partial non gaussian state space summary in this paper we suggest the use of simulation techniques to extend the applicability of the usual gaussian state space filtering and smoothing techniques to a class of nongaussian time series models this allows a fully bayesian or maximum likelihood analysis of some interesting models including outlier models discrete markov chain components multiplicative models and stochastic variance models finally we discuss at some length the use of a non gaussian model to seasonally adjust the published money supply figures

state space modelling of time series sampled from continuous processes with pulses summary a non gaussian time series model useful for describing the dynamics of endocrinological data is introduced by using a state space representation this model is applicable even when the data are sparsely sampled in comparison with time lengths of pulses likelihood based methods of inference for the model are developed by fitting the present model to partially observed hormonal time series data we can estimate the locations and heights of the peaks of the pulses as well as their onset times models with different shapes of pulses are considered for a comparison of the goodness of fit

the likelihood for a state space model summary this paper derives an expression for the likelihood for a state space model the expression can be evaluated with the kalman filter initialized at a starting state estimate of zero and associated estimation error covariance matrix of zero adjustment for initial conditions can be made after filtering accordingly initial conditions can be modelled without filtering implications in particular initial conditions can be modelled as diffuse the connection between the diffuse and concentrated likelihood is also displayed

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

dynamic stability of skew plates subjected to aerodynamic and random in plane forces this paper presents an investigation into the dynamic stability of skew plates acted upon simultaneously by an aerodynamic force in the chordwise direction and a random in plane force in the spanwise direction due to this random in plane force the plate may become unstable before the aerodynamic force reaches its critical value in this work the finite element formulation is applied to obtain the discretized system equations the system equations are then partially uncoupled and reduced in size by the modal truncation method finally the unsmoothed and the smoothed versions of the stochastic averaging are used to calculate the system response and the second moment stability criterion is utilized to determine the stability boundary of the system numerical results show that the stability boundary obtained by the smoothed stochastic averaging is less conservative than that obtained by the unsmoothed version and the former is the tangent of the latter at zero spectral density of the random in plane force

stability of skew plates subjected to aerodynamic and in plane forces abstract in this paper an investigation is presented into the stability of skew plates acted upon by both aerodynamic and in plane forces simultaneously the in plane force is assumed to be small in magnitude compared to the aerodynamic force due to this small in plane force the system may become unstable before the aerodynamic force reaches its critical value a finite element formulation is used to obtain the discretized system equations the system equations are then partially uncoupled and reduced in size by the modal truncation method finally the method of multiple scales is used to determine the transition curves of the system the effects of system parameters on the boundaries of the unstable regions are studied numerically

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

a comparison of methods that characterize pulses in a time series there is general recognition that some glands secrete hormones primarily as a series of pulses one can generally classify the proposed methods of pulse identification and characterization as either i criterion based that is they use a criterion such as a test statistic to identify a rise and or fall in hormone level within a moving window or ii model based that is they specify a statistical model for the time varying portion of the signal and estimate its parameters using simulated data we compare and contrast seven criterion based methods and three model based methods the model based methods perform better in estimating the parameters of interest they are most effective with the sampling rate chosen so that there are 3 5 samples taken during the half life of the hormone at higher sampling rates the methods may overidentify pulses false positives and at lower sampling rates they may miss pulses false negatives both of which lead to biased estimates for the parameters of the signal

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

nonparametric spline regression with prior information summary by using prior information about the regression curve we propose new nonparametric regression estimates we incorporate two types of information first we suppose that the regression curve is similar in shape to a family of parametric curves characterized as the solution to a linear differential equation the regression curve is estimated by penalized least squares with the differential operator defining the smoothness penalty we discuss in particular growth and decay curves and take a time transformation to obtain a tractable solution the second type of prior information is linear equality constraints we estimate unknown parameters by generalized cross validation or maximum likelihood and obtain efficient 0 n algorithms to compute the estimate of the regression curve and the cross validation and maximum likelihood criterion functions

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

a state space approach to super optimal h sup infinity control problems a numerically stable algorithm is presented for solving the strengthened or super optimal model matching problem the steps of the algorithm follows closely those given by n j young 1986 except that for each step a reliable implementation using state space models is provided

state space algorithm for the computation of superoptimal matrix interpolating functions a state space algorithm is studied which generates the unique superoptimal nehari extension of a general rational matrix the procedure is to use a set of all pass transformations to sequentially minimize each frequency dependent singular value of the interpolating function in a dimension peeling algorithm these all pass transformations are determined by the maximal schmidt pairs of a sequence of hankel operators the process terminates when the original problem is reduced to one of rank one at this stage all the available degrees of freedom have been exhausted the work is an extension of that by young 1986 and gives a concrete state space implementation of his operator theoretic arguments in addition bounds are given on the minimum achievable values for s1 e sup ersi e j i 1 2 rank g0 and also the mcmillan degree of the final superoptimal extension here si denotes the ith singular value of a frequency dependent matrix and the numbering is taken to be in decrea

