kalman filtering in triplet markov chains let x xn nisinin be a hidden process y yn nisinin an observed process and r rn nisinin some additional process we assume that t x r y is a so called triplet vector markov chain tmc we first show that the linear tmc model encompasses and generalizes among other models the classical state space systems with colored process and or measurement noise s we next propose restoration kalman like filters for arbitrary linear gaussian lg tmc

a solution to the continuous time rm h _ infty fixed interval smoother problem the minimum variance fixed interval smoother is a state space realization of the wiener solution generalized for time varying problems it involves forward and adjoint wiener hopf factor inverses in which the gains are obtained by solving a riccati equation this technical note introduces a continuous time h smoother having the structure of the minimum variance version in which the gains are obtained by solving a riccati equation that possesses an indefinite quadratic term it is shown that the smoother exhibits an increase in mean square error the error is bounded and the upper error bound is greater than that for the h filter

bias due to missing exposure data using complete case analysis in the proportional hazards regression model we studied bias due to missing exposure data in the proportional hazards regression model when using complete case analysis cca eleven missing data scenarios were considered one with missing completely at random mcar four missing at random mar and six non ignorable missingness scenarios with a variety of hazard ratios censoring fractions missingness fractions and sample sizes when missingness was mcar or dependent only on the exposure there was negligible bias 2 3 per cent that was similar to the difference between the estimate in the full data set with no missing data and the true parameter in contrast substantial bias occurred when missingness was dependent on outcome or both outcome and exposure for models with hazard ratio of 3 5 a sample size of 400 20 per cent censoring and 40 per cent missing data the relative bias for the hazard ratio ranged between 7 per cent and 64 per cent we observed important differences in the direction and magnitude of biases under the various missing data mechanisms for example in scenarios where missingness was associated with longer or shorter follow up the biases were notably different although both mechanisms are mar the hazard ratio was underestimated with larger bias when missingness was associated with longer follow up and overestimated with smaller bias when associated with shorter follow up if it is known that missingness is associated with a less frequently observed outcome or with both the outcome and exposure cca may result in an invalid inference and other methods for handling missing data should be considered

recursive noise adaptive kalman filtering by variational bayesian approximations this article considers the application of variational bayesian methods to joint recursive estimation of the dynamic state and the time varying measurement noise parameters in linear state space models the proposed adaptive kalman filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and noise parameters on each time step separately the result is a recursive algorithm where on each step the state is estimated with kalman filter and the sufficient statistics of the noise variances are estimated with a fixed point iteration the performance of the algorithm is demonstrated with simulated data

variational bayesian inference for a nonlinear forward model variational bayes vb has been proposed as a method to facilitate calculations of the posterior distributions for linear models by providing a fast method for bayesian inference by estimating the parameters of a factorized approximation to the posterior distribution here a vb method for nonlinear forward models with gaussian additive noise is presented in the case of noninformative priors the parameter estimates obtained from this vb approach are identical to those found via nonlinear least squares however the advantage of the vb method lies in its bayesian formulation which permits prior information to be included in a hierarchical structure and measures of uncertainty for all parameter estimates to be obtained via the posterior distribution unlike other bayesian methods vb is only approximate in comparison with the sampling method of mcmc however the vb method is found to be comparable and the assumptions made about the form of the posterior distribution reasonable practically the vb approach is substantially faster than mcmc as fewer calculations are required some of the advantages of the fully bayesian nature of the method are demonstrated through the extension of the noise model and the inclusion of automatic relevance determination ard within the vb algorithm

exact multiplicity for degenerate two point boundary value problems with p convex nonlinearity the exact number of positive solutions of a degenerate quasilinear two point boundary value problem is investigated for the generalization of earlier results concerning the nondegenerate case with convex nonlinearity suitably defined p convex nonlinearities are considered strictly p convex c2 functions having a non negative root are classified according to the shape of the bifurcation diagram of positive solutions versus the length of the interval we have uniqueness when f 0 0 and 0 1 or 2 solutions when f 0 0 similarly to the non degenerate case provided that the number of solutions is finite however now there may also occur a continuum of solutions connected to a dead core type phenomenon the proof of our results relies on the shooting method for the characterization of the shape of the time map in contrast to the non degenerate case the shooting method does not determine directly the number of solutions owing to the lack of uniqueness of the corresponding ivp exact conditions on the uniqueness of the ivp and in the case of non uniqueness the number and types of its local solutions are given based on this all the positive solutions of the bvp can be compiled

