applications of non uniform in time robust global asymptotic output stability to robust partial state feedback stabilization the problem of adding an integrator is considered for time varying control systems sufficient conditions for the solution of this problem are given which are weaker than the corresponding conditions given in the literature to this end the notion of non uniform in time robust global asymptotic output stability rgaos is used applications to problems of partial state feedback global stabilization are considered 2005 elsevier b v all rights reserved

bayes methods for outliers in exponential samples on presente une approche bayesienne a la modelisation des observations aberrantes et on l examine en relation avec les membres de la famille exponentielle en general et avec la distribution exponentielle en particulier

approximate methods for assessing influence and sensitivity in bayesian