optimal robust filtering with time varying parameter uncertainty stochastic linear systems subject to time varying parameter uncertainties affecting both system dynamics and noise statistics are considered a linear filter is used to estimate a linear combination of the states of the system when the filter is given the stabilizing solution of a suitable riccati equation is shown to yield an upper bound for the covariance of the estimator error the main problem addressed in the paper is the design of an optimal robust filter that minimizes such a covariance bound necessary conditions are given for the existence of an optimal reduced order robust filter as well as necessary and sufficient conditions for the full order case the computation of the optimal filter calls for the solution of a riccati equation that generalizes the standard riccati equation for the kalman filtering problem a numerical example is provided in which the new filter is compared with both the kalman and h filters

a semi parametric bayesian approach to the instrumental variable problem we develop a bayesian semi parametric approach to the instrumental variable problem we assume linear structural and reduced form equations but model the error distributions non parametrically a dirichlet process prior is used for the joint distribution of structural and instrumental variable equations errors our implementation of the dirichlet process prior uses a normal distribution as a base model it can therefore be interpreted as modeling the unknown joint distribution with a mixture of normal distributions with a variable number of mixture components we demonstrate that this procedure is both feasible and sensible using actual and simulated data sampling experiments compare inferences from the non parametric bayesian procedure with those based on procedures from the recent literature on weak instrument asymptotics when errors are non normal our procedure is more efficient than standard bayesian or classical methods

bayesian sparse multiple regression for simultaneous rank reduction and variable selection we develop a bayesian methodology aimed at simultaneously estimating low rank and row sparse matrices in a high dimensional multiple response linear regression model we consider a carefully devised shrinkage prior on the matrix of regression coefficients which obviates the need to specify a prior on the rank and shrinks the regression matrix towards low rank and row sparse structures we provide theoretical support to the proposed methodology by proving minimax optimality of the posterior mean under the prediction risk in ultra high dimensional settings where the number of predictors can grow sub exponentially relative to the sample size a one step post processing scheme induced by group lasso penalties on the rows of the estimated coefficient matrix is proposed for variable selection with default choices of tuning parameters we additionally provide an estimate of the rank using a novel optimization function achieving dimension reduction in the covariate space we exhibit the performance of the proposed methodology in an extensive simulation study and a real data example

multiple output regression with latent noise in high dimensional data structured noise caused by observed and unobserved factors affecting multiple target variables simultaneously imposes a serious challenge for modeling by masking the often weak signal therefore 1 explaining away the structured noise in multiple output regression is of paramount importance additionally 2 assumptions about the correlation structure of the regression weights are needed we note that both can be formulated in a natural way in a latent variable model in which both the interesting signal and the noise are mediated through the same latent factors under this assumption the signal model then borrows strength from the noise model by encouraging similar effects on correlated targets we introduce a hyperparameter for the latent signal to noise ratio which turns out to be important for modelling weak signals and an ordered infinite dimensional shrinkage prior that resolves the rotational unidentifiability in reduced rank regression models simulations and prediction experiments with metabolite gene expression fmri measurement and macroeconomic time series data show that our model equals or exceeds the state of the art performance and in particular outperforms the standard approach of assuming independent noise and signal models

robust state estimation for perturbed continuous systems with circular pole and error variance constraints in this paper the problem of circular pole and variance constrained state estimator design is studied for perturbed linear continuous time systems the system under consideration is subject to unstructured time invariant norm bounded parameter perturbations in both the state and measurement matrices the problem we address is the design of a state estimator such that for all admissible time invariant perturbations the poles of the steady state filtering matrix are assigned inside a prespecified circular region and the variance of the estimation error of each state is not more that the individual prespecified value simultaneously an algebraic riccati like matrix inequality approach is proposed to solve the above problem specifically the existence conditions and an explicit expression for the desired estimators are obtained furthermore an illustrative example is presented to demonstrate the effectiveness of the proposed design procedure