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

adaptive gaussian sum filter for nonlinear bayesian estimation a nonlinear filter is developed by representing the state probability density function by a finite sum of gaussian density kernels whose mean and covariance are propagated from one time step to the next using linear system theory methods such as extended kalman filter or unscented kalman filter the novelty in the proposed method is that the weights of the gaussian kernels are updated at every time step by solving a convex optimization problem posed by requiring the gaussian sum approximation to satisfy the fokker planck kolmogorov equation for continuous time dynamical systems and the chapman kolmogorov equation for discrete time dynamical systems the numerical simulation results show that updating the weights of different mixture components during propagation mode of the filter not only provides us with better state estimates but also with a more accurate state probability density function

proportional hazards regression with missing covariates abstract nonparametric maximum likelihood npml is used to estimate regression parameters in a proportional hazards regression model with missing covariates the npml estimator is shown to be consistent and asymptotically normally distributed under some conditions em type algorithms are applied to solve the maximization problem variance estimates of the regression parameters are obtained by a profile likelihood approach that uses em aided numerical differentiation simulation results indicate that the npml estimates of the regression parameters are more efficient than the approximate partial likelihood estimates and estimates from complete case analysis when missing covariates are missing completely at random and that the proposed method corrects for bias when the missing covariates are missing at random

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

likelihood based methods for missing covariates in the cox proportional hazards model problems associated with missing covariate data are well known but often ignored we present a method for estimating the parameters in the cox proportional hazards model when the missing data are missing at random mar and censoring is noninformative due to the computational burden of this method we introduce an approximation that allows us to use a weighted expectation maximization em algorithm to estimate the parameters more easily when the missing covariates are continuous rather than categorical we implement a monte carlo version of the em algorithm along with the gibbs sampler to obtain parameter estimates we also give the asymptotic distribution of these estimates the primary advantage of this method over complete case analysis is that it produces more efficient parameter estimates and corrects for bias in the mar setting to motivate the methodology we present an analysis of a phase iii melanoma clinical trial conducted by the eastern cooperative oncology group

greedy adaptive linear compression in signal plus noise models in this paper we examine adaptive compression policies when the sequence of vector valued measurements to be compressed is noisy and the compressed variables are themselves noisy the optimization criterion is information gain in the case of sequential scalar compressions the unit norm compression vectors that greedily maximize per stage information gain are eigenvectors of an a priori error covariance matrix and the greedy policy selects them according to eigenvalues of a posterior covariance matrix these eigenvalues depend on all previous compressions and are computed recursively a water filling solution is given for the optimum compression policy that maximizes net information gain under a constraint on the average norm of compression vectors we provide sufficient conditions under which the greedy policy for maximizing stepwise information gain actually is optimal in the sense of maximizing the net information gain in the case of scalar compressions our examples and simulation results illustrate that the greedy policy can be quite close to optimal when the noise sequences are white

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

derivation of fixed interval smoothing algorithm using covariance information in distributed parameter systems this paper proposes a recursive least mean squared error fixed interval smoothing algorithm in distributed parameter systems it is assumed that the state space model of the signal to be estimated is unknown and the algorithm only requires the second order moments of the signal and the white noise perturbing its observations practical application of the proposed algorithm is illustrated with a restoration image problem