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

estimation filtering and smoothing in state space models with incompletely specified initial conditions on definit la vraisemblance pour un modele d espace d etats avec des conditions initiales incompletement specifiees par transformation des donnees pour eliminer la dependance sur des conditions non specifiees on etend cette approche pour obtenir des estimations sur les vecteurs d etat les predicteurs et les interpolateurs pour des observations manquantes

dynamic linear models with switching abstract the problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time varying independent random process we derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process a maximum likelihood estimation procedure is given that uses a pseudo expectation maximization algorithm in the initial stages and nonlinear optimization we relate the models to those considered previously in the literature and give an application involving the tracking of multiple targets

characterization and use of the degrees of freedom in the h problem this paper characterizes the degrees of freedom in the h 1 block problem and subsequently uses these degrees of freedom to obtain desirable properties in the hankel approximation in particular for a special class of transfer function matrices the degrees of freedom can be deployed to obtain station arity of the approximation system gramians which in turn imposes flatness on all of the error system singular values as well as providing completely stable projections in the context of a super optimal algorithm subsequently the class constraints are relaxed in order to generalize the results

stability of viscoelastic plate in supersonic flow under random loading the stability of a viscoelastic plate subjected to a random load in a supersonic flow is investigated the stationary load is assumed in the form of gaussian white noise the relaxation kernel of the plate material is represented by a sum of exponents the influence of such parameters as external damping material viscosity flow speed and probabilistic characteristics of the load on the stability of the plate in mean square form is analyzed nomenclature d bending stiffness of the plate k coefficient of the external and aerodynamic damping width of the plate q uniform external load r relaxation operator r t t relaxation kernel t time u coefficient depending on the flow speed v speed of the flow w transverse deflection of the plate x coordinate 8 thickness of the plate ae lk parameters of the kernel of the relaxation p mass per unit of the plate volume

gramian assignment based on the lyapunov equation a theorem on the assignability of the controllability gramian using state feedback is presented the approach is based on the lyapunov equation specifically it shows that the set of gramian matrices which are assignable using state feedback lies in a vector space and is precisely the intersection of that vector space with the set of positive definite matrices the results show that it may be possible to reshape the structure of the system indirectly by specifying a desired closed loop lyapunov function rather than by directly assigning eigenvalues or eigenvectors

markov chain monte carlo in conditionally gaussian state space models summary a bayesian analysis is given for a state space model with errors that are finite mixtures of normals and with coefficients that can assume a finite number of different values a sequence of indicator variables determines which components the errors belong to and the values of the coefficients the computation is carried out using markov chain monte carlo with the indicator variables generated without conditioning on the states previous approaches use the gibbs sampler to generate the indicator variables conditional on the states in many problems however there is a strong dependence between the indicator variables and the states causing the gibbs sampler to converge unacceptably slowly or even not to converge at all the new sampler is implemented in o n operations where n is the sample size permitting an exact bayesian analysis of problems that previously had no computationally tractable solution we show empirically that the new sampler can be much more efficient than previous approaches and illustrate its applicability to robust nonparametric regression with discontinuities and to a time series change point problem

smoothing spline models for the analysis of nested and crossed samples of curves abstract we introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors generalizing smoothing splines to such samples by associating them with a corresponding mixed effects model the models are also useful for imputation of missing data and exploratory analysis of variance we prove that the best linear unbiased predictors blups from the extended mixed effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components and we show that these solutions are natural cubic splines the model parameters are estimated using a highly efficient implementation of the em algorithm for restricted maximum likelihood reml estimation based on a preliminary eigenvector decomposition variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed effects models our methods are applied to me

stability of fluttered panels subjected to in plane harmonic forces this paper presents an investigation into the stability of a fluttered panel acted on by an in plane harmonic force the in plane force is assumed to be slow varying and small in magnitude compared to the aerodynamic force because of this small harmonic force the system may become stable although the aerodynamic force exceeds its critical value in this work the finite element formulation is applied to obtain the discretized system equations the autonomous terms in the system equations are then uncoupled by transforming these terms into jordan canonical forms finally the method of multiple scales is used to solve for analytical solutions of the system the effects of system parameters on the changes of stability boundaries are studied numerically

a smoothness priors state space modeling of time series with trend and seasonality abstract a smoothness priors modeling of time series with trends and seasonalities is shown an observed time series is decomposed into local polynomial trend seasonal globally stationary autoregressive and observation error components each component is characterized by an unknown variance white noise perturbed difference equation constraint the constraints or bayesian smoothness priors are expressed in state space model form trading day factors are also incorporated in the model a kalman predictor yields the likelihood for the unknown variances hyperparameters likelihoods are computed for different constraint order models in different subsets of constraint equation model classes akaike s minimum aic procedure is used to select the best model fitted to the data within and between the alternative model classes smoothing is achieved by using a fixed interval smoother algorithm examples are shown

the simulation smoother for time series models summary recently suggested procedures for simulating from the posterior density of states given a gaussian state space time series are refined and extended we introduce and study the simulation smoother which draws from the multivariate posterior distribution of the disturbances of the model so avoiding the degeneracies inherent in state samplers the technique is important in gibbs sampling with non gaussian time series models and for performing bayesian analysis of gaussian time series

a signal extraction approach to modeling hormone time series with pulses and a changing baseline abstract hormones serve as regulating signals for many biological processes in recent years it was determined that many hormones are secreted in a pulsatile manner and that the pulsatile secretion pattern in addition to the absolute concentration level is important in regulating biological processes consequently it is necessary to characterize the latent secretion patterns from measurements of concentration levels the characterization is complicated by the presence of a biological circadian rhythm when hormone concentrations are plotted over time the resultant time series usually exhibits occasional short rises superimposed on a slowly changing baseline this is a result of a mixture of pulsatile secretions and a circadian rhythm in this article we present a signal extraction approach to model simultaneously a slowly changing component and a pulsatile component of a time series a smoothing spline is used to model the baseline and a multiprocess dynamic linear model is used to model the pulsati

a non gaussian model for time series with pulses abstract a non gaussian autoregressive like model is presented for time series that exhibit occasional large increases in value termed pulses and exponential decay between pulses the model differs from a first order autoregressive process in its incorporation of feedback between the distribution of the current innovation and the history of the process likelihood based methods of inference for the model are developed and an application to endocrinological data is given