modularity in orbifold theory for vertex operator superalgebras this paper is about the orbifold theory for vertex operator superalgebras given a vertex operator superalgebra v and a finite automorphism group g of v we show that the trace functions associated to the twisted sectors are holomorphic in the upper half plane for any commuting pairs in g under the c2 cofinite condition we also establish that these functions afford a representation of the full modular group if v is c2 cofinite and g rational for any g g

getting it right joint distribution tests of posterior simulators analytical or coding errors in posterior simulators can produce reasonable but incorrect approximations of posterior moments this article develops simple tests of posterior simulators that detect both kinds of errors and uses them to detect and correct errors in two previously published articles the tests exploit the fact that a bayesian model specifies the joint distribution of observables data and unobservables parameters there are two joint distribution simulators the marginal conditional simulator draws unobservables from the prior and then observables conditional on unobservables the successive conditional simulator alternates between the posterior simulator and an observables simulator formal comparison of moment approximations of the two simulators reveals existing analytical or coding errors in the posterior simulator

robust h sub 2 h sub spl infin filtering for linear systems with error variance constraints in this correspondence we consider the robust h sub 2 h sub spl infin filtering problem for linear perturbed systems with steady state error variance constraints the purpose of this multiobjective problem is to design a linear filter that does not depend on the parameter perturbations such that the following three performance requirements are simultaneously satisfied 1 the filtering process is asymptotically stable 2 the steady state variance of the estimation error of each state is not more than the individual prespecified value 3 the transfer function from exogenous noise inputs to error state outputs meets the prespecified h sub spl infin norm upper bound constraint we show that in both continuous and discrete time cases the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like equations inequalities we present both the existence conditions and the explicit expression of desired robust filters an illustrative numerical example is provided to demonstrate the flexibility of the proposed design approach

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

h optimal control part 2 solution for controllers abstract the problem is considered of bounding the h norm of the transfer function t y1u1 relating the output y 1 to the input u 1 for the feedback configuration shown in fig 1 subject to the closed loop system being internally stable a new criterion for internal stability is derived in terms of the q parameterization where q k i p22 k 1 by means of such a stability theory it is shown that the h control problem can be decomposed into two one sided model matching problems of the form considered in part 1 hung 1989 of the paper a closed form state space solution with a tight mcmillan degree bound is obtained for h optimal or suboptimal controllers an iterative algorithm for obtaining the h optimal controller is provided computationally the algorithm requires the solution of only two algebraic riccati equations in each iteration for which the upper bound on t y1u1 is adjusted

natural conjugate priors for the instrumental variables regression model applied to the angrist krueger data we propose a natural conjugate prior for the instrumental variables regression model the prior is a natural conjugate one since the marginal prior and posterior of the structural parameter have the same functional expressions which directly reveal the update from prior to posterior the jeffreys prior results from a specific setting of the prior parameters and results in a marginal posterior of the structural parameter that has an identical functional form as the sampling density of the limited information maximum likelihood estimator we construct informative priors for the angrist krueger 1991 does compulsory school attendance affect schooling and earnings quarterly journal of economics 106 979 1014 data and show that the marginal posterior of the return on education in the us coincides with the marginal posterior from the southern region when we use the jeffreys prior this result occurs since the instruments are the strongest in the southern region and the posterior using the jeffreys prior identical to maximum likelihood focusses on the strongest available instruments we construct informative priors for the other regions that make their posteriors of the return on education similar to that of the us and the southern region these priors show the amount of prior information needed to obtain comparable results for all regions

robust spl hscr sub spl infin filtering for continuous time varying uncertain systems with deterministic input signals many dynamical systems involve not only process and measurement noise signals but also parameter uncertainty and known input signals when spl lscr sub 2 or spl hscr sub spl infin filters that were designed based on a nominal model of the system are applied the presence of parameter uncertainty will not only affect the noise attenuation property of the filter but also introduce a bias proportional to the known input signal and the latter may be very appreciable we introduce a finite horizon robust spl hscr sub spl infin filtering method that provides a guaranteed spl hscr sub spl infin bound for the estimation error in the presence of both parameter uncertainty and a known input signal this method is developed by using a game theoretic approach and the results generalize those obtained for cases without parameter uncertainty or without a known input signal it is also demonstrated via an example that the proposed method provides significantly improved signal estimates