on the approximability of budgeted allocations and improved lower bounds for submodular welfare maximization and gap in this paper we consider the following maximum budgeted allocation mba problem given a set of m indivisible items and n agents with each agent i willing to pay b ij on item j and with a maximum budget of b i the goal is to allocate items to agents to maximize revenue the problem naturally arises as auctioneer revenue maximization in budget constrained auctions and as the winner determination problem in combinatorial auctions when utilities of agents are budgeted additive our main results are as follows i we give a 3 4 approximation algorithm for mba improving upon the previous best of simeq0 632 n andelman and y mansour proceedings of the 9th scandinavian workshop on algorithm theory swat 2004 pp 26 38 j vondrak proceedings of the 40th annual acm symposium on the theory of computing stoc 2008 pp 67 74 also implied by the result of u feige and j vondrak proceedings of the 47th ieee symposium on foundations of computer science focs 2006 pp 667 676 our techniques are based on a natural lp relaxation of mba and our factor is optimal in the sense that it matches the integrality gap of the lp ii we prove it is np hard to approximate mba to any factor better than 15 16 previously only np hardness was known t sandholm and s suri games econom behav 55 2006 pp 321 330 b lehmann d lehmann and n nisan proceedings of the 3rd acm conference on electronic commerce ec 2001 pp 18 28 our result also implies np hardness of approximating maximum submodular welfare with demand oracle to a factor better than 15 16 improving upon the best known hardness of 275 276 u feige and j vondrak proceedings of the 47th ieee symposium on foundations of computer science focs 2006 pp 667 676 iii our hardness techniques can be modified to prove that it is np hard to approximate the generalized assignment problem gap to any factor better than 10 11 this improves upon the 422 423 hardness of c chekuri and s khanna proceedings of the 11th annual acm siam symposium on discrete algorithms soda 2000 pp 213 222 m chlebik and j chlebikova proceedings of the 8th scandinavian workshop on algorithm theory swat 2002 pp 170 179 we use iterative rounding on a natural lp relaxation of the mba problem to obtain the 3 4 approximation we also give a 3 4 epsilon factor algorithm based on the primal dual schema which runs in tilde o nm time for any constant epsilon 0

regression with missing x s a review abstract the literature of regression analysis with missing values of the independent variables is reviewed six classes of procedures are distinguished complete case analysis available case methods least squares on imputed data maximum likelihood bayesian methods and multiple imputation methods are compared and illustrated when missing data are confined to one independent variable and extensions to more general patterns are indicated attention is paid to the performance of methods when the missing data are not missing completely at random least squares methods that fill in missing x s using only data on the x s are contrasted with likelihood based methods that use data on the x s and y the latter approach is preferred and provides methods for elaboration of the basic normal linear regression model it is suggested that more widely distributed software is needed that advances beyond complete case analysis available case analysis and naive imputation methods bayesian simulation methods and mu

on bayesian fixed interval smoothing algorithms in this note we revisit fixed interval kalman like smoothing algorithms we have two results we first unify the family of existing algorithms by deriving them in a common bayesian framework as we shall see all these algorithms stem from forward and or backward markovian properties of the state process involve one or two out of four canonical probability density functions and can be derived from the systematic use of some generic properties of gaussian variables which we develop in a specific toolbox on the other hand the methodology we use enables us to complete the set of existing algorithms by five new kalman like smoothing algorithms which is our second result

fitting cox s proportional hazards models from survey data summary the proportional hazards model makes a number of assumptions which may not always be completely satisfied however fitting such models can have both descriptive and analytical value we discuss the implications of the survey design for large scale studies we propose a weighted estimator and derive a design based estimator for the variance of the estimated parameters the derivation requires using methods not previously used in the context of analysis of survey data we conduct a small simulation study comparing the proposed method with others in the literature

fast kalman like filtering for large dimensional linear and gaussian state space models this article considers the filtering problem for linear and gaussian state space models with large dimensions a setup in which the optimal kalman filter kf might not be applicable owing to the excessive cost of manipulating huge covariance matrices among the most popular alternatives that enable cheaper and reasonable computation is the ensemble kf enkf a monte carlo based approximation in this article we consider a class of a posteriori distributions with diagonal covariance matrices and propose fast approximate deterministic based algorithms based on the variational bayesian vb approach more specifically we derive two iterative kf like algorithms that differ in the way they operate between two successive filtering estimates one involves a smoothing estimate and the other involves a prediction estimate despite its iterative nature the prediction based algorithm provides a computational cost that is on the one hand independent of the number of iterations in the limit of very large state dimensions and on the other hand always much smaller than the cost of the enkf the cost of the smoothing based algorithm depends on the number of iterations that may in some situations make this algorithm slower than the enkf the performances of the proposed filters are studied and compared to those of the kf and enkf through a numerical example

