasites in a population have a frequency or probability distribution called a tolerance distribution many tolerance distributions in bioassay studies can be the result of a rather heterogeneous population of individuals and can often be modelled as a mixture of a number of standard unimodal distributions a probit analysis can be generalized to the case where the tolerance distribution is a mixture of location and scale parameter distributions in this article the existence and determination of the maximum likelihood estimates are investigated an expectation maximization em algorithm for probits of mixtures is developed and it is shown that by application of the em algorithm the problem of probits of mixtures can be separated into a series of probits of individual component tolerance distributions

linear programming formulation for optimal stopping problems optimal stopping problems for continuous time markov processes are shown to be equivalent to infinite dimensional linear programs over a space of pairs of measures under very general conditions the measures involved represent the joint distribution of the stopping time and stopping location and the occupation measure of the process until it is stopped these measures satisfy an identity for each function in the domain of the generator which is sufficient to characterize the stochastic process finite dimensional linear programs obtained using markov chain approximations are solved in two examples to illustrate the numerical accuracy of the linear programming formulation

sensor array calibration using a maximum likelihood approach high resolution array processing algorithms for source localization are known to be sensitive to errors in the model for the sensor array spatial response in particular unknown gain phase and mutual coupling as well as errors in the sensor positions can seriously degrade the performances of array processing algorithms this paper describes a calibration algorithm that estimates the calibration matrix consisting of the unknown gain phase and mutual coupling coefficients as well as the sensor positions using a set of calibration sources in known locations the estimation of the various parameters is based on a maximum likelihood approach cramer rao lower bound crb expressions for the sensor positions and the calibration matrix parameters are also derived numerical results are shown to illustrate the potential usefulness of the proposed calibration algorithm toward better accuracy and resolution in parametric array processing algorithms

roughness penalties on finite domains a class of penalty functions for use in estimation and image regularization is proposed these penalty functions are defined for vectors whose indexes are locations in a finite lattice as the discrepancy between the vector and a shifted version of itself after motivating this class of penalty functions their relationship to markov random field priors is explored one of the penalty functions proposed a divergence roughness penalty is shown to be a discretization of a penalty proposed by good and gaskins 1971 for use in density estimation one potential use in estimation problems is explored an iterative algorithm that takes advantage of induced neighborhood structures is proposed and convergence of the algorithm is proven under specified conditions examples in emission tomographic imaging and radar imaging are given

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

nonparametric estimation of the distribution of time to onset for specific diseases in survival sacrifice experiments this paper concerns the analysis of an animal survival sacrifice experiment designed to investigate the incidence of a particular disease of interest the disease is assumed to be irreversible and detectable only at death for example by a necropsy each observation can be of one of three types i death caused by the disease ii death from a competing cause such as sacrifice with the disease present or iii death with the disease absent a two dimensional em algorithm is proposed for the nonparametric maximum likelihood estimation of the distributions of the time to onset and of the time to death from the disease these can be compared with nonparametric estimators recently proposed by kodell shaw and johnson 1982 biometrics 38 43 58 and by dinse and lagakos 1982 biometrics 38 921 932 a slight modification of the algorithm permits the construction of likelihood based interval estimates of quantiles of the distributions some extensions and generalizations are indicated

direction of arrival estimation using a sparse representation of array covariance vectors a new direction of arrival doa estimation method is proposed based on a novel data model using the concept of a sparse representation of array covariance vectors sracv in which doa estimation is achieved by jointly finding the sparsest coefficients of the array covariance vectors in an overcomplete basis the proposed method not only has high resolution and the capability of estimating coherent signals based on an arbitrary array but also gives an explicit error suppression criterion that makes it statistically robust even in low signal to noise ratio snr cases simulation experiments are conducted to validate the effectiveness of the proposed method the performance is compared with several existing doa estimation methods and the cramer rao lower bound crlb

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

asymptotically optimal blind calibration of uniform linear sensor arrays for narrowband gaussian signals an asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband gaussian signals is proposed rather than taking the direct maximum likelihood ml approach for joint estimation of all the unknown model parameters which leads to a multi dimensional optimization problem with no closed form solution we revisit paulraj and kailath s p k s classical approach in exploiting the special toeplitz structure of the observations covariance however we offer a substantial improvement over p k s ordinary least squares ls estimates by using asymptotic approximations in order to obtain simple non iterative quasi linear optimally weighted ls owls estimates of the sensors gains and phases offsets with asymptotically optimal weighting based only on the empirical covariance matrix of the measurements moreover we prove that our resulting estimates are also asymptotically optimal w r t the raw data and can therefore be deemed equivalent to the ml estimates mle which are otherwise obtained by joint ml estimation of all the unknown model parameters after deriving computationally convenient expressions of the respective cramer rao lower bounds we also show that our estimates offer improved performance when applied to non gaussian signals and or noise as quasi mle in a similar setting the optimal performance of our estimates is demonstrated in simulation experiments with a considerable improvement reaching an order of magnitude and more in the resulting mean squared errors w r t p k s ordinary ls estimates we also demonstrate the improved accuracy in a multiple sources directions of arrivals estimation task