bayesian reduced rank regression in econometrics abstract the reduced rank regression model arises repeatedly in theoretical and applied econometrics to date the only general treatment of this model have been frequentist this paper develops general methods for bayesian inference with noninformative reference priors in this model based on a markov chain sampling algorithm and procedures for obtaining predictive odds ratios for regression models with different ranks these methods are used to obtain evidence on the number of factors in a capital asset pricing model

steady state kalman filtering with an h error bound abstract an estimator design problem is considered which involves both l 2 least squares and h worst case frequency domain aspects specifically the goal of the problem is to minimize an l 2 state estimation error criterion subject to a prespecified h constraint on the state estimation error the h estimation error constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on the l 2 state estimation error the principal result is a sufficient condition for characterizing fixed order i e full and reduced order estimators with bounded l 2 and h estimation error the sufficient condition involves a system of modified riccati equations coupled by an oblique projection i e idempotent matrix when the h constraint is absent the sufficient condition specializes to the l 2 state estimation result given in 2

corrigendum to bayesian reduced rank regression in econometrics j econometrics 75 1996 121 146 corrigendum to bayesian reduced rank regression in econometrics j econometrics 75 1996 121 146

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

filtering for nonlinear genetic regulatory networks with stochastic disturbances in this paper the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition the stochastic perturbation is in the form of a scalar brownian motion and the time delays exist in both the translation process and the feedback regulation process the purpose of the addressed filtering problem is to estimate the true concentrations of the mrna and protein specifically we are interested in designing a linear filter such that in the presence of time delays stochastic disturbances as well as sector nonlinearities the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta by using the linear matrix inequality lmi technique sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model and the filter gain is then characterized in terms of the solution to an lmi which can be easily solved by using standard software packages a simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

a parameter dependent approach to robust h_ infty filtering for time delay systems this paper is concerned with the problem of robust h infin filtering for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state we utilize the polynomially parameter dependent idea to solve the robust h infin filtering problem with new linear matrix inequality conditions obtained for the existence of admissible filters these conditions are developed based on homogeneous polynomially parameter dependent matrices of arbitrary degree the delay dependence and polynomial parameter dependence guarantee the proposed approach to be potentially less conservative which is shown via a numerical example

modular invariance for twisted modules over a vertex operator superalgebra the purpose of this paper is to generalize zhu s theorem about characters of modules over a vertex operator algebra graded by integer conformal weights to the setting of a vertex operator superalgebra graded by rational conformal weights to recover sl 2 mathbb z invariance of the characters it turns out to be necessary to consider twisted modules alongside ordinary ones it also turns out to be necessary in describing the space of conformal blocks in the supersymmetric case to include certain odd traces on modules alongside traces and supertraces we prove that the set of supertrace functions thus supplemented spans a finite dimensional sl 2 mathbb z invariant space we close the paper with several examples

design of low order linear phase iir filters via orthogonal projection this paper presents an indirect linear phase iir filter design technique based on a reduction of linear phase fir filters the desired filter is obtained by minimizing the l sub 2 norm of the difference between the original fir filter and the lower order iir filter we first establish a relationship between the hankel singular values of the discarded part of the fir filter and the l sub 2 norm of the corresponding filter approximation error based on model truncation this result motivates us to propose a simple finite search method that will achieve better approximation results than commonly used truncation methods such as the balanced truncation bt and the impulse response gramian irg methods we then develop an iterative algorithm for finding an optimal iir filter based on a matrix projection of the original fir filter the convergence of the proposed algorithm is established filters designed using the proposed algorithm are compared with those obtained by other techniques with respect to the amplitude response and group delay characteristics in the passband numerical examples show that the proposed algorithm offers the best performance