bayes smoothing algorithms for segmentation of binary images modeled by markov random fields a new image segmentation algorithm is presented based on recursive bayes smoothing of images modeled by markov random fields and corrupted by independent additive noise the bayes smoothing algorithm yields the a posteriori distribution of the scene value at each pixel given the total noisy image in a recursive way the a posteriori distribution together with a criterion of optimality then determine a bayes estimate of the scene the algorithm presented is an extension of a 1 d bayes smoothing algorithm to 2 d and it gives the optimum bayes estimate for the scene value at each pixel computational concerns in 2 d however necessitate certain simplifying assumptions on the model and approximations on the implementation of the algorithm in particular the scene noiseless image is modeled as a markov mesh random field a special class of markov random fields and the bayes smoothing algorithm is applied on overlapping strips horizontal vertical of the image consisting of several rows columns it is assumed that the signal scene values vector sequence along the strip is a vector markov chain since signal correlation in one of the dimensions is not fully used along the edges of the strip estimates are generated only along the middle sections of the strips the overlapping strips are chosen such that the union of the middle sections of the strips gives the whole image the bayes smoothing algorithm presented here is valid for scene random fields consisting of multilevel discrete or continuous random variables

h_ infty fixed interval smoothing estimation for time delay systems this paper is concerned with the h fixed interval smoothing estimation for time delay systems which include continuous time case and discrete time case in the case of discrete time systems the problem can be solved by using the conventional state augmentation approach however this approach is not suitable for the continuous time case in this paper we will propose a unified approach to study the h fixed interval smoothing problem for both continuous time and discrete time systems with l output delays by introducing a suitable stochastic linear time delay models in an indefinite space it is shown that the h fixed interval smoother can be obtained by calculating h2 fixed interval smoother for time delay systems in an indefinite space therefore based on the orthogonal projection theory in an indefinite space the h fixed interval smoothers for time delay systems are designed by performing l 1 riccati equations with the same dimension as the original systems moreover a necessary and sufficient conditions for the existence of the h fixed interval smoother will also be given

an iterative kalman like algorithm ignoring noise and initial conditions we address a p shift finite impulse response fir unbiased estimator ue for linear discrete time varying filtering p 0 p step prediction p 0 and p lag smoothing p 0 in state space with no requirements for initial conditions and zero mean noise a solution is found in a batch form and represented in a computationally efficient iterative kalman like one it is shown that the kalman like fir ue is able to outperform the kalman filter if the noise covariances and initial conditions are not known exactly noise is not white and both the system and measurement noise components need to be filtered out otherwise the errors are similar extensive numerical studies of the fir ue are provided in gaussian and non gaussian environments with outliers and temporary uncertainties

estimating equations with incomplete categorical covariates in the cox model incomplete covariate data is a common occurrence in many studies in which the outcome is survival time when a full likelihood is specified a useful technique for obtaining parameter estimates is the em algorithm we propose a set of estimating equations to estimate the parameters of cox s proportional hazards model when some covariate values are missing these estimating equations can be solved by an algorithm similar to the em algorithm because of the computational burden of finding a solution to these estimating equations we propose obtaining parameter estimates via monte carlo methods asymptotic variances of the parameter estimates are also derived we present a clinical trials example with three covariates two of which have some missing values

recursive algorithms for bayes smoothing with uncertain observations recursive algorithms for the bayes solution of fixed interval fixed point and fixed lag smoothing under uncertain observations are presented the bayes smoothing algorithms are obtained for a markovian system model with markov uncertainty a model more general than the one used in linear smoothing algorithms the bayes fixed interval smoothing algorithm is applied to a gauss markov example the simulation results for this example indicate that the mse performance of the bayes smoother is significantly better than that of the linear smoother

a numerical algorithm for finding solutions of p laplacian dirichlet problems abstract in this paper we investigate numerically positive solution of the equation pu u r 2u g u with dirichlet boundary condition in a boundary domain for 0 and 1