existence of markov controls and characterization of optimal markov controls given a solution of a controlled martingale problem it is shown under general conditions that there exists a solution having markov controls which has the same cost as the original solution this result is then used to show that the original stochastic control problem is equivalent to a linear program over a space of measures under a variety of optimality criteria existence and characterization of optimal markov controls then follows an extension of echeverria s theorem characterizing stationary distributions for uncontrolled markov processes is obtained as a corollary in particular this extension covers diffusion processes with discontinuous drift and diffusion coefficients

an em algorithm for fitting two level structural equation models maximum likelihood is an important approach to analysis of two level structural equation models different algorithms for this purpose have been available in the literature in this paper we present a new formulation of two level structural equation models and develop an em algorithm for fitting this formulation this new formulation covers a variety of two level structural equation models as a result the proposed em algorithm is widely applicable in practice a practical example illustrates the performance of the em algorithm and the maximum likelihood statistic

minimum mean square distance estimation of a subspace we consider the problem of subspace estimation in a bayesian setting since we are operating in the grassmann manifold the usual approach which consists of minimizing the mean square error mse between the true subspace u and its estimate u may not be adequate as the mse is not the natural metric in the grassmann manifold gn p i e the set of p dimensional subspaces in rn as an alternative we propose to carry out subspace estimation by minimizing the mean square distance between u and its estimate where the considered distance is a natural metric in the grassmann manifold viz the distance between the projection matrices we show that the resulting estimator is no longer the posterior mean of u but entails computing the principal eigenvectors of the posterior mean of uut derivation of the minimum mean square distance mmsd estimator is carried out in a few illustrative examples including a linear gaussian model for the data and bingham or von mises fisher prior distributions for u in all scenarios posterior distributions are derived and the mmsd estimator is obtained either analytically or implemented via a markov chain monte carlo simulation method the method is shown to provide accurate estimates even when the number of samples is lower than the dimension of u an application to hyperspectral imagery is anally investigated

properties of mean shift we study properties of the mean shift ms type algorithms for estimating modes of probability density functions pdfs via regarding these algorithms as gradient ascent on estimated pdfs with adaptive step sizes we rigorously prove convergence of mode estimate sequences generated by the ms type algorithms under the assumption that an analytic kernel function is used moreover our analysis on the ms function finds several new properties of mode estimate sequences and corresponding density estimate sequences including the result that in the ms type algorithm using a gaussian kernel the density estimate monotonically increases between two consecutive mode estimates this implies that in the one dimensional case the mode estimate sequence monotonically converges to the stationary point nearest to an initial point without jumping over any stationary point

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

on the distribution of multidimensional reflected brownian motion let z z t t 0 be a reflected brownian motion on the k dimensional nonnegative orthant with the direction of reflection constant over each boundary surface such processes arise in heavy traffic theory for k station networks of queues this paper continues our study of the diffusion process z with attention restricted to the case k 2 for simplicity most of the results extend directly to higher dimensions our notation and style of argument are designed to suggest appropriate generalizations for arbitrary k wherever possible the backward equation for the transition density function with boundary and initial conditions the corresponding forward equation and the equation for the steady state distribution are all derived informally also presented are various calculations relating to steady state distributions including a moment formula and the derivation of a condition involving the drifts and directions of reflection that we conjecture to be necessary and sufficient for existence

cs decomposition based bayesian subspace estimation in numerous applications it is required to estimate the principal subspace of the data possibly from a very limited number of samples additionally it often occurs that some rough knowledge about this subspace is available and could be used to improve subspace estimation accuracy in this case this is the problem we address herein and in order to solve it a bayesian approach is proposed the main idea consists of using the cs decomposition of the semi orthogonal matrix whose columns span the subspace of interest this parametrization is intuitively appealing and allows for non informative prior distributions of the matrices involved in the cs decomposition and very mild assumptions about the angles between the actual subspace and the prior subspace the posterior distributions are derived and a gibbs sampling scheme is presented to obtain the minimum mean square distance estimator of the subspace of interest numerical simulations and an application to real hyperspectral data assess the validity and the performances of the estimator