methods for computing marginal data densities from the gibbs output abstract we introduce two estimators for estimating the marginal data density mdd from the gibbs output our methods are based on exploiting the analytical tractability condition which requires that some parameter blocks can be analytically integrated out from the conditional posterior densities this condition is satisfied by several widely used time series models an empirical application to six variate var models shows that the bias of a fully computational estimator is sufficiently large to distort the implied model rankings one of the estimators is fast enough to make multiple computations of mdds in densely parameterized models feasible

bayesian analysis of the error correction model this paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model a second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space this prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in bayesian cointegration analysis using this new prior and laplace approximation an estimator for the posterior probability of the rank is given the approach performs well compared with information criteria in monte carlo experiments

finite escapes and convergence properties of guaranteed cost robust filters the design of robust filters for linear time varying systems subject to parameter perturbations is considered the design is based on the minimization of an upper bound for the error covariance the computation of the filter matrices calls for the solution of a pair of differential riccati equations parameterized by a scalar design parameter the main results of the paper concern the asymptotic properties of the filter when it is applied to time invariant systems differently from the standard kalman filter the robust filter may abruptedly cease to exist owing to the presence of finite escape times in the associated riccati equations nevertheless provided that the parameter perturbations do not affect the unstable dynamics convergence to a stable steady state filter can always be ensured by properly adjusting the scalar design parameter since such an adjustment might deteriorate the steady state performance a time varying strategy for the tuning of the scalar parameter is developed in order to guarantee both convergence and performance

robust h sub 2 filtering for uncertain systems with measurable inputs this paper deals with the robust minimum variance filtering problem for linear time varying systems subject to a measurable input and to norm bounded parameter uncertainty in the state and or the output matrices of the state space model the problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty and any input of bounded energy three types of input signals are considered a signal that is a priori known for the whole time interval an unknown signal of very large bandwidth that is perfectly measured on line and a large bandwidth signal that is measured ahead of time in a fixed preview time interval both the time varying finite horizon and stationary infinite horizon cases are treated

h sub infinity minimum error state estimation of linear stationary processes a state estimator is derived which minimizes the h sub infinity norm of the estimation error power spectrum matrix two approaches are presented the first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution the second approach establishes a duality between the problem of h sub infinity filtering and the problem of unconstrained input h sub infinity optimal regulation using this duality previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding kalman filter the two approaches usually lead to different results they are compared by a simple example which also demonstrates a clear advantage of the h sub infinity estimate over the conventional l sub 2 estimate

monstrous moonshine and monstrous lie superalgebras we prove conway and norton s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by frenkel lepowsky and meurman to do this we use the no ghost theorem from string theory to construct a family of generalized kac moody superalgebras of rank 2 which are closely related to the monster and several of the other sporadic simple groups the denominator formulas of these superalgebras imply relations between the thompson functions of elements of the monster i e the traces of elements of the monster on frenkel lepowsky and meurman s representation which are the replication formulas conjectured by conway and norton these replication formulas are strong enough to verify that the thompson functions have most of the moonshine properties conjectured by conway and norton and in particular they are modular functions of genus 0 we also construct a second family of kac moody superalgebras related to elements of conway s sporadic simple group col these superalgebras have even rank between 2 and 26 for example two of the lie algebras we get have ranks 26 and 18 and one of the superalgebras has rank 10 the denominator formulas of these algebras give some new infinite product identities in the same way that the denominator formulas of the a n n e kac moody algebras give the macdonald identities

robust kalman filtering for continuous time lag systems the linear continuous time kalman filter for a class of time lag systems with norm bounded uncertain parameters is considered we investigate the conditions for linear delayless state estimator such that the estimation error covariance is guaranteed to lie within a prescribed bound for all admissible uncertainties it is proven that a robust kalman filter algorithm can be determined in terms of two riccati equations involving scalar parameters the developed theory is illustrated by numerical simulation