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

submodular utility maximization for deadline constrained data collection in sensor networks we study the utility maximization problem for data collection in a wireless sensor network subject to a deadline constraint where the data on a selected subset of nodes are collected through a routing tree subject to the 1 hop interference model our problem is closely related to the traditional utility maximization problems in networking and communications however instead of a separable concave form of utility functions commonly seen in this area we consider the class of monotone submodular utility functions defined on subsets of nodes which is more appropriate for the applications we consider while submodular maximization subject to a cardinality constraint has been well understood our problem is more challenging due to the multi hop data forwarding nature even under the simple interference model we have derived efficient approximation solutions to this problem both for raw data collection and when in network data aggregation is applied

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

two filter formulae for discrete time non linear bayesian smoothing two filler formulae for the bayes solution of the fixed interval discrete time nonlinear smoothing problem are obtained the smoothed a posteriori density is computed under the assumptions of a general markov signal observed through a general memoryless noisy channel the case where there is feedback from the observation to the signal is also considered the derived algorithms complement a two pass algorithm obtained under somewhat more restrictive assumptions by askar and derin 1981 known smoothing results for the linear gaussian case are interpreted in the light of the general bayesian results

variational bayesian filtering the use of the variational bayes vb approximation in bayesian filtering is studied both as a means to accelerate marginalized particle filtering and as a deterministic local one step approximation the vb method of approximation is reviewed together with restrictions that allow various computational savings to be achieved these variants provide a range of algorithms that can be used in a principled tradeoff between quality of approximation and computational cost in combination with marginalized particle filtering they generalize previously published work on variational filtering and extend currently available methods for speeding up stochastic approximations in bayesian filtering in particular the free form nature of the vb approximation allows optimal selection of moments which summarize the particles other bayesian filtering schemes are developed by replacing the marginalization operator in bayesian filtering with vb marginals this leads to further computational savings at the cost of quality of approximation the performance of the various vb filtering schemes is illustrated in the context of a gaussian model with a nonlinear substate and a hidden markov model

the h_infty fixed interval smoothing problem for continuous systems the hinfin smoothing problem for continuous systems is treated in a state space representation by means of variational calculus techniques the smoothing problem is introduced in an hinfin criterion by means of an artificial discontinuity that splits the problem in term of hinfin forward and hinfin backward filtering problems hence the smoother design is realized in three steps first a forward filter is developed secondly a backward filter is developed taking into account the backward markovian model the third step consists of combining the two previous steps in order to compute the hinfin smoothed estimate an example shows the efficiency of this proposed smoother

on using the cox proportional hazards model with missing covariates summary we propose two methods for handling missing covariates in using the cox proportional hazards model the maximum partial likelihood estimator based only on study subjects having complete covariates does not utilise all available information also it is biased when the probability of missingness depends on the failure or censoring time our suggestion is to impute the conditional expectation of the statistic involving missing covariates given the available information the proposed method provides a consistent regression parameter estimator when the probability of missingness depends on the failure or censoring time as well as on the observed covariates also the proposed estimator is more efficient than the estimator suggested previously by lin ying 1993 when data are missing completely at random

bifurcation phenomena associated to the p laplace operator on determine la structure de l ensemble des solutions u de u x p 2 u x x f u u p 2 u sur 0 1 telles que u 0 u 1 0 ou p 1 et r on demontre que les solutions avec k zeros sont uniques quand 1 2

bayesian parameter estimation taking the bayesian approach in solving the discrete time parameter estimation problem has two major results the unknown parameters are legitimately included as additional system states and the computational objective becomes calculation of the entire posterior density instead of just its first few moments this viewpoint facilitates intuitive analysis allowing increased qualitative understanding of the system behavior with the actual posterior density in hand the true optimal estimate for any given loss function can be calculated although the computational burden of doing so might preclude online use it does not provide a clearly justified baseline for comparative studies these points are demonstrated by analyzing a scalar problem with a single unknown and by comparing an established point estimator s performance to the true optimal estimate

practical implementation of an efficient forward backward algorithm for an explicit duration hidden markov model this correspondence addresses several practical problems in implementing a forward backward fb algorithm for an explicit duration hidden markov model first the fb variables are redefined in terms of posterior probabilities to avoid possible underflows that may occur in practice then a forward recursion is used that is symmetric to the backward one and can reduce the number of logic gates required to implement on a field programmable gate array fpga chip