hierarchical color correction for camera cell phone images in this paper we propose a hierarchical color correction algorithm for enhancing the color of digital images obtained from low quality digital image capture devices such as cell phone cameras the proposed method is based on a multilayer hierarchical stochastic framework whose parameters are learned in an offline training procedure using the well known expectation maximization em algorithm this hierarchical framework functions by first making soft assignments of images into defect classes and then processing the images in each defect class with an optimized algorithm the hierarchical color correction is performed in three stages in the first stage global color attributes of the low quality input image are used in a gaussian mixture model gmm framework to perform a soft classification of the image into m predefined global image classes in the second stage the input image is processed with a nonlinear color correction algorithm that is designed for each of the m global classes this color correction algorithm which we refer to as resolution synthesis color correction rscc applies a spatially varying color correction determined by the local color attributes of the input image in the third stage the outputs of the rscc predictors are combined using the global classification weights to yield the color corrected output image we compare the performance of the proposed method to other commercial color correction algorithms on cell phone camera images obtained from different sources both subjective and objective measures of quality indicate that the new color correction algorithm improves quality over the existing methods

maximum likelihood estimation of delta domain model parameters from noisy output signals fast sampling is desirable to describe signal transmission through wide bandwidth systems the delta operator provides an ideal discrete time modeling description for such fast sampled systems however the estimation of delta domain model parameters is usually biased by directly applying the delta transformations to a sampled signal corrupted by additive measurement noise this problem is solved here by expectation maximization where the delta transformations of the true signal are estimated and then used to obtain the model parameters the method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

accelerated iterative reconstruction for positron emission tomography based on the em algorithm for maximum likelihood estimation the em method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography pet the result is an iterative algorithm for image reconstruction that is finding increasing use in pet due to its attractive theoretical and practical properties its major disadvantage is the large amount of computation that is often required due to the algorithm s slow rate of convergence this paper presents an accelerated form of the em algorithm for pet in which the changes to the image as calculated by the standard algorithm are multiplied at each iteration by an overrelaxation parameter the accelerated algorithm retains two of the important practical properties of the standard algorithm namely the selfnormalization and nonnegativity of the reconstructed images experimental results are presented using measured data obtained from a hexagonal detector system for pet the likelihood function and the norm of the data residual were monitored during the iterative process according to both of these measures the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm for two different sets of data important theoretical properties remain to be investigated namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator

convergence theorems for generalized alternating minimization procedures the em algorithm is widely used to develop iterative parameter estimation procedures for statistical models in cases where these procedures strictly follow the em formulation the convergence properties of the estimation procedures are well understood in some instances there are practical reasons to develop procedures that do not strictly fall within the em framework we study em variants in which the e step is not performed exactly either to obtain improved rates of convergence or due to approximations needed to compute statistics under a model family over which e steps cannot be realized since these variants are not em procedures the standard g em convergence results do not apply to them we present an information geometric framework for describing such algorithms and analyzing their convergence properties we apply this framework to analyze the convergence properties of incremental em and variational em for incremental em we discuss conditions under these algorithms converge in likelihood for variational em we show how the e step approximation prevents convergence to local maxima in likelihood

carrier phase and frequency estimation for pilot symbol assisted transmission bounds and algorithms in this paper we consider the cramer rao lower bound crb for the joint estimation of the carrier phase and the frequency offset from a noisy linearly modulated burst signal containing random data symbols dss as well as known pilot symbols pss we point out that the crb depends on the location of the pss in the burst the number of pss the number of dss the signal to noise ratio snr and the data modulation scheme distributing the pss symmetrically about the center of the burst and estimating the carrier phase in the center of the burst interval decouples the frequency and phase estimation making the crb for phase estimation independent of the specific location of the pss at low and moderate snr the crbs for both phase and frequency estimation decrease as the fraction of the pss in the burst increases in addition the crb for frequency estimation decreases as the pss are separated with more dss numerical evaluation of the crb indicates that the carrier phase and frequency of a hybrid burst i e containing pss and dss can be estimated more accurately when exploiting both the presence of the dss and the a priori knowledge about the pss instead of using only the knowledge about the pss and ignoring the dss or considering all the received symbols pss and dss as unknown and ignoring the knowledge about the pss comparison of the crb with the performance of existing carrier synchronizers shows that the iterative soft decision directed sdd estimator with data aided da initialization performs very closely to the crb and provides a large improvement over the classical non data aided nda estimator at lower snr