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

robust kalman filtering for uncertain systems abstract this paper studies the problem of kalman filter design for uncertain systems the system under consideration is subjected to time varying norm bounded parameter uncertainties in both the state and measurement matrices the problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties a riccati equation approach is proposed to solve the above problem furthermore a suboptimal covariance upper bound can be computed by a convex optimization

robust filter design with time varying parameter uncertainty and error variance constraints in this paper we consider the design of robust filters for linear continuous and discrete time systems subjected to timevarying parameter uncertainties and estimation error variance constraints the problem addressed is the design of robust filters which do not depend on uncertainty such that for all admissible time varying parameter perturbations the variance of the estimation error of each state is guaranteed to be not more than the individual prespecified upper bound in both continuous and discrete time cases it is shown that the computation of the filter matrices calls for the solution of a pair of algebraic riccati equations specifically the existence conditions and the explicit expression of the desired filters are obtained furthermore two illustrative examples are presented to demonstrate the effectiveness of the proposed design procedure

technical communique robust h observer design of linear state delayed systems with parametric uncertainty the discrete time case in this note we consider the problem of h observer design for a class of uncertain linear discrete time systems with delayed state and parameter uncertainties the goal of this problem is to design a linear state observer such that for the positive integer state time delay and all admissible norm bounded parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint the observer structure does not depend on the parameter uncertainties a simple effective algebraic methodology is developed to derive the conditions for the existence of the desired robust h observers and the analytical expression of these observers is then characterized in terms of the matrix riccati like equations inequalities we provide a numerical example to demonstrate the validity and the applicability of the proposed approach

generalized high dimensional trace regression via nuclear norm regularization abstract we study the generalized trace regression with a near low rank regression coefficient matrix which extends notion of sparsity for regression coefficient vectors specifically given a matrix covariate x the probability density function of the response y is f y x c y exp 1 y b where tr t x this model accommodates various types of responses and embraces many important problem setups such as reduced rank regression matrix regression that accommodates a panel of regressors matrix completion among others we estimate through minimizing empirical negative log likelihood plus nuclear norm penalty we first establish a general theory and then for each specific problem we derive explicitly the statistical rate of the proposed estimator they all match the minimax rates in the linear trace regression up to logarithmic factors numerical studies confirm the rates we established and demonstrate the advantage of generalized trace regression over linear trace regression when the response is dichotomous we also show the benefit of incorporating nuclear norm regularization in dynamic stock return prediction and in image classification

optimal linear filtering under parameter uncertainty this paper addresses the problem of designing a guaranteed minimum error variance robust filter for convex bounded parameter uncertainty in the state output and input matrices the design procedure is valid for linear filters that are obtained from the minimization of an upper bound of the error variance holding for all admissible parameter uncertainty the results provided generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured assuming the order of the uncertain system is known the optimal robust linear filter is proved to be of the same order as the order of the system in the present case of convex bounded parameter uncertainty the basic numerical design tools are linear matrix inequality lmi solvers instead of the riccati equation solvers used for the design of robust filters available in the literature to date the paper that contains the most important and very recent results on robust filtering is used for comparison purposes in particular it is shown that under the same assumptions our results are generally better as far as the minimization of a guaranteed error variance is considered some numerical examples illustrate the theoretical results

structural analysis with multivariate autoregressive index models we address the issue of parameter dimensionality reduction in vector autoregressive models vars for many variables by imposing specific reduced rank restrictions on the coefficient matrices that simplify the vars into multivariate autoregressive index mai models we derive the wold representation implied by the mais and show that it is closely related to that associated with dynamic factor models then the theoretical analysis is extended to the case of general rank restrictions on the var coefficients next we describe classical and bayesian estimation of large mais and discuss methods for rank determination finally the performance of the mais is compared with that of large bayesian vars in the context of monte carlo simulations and two empirical applications on the transmission mechanism of monetary policy and on the propagation of demand and supply shocks