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

least informative bayesian prior distributions for finite samples based on information theory a procedure is presented based on shannon information theory for producing least informative prior distributions for bayesian estimation and identification this approach relies on constructing an optimal mixture distribution and applies in small sample sizes unlike certain approaches based on asymptotic theory the procedure is illustrated in a small scale numerical study and is contrasted with an approach based on maximum entropy

robust blind pairwise kalman algorithms using qr decompositions the pairwise kalman filter pkf w pieczynski and f desbouvries kalman filtering using pairwise gaussian models in proc int conf acoust speech signal process icassp hong kong apr 2003 is an extension of the classical kalman filter that keeps propagation equations explicit i e it does not require time consuming simulations the contribution of this note is twofold first new robust equations for filtering smoothing and unsupervised off lined parameters estimation based on qr decompositions are presented second since the model is over parametrized we give a simple condition to uniquely characterize a filter of interest when the dimension of observations is equal to the dimension of states unsupervised experiments based on simulated data confirm the nice behavior of the robust pkf even for a limited number of observations

an iterative ensemble kalman filter the ensemble kalman filter is a monte carlo method for state estimation of nonlinear models developed as an alternative or improvement of the extended kalman filter in this technical note we introduce an iterative extension to the ensemble kalman filter iterations are introduced to improve the estimates in the cases where the relationship between the model and observations is not linear the iterations converge but to a solution where the data are overfitted an essential stopping criteria is therefore introduced for the proposed method

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

log linear analysis of censored survival data with partially observed covariates abstract log linear models provide a flexible means of extending life table techniques for the analysis of censored survival data with categorical covariates as discussed by holford 1980 and laird and olivier 1981 we extend this methodology to incorporate cases in which one or more of the categorical covariates are sometimes missing maximum likelihood estimates of the parameters are calculated using data from all cases this can result in large gains in efficiency over standard methods that require the exclusion of cases with incomplete data with this approach we assume that the hazard function conditional on the covariates is a stepwise function over disjoint intervals of time the model has two parts a log linear model describing the hazard parameters and a multinomial model describing the probabilities in the contingency table defined by the covariates the main interest is in the model for the hazard parameters we show how to calculate maximum likelihood estimates of parameters of the mo

on certain second order ordinary differential equations associated with sobolev poincare type inequalities on considere l equation e i 1 n u x i p 2 u x i x i u q 2 u 0 dans u x 0 sur on donne les proprietes des solutions de e pour le cas n 1 et a b mais pour p q 1 avec p q regularite existence et unicite de solutions positives

string submodular functions with curvature constraints consider the problem of choosing a string of actions to optimize an objective function that is string submodular it was shown in previous papers that the greedy strategy consisting of a string of actions that only locally maximizes the step wise gain in the objective function achieves at least a 1 e 1 approximation to the optimal strategy this paper improves this approximation by introducing additional constraints on curvature namely total backward curvature total forward curvature and elemental forward curvature we show that if the objective function has total backward curvature sigma then the greedy strategy achieves at least a 1 sigma 1 e sigma approximation of the optimal strategy if the objective function has total forward curvature epsilon then the greedy strategy achieves at least a 1 epsilon approximation of the optimal strategy moreover we consider a generalization of the diminishing return property by defining the elemental forward curvature we also introduce the notion of string matroid and consider the problem of maximizing the objective function subject to a string matroid constraint we investigate two applications of string submodular functions with curvature constraints 1 choosing a string of actions to maximize the expected fraction of accomplished tasks and 2 designing a string of measurement matrices such that the information gain is maximized

on the asymptotic stability of boundary trajectories for a class of dynamical systems it is shown that trajectories which remain on the boundary of a non empty connected subset of a reachable set must be asymptotically stable using this result and a reachability maximum principle we obtain a control law which will drive the system from the origin to the boundary of the reachable set for a class of two dimensional linear control systems using this control law the reachable set is easily constructed

a recursive algorithm for the bayes solution of the smoothing problem the optimum fixed interval smoothing problem is solved using a bayesian approach assuming that the signal is markov and is corrupted by independent noise not necessarily additive a recursive algorithm to compute the a posteriori smoothed density is obtained using this recursive algorithm the smoothed estimate of a binary markov signal corrupted by an independent noise in a nonlinear manner is determined demonstrating that the bayesian approach presented in this paper is not restricted to the gauss markov problem