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

modularity of n point functions and theta functions for vertex operator superalgebras abstract the modularity of the n point trace functions and theta functions associated with vertex operator superalgebras are established

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

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

on the almost sure and mean square exponential convergence of some stochastic observers it is pointed out that linear observers used for estimating the state of the discrete time stochastic parameter systems are both almost surely and mean square ms exponentially convergent under the same conditions guaranteeing mean square convergence in addition to the mean square convergence properties of linear observers constructed for mean square stable stochastic parameter systems they also possess an almost sure exponential convergence property and the rate of ms convergence is exponential this rate depends on the parameters used in the design

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

one point theta functions for vertex operator algebras abstract one point theta functions for modules of vertex operator algebras voas are defined and studied these functions are a generalization of the character theta functions studied by miyamoto and are deviations of the classical one point functions for modules of a voa transformation laws with respect to the group sl 2 z are established

robust minimum variance filtering this paper deals with the robust minimum variance filtering problem for linear systems subject to norm bounded parameter uncertainty in both the state and the output matrices of the state space model the problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty two methods for designing robust filters are investigated the first one deals with constant parameter uncertainty and focuses on the design of steady state filters that yield an upper bound to the worst case asymptotic error variance this bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system and it can be made tighter if a tight bound on the latter power spectrum can be obtained the second method allows for time varying parameter uncertainty and for general time varying systems and is more systematic we develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems

robustness of exponential stability of stochastic differential delay equations regard the stochastic differential delay equation dx t a a t b b t spl tau x t spl tau dt g t x t x t spl tau dw t as the result of the effects of uncertainty stochastic perturbation and time lag to a linear ordinary differential equation x spl dot t a b x t assume the linear system is exponentially stable in this paper we characterize how much the uncertainty stochastic perturbation and time lag the linear system can bear such that the stochastic delay system remains exponentially stable the result can also be extended to nonlinear systems

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

efficient parametrisations for normal linear mixed models summary the generality and easy programmability of modern sampling based methods for maximisation of likelihoods and summarisation of posterior distributions have led to a tremendous increase in the complexity and dimensionality of the statistical models used in practice however these methods can often be extremely slow to converge due to high correlations between or weak identifiability of certain model parameters we present simple hierarchical centring reparametrisations that often give improved convergence for a broad class of normal linear mixed models in particular we study the two stage hierarchical normal linear model the laird ware model for longitudinal data and a general structure for hierarchically nested linear models using analytical arguments simulation studies and an example involving clinical markers of acquired immune deficiency syndrome aids we indicate when reparametrisation is likely to provide substantial gains in efficiency

robust h sub 2 h sub spl infin state estimation for systems with error variance constraints the continuous time case the paper is concerned with the state estimator design problem for perturbed linear continuous time systems with h sub spl infin norm and variance constraints the perturbation is assumed to be time invariant and norm bounded and enters into both the state and measurement matrices the problem we address is to design a linear state estimator such that for all admissible measurable perturbations the variance of the estimation error of each state is not more than the individual prespecified value and the transfer function from disturbances to error state outputs satisfies the prespecified h sub spl infin norm upper bound constraint simultaneously existence conditions of the desired estimators are derived in terms of riccati type matrix inequalities and the analytical expression of these estimators is also presented a numerical example is provided to show the directness and effectiveness of the proposed design approach

robust filtering for a class of stochastic uncertain nonlinear time delay systems via exponential state estimation we investigate the robust filter design problem for a class of nonlinear time delay stochastic systems the system under study involves stochastics unknown state time delay parameter uncertainties and unknown nonlinear disturbances which are all often encountered in practice and the sources of instability the aim of this problem is to design a linear delayless uncertainty independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances the dynamics of the estimation error is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are proposed to guarantee the existence of desired robust exponential filters which are derived in terms of the solutions to algebraic riccati inequalities the developed theory is illustrated by numerical simulation