game theory approach to finite time horizon optimal estimation in this game a measurement record is given and the first player looks for the best estimate of a prespecified combination of the system states in the presence of a hostile process noise signal and system initial condition that are applied by his adversary it turns out that the game possesses a saddle point solution which leads to an optimal smoothed estimate that is identical to the corresponding l sub 2 optimal estimate a similar game in which the estimate is restricted to be causal is formulated and solved this game provides for the first time a saddle point equilibrium interpretation to finite time h sub infinity optimal filtered estimation the two games are very closely related it is shown that in the first game the first player s strategy which is the optimal smoothed estimate is a linear fractional transformation of the h sub infinity optimal filter which applies a nonzero free contracting q parameter it therefore achieves a unity h sub infinity norm bound for the operator that relates the exogeneous signals to the estimation error

incomplete data in generalized linear models abstract this article examines incomplete data for the class of generalized linear models in which incompleteness is due to partially missing covariates on some observations under the assumption that the missing data are missing at random it is shown that the e step of the em algorithm for any generalized linear model can be expressed as a weighted complete data log likelihood when the unobserved covariates are assumed to come from a discrete distribution with finite range expressing the e step in this manner allows for a straightforward maximization in the m step thus leading to maximum likelihood estimates mle s for the parameters asymptotic variances of the mle s are also derived and results are illustrated with two examples

indicator and stratification methods for missing explanatory variables in multiple linear regression abstract the statistical literature and folklore contain many methods for handling missing explanatory variable data in multiple linear regression one such approach is to incorporate into the regression model an indicator variable for whether an explanatory variable is observed another approach is to stratify the model based on the range of values for an explanatory variable with a separate stratum for those individuals in which the explanatory variable is missing for a least squares regression analysis using either of these two missing data approaches the exact biases of the estimators for the regression coefficients and the residual variance are derived and reported the complete case analysis in which individuals with any missing data are omitted is also investigated theoretically and is found to be free of bias in many situations though often wasteful of information a numerical evaluation of the bias of two missing indicator methods and the complete case analysis is reported the missing indi

recursive algorithms for the bayes solution of the fixed point and fixed lag smoothing problems recursive algorithms for the bayes solutions of the fixed point and fixed lag smoothing problems are obtained recursive algorithms for the respective smoothed a posteriori densities are derived under assumptions that the signal to be estimated is a markov process and the observation is a signal embedded in independent noise not necessarily additive which is also independent of the signal the recursive algorithm for the fixed point smoothing is applied to a binary markov signal corrupted by an independent noise in a nonlinear manner

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f

maximum penalized likelihood estimation for independent and markov dependent mixture models summary this paper concerns the use and implementation of maximum penalized likelihood procedures for choosing the number of mixing components and estimating the parameters in independent and markov dependent mixture models computation of the estimates is achieved via algorithms for the automatic generation of starting values for the em algorithm computation of the information matrix is also discussed poisson mixture models are applied to a sequence of counts of movements by a fetal lamb in utero obtained by ultrasound the resulting estimates are seen to provide plausible mechanisms for the physiological process the analysis of count data that are overdispersed relative to the poisson distribution i e variance mean has received considerable recent attention such data might arise in a clinical study in which overdispersion is caused by unexplained or random subject effects alternatively we might observe a time series of counts in which temporal patterns in the data suggest that a poisson model and its implied randomness are inappropriate this paper is motivated by analysis of a time series of overdispersed count data generated in a study of central nervous system development in fetal lambs our data set consists of observed movement counts in 240 consecutive 5 second intervals obtained from a single animal in analysing these data we focus on the use of poisson mixture models assuming independent observations and also markov dependent mixture models or hidden markov models these models assume that the counts follow independent poisson distributions conditional on the rates which are generated from a mixing distribution either independently or with markov dependence we believe finite mixture models are particularly attractive because they provide plausible explanations for variation in the data this paper will emphasize the following issues concerning estimation inference and application of mixture models i choosing the number of model components ii applying the em algorithm to obtain parameter estimates iii generating sufficiently many starting values to identify a global maximum of the likelihood iv avoiding numerical instability

online model selection based on the variational bayes the bayesian framework provides a principled way of model selection this framework estimates a probability distribution over an ensemble of models and the prediction is done by averaging over the ensemble of models accordingly the uncertainty of the models is taken into account and complex models with more degrees of freedom are penalized however integration over model parameters is often intractable and some approximation scheme is needed recently a powerful approximation scheme called the variational bayes vb method has been proposed this approach defines the free energy for a trial probability distribution which approximates a joint posterior probability distribution over model parameters and hidden variables the exact maximization of the free energy gives the true posterior distribution the vb method uses factorized trial distributions the integration over model parameters can be done analytically and an iterative expectation maximization like algorithm whose convergence is guaranteed is derived in this article we derive an online version of the vb algorithm and prove its convergence by showing that it is a stochastic approximation for finding the maximum of the free energy by combining sequential model selection procedures the online vb method provides a fully online learning method with a model selection mechanism in preliminary experiments using synthetic data the online vb method was able to adapt the model structure to dynamic environments

variational bayes for generalized autoregressive models we describe a variational bayes vb learning algorithm for generalized autoregressive gar models the noise is modeled as a mixture of gaussians rather than the usual single gaussian this allows different data points to be associated with different noise levels and effectively provides robust estimation of ar coefficients the vb framework is used to prevent overfitting and provides model order selection criteria both for ar order and noise model order we show that for the special case of gaussian noise and uninformative priors on the noise and weight precisions the vb framework reduces to the bayesian evidence framework the algorithm is applied to synthetic and real data with encouraging results

maximizing a monotone submodular function subject to a matroid constraint let f 2 x rightarrow cal r be a monotone submodular set function and let x cal i be a matroid we consider the problem rm max s in cal i f s it is known that the greedy algorithm yields a 1 2 approximation m l fisher g l nemhauser and l a wolsey math programming stud no 8 1978 pp 73 87 for this problem for certain special cases e g rm max s leq k f s the greedy algorithm yields a 1 1 e approximation it is known that this is optimal both in the value oracle model where the only access to f is through a black box returning f s for a given set s g l nemhauser and l a wolsey math oper res 3 1978 pp 177 188 and for explicitly posed instances assuming p neq np u feige j acm 45 1998 pp 634 652 in this paper we provide a randomized 1 1 e approximation for any monotone submodular function and an arbitrary matroid the algorithm works in the value oracle model our main tools are a variant of the pipage rounding technique of ageev and sviridenko j combin optim 8 2004 pp 307 328 and a continuous greedy process that may be of independent interest as a special case our algorithm implies an optimal approximation for the submodular welfare problem in the value oracle model j vondrak proceedings of the 38 th acm symposium on theory of computing 2008 pp 67 74 as a second application we show that the generalized assignment problem gap is also a special case although the reduction requires x to be exponential in the original problem size we are able to achieve a 1 1 e o 1 approximation for gap simplifying previously known algorithms additionally the reduction enables us to obtain approximation algorithms for variants of gap with more general constraints

submodular maximization over multiple matroids via generalized exchange properties submodular function maximization is a central problem in combinatorial optimization generalizing many important np hard problems including max cut in digraphs graphs and hypergraphs certain constraint satisfaction problems maximum entropy sampling and maximum facility location problems our main result is that for any k 2 and any e 0 there is a natural local search algorithm that has approximation guarantee of 1 k e for the problem of maximizing a monotone submodular function subject to k matroid constraints this improves upon the 1 k 1 approximation of fisher nemhauser and wolsey obtained in 1978 fisher m g nemhauser l wolsey 1978 an analysis of approximations for maximizing submodular set functions ii math programming stud 8 73 87 also our analysis can be applied to the problem of maximizing a linear objective function and even a general nonmonotone submodular function subject to k matroid constraints we show that in these cases the approximation guarantees of our algorithms are 1 k 1 e and 1 k 1 1 k 1 e respectively our analyses are based on two new exchange properties for matroids one is a generalization of the classical rota exchange property for matroid bases and another is an exchange property for two matroids based on the structure of matroid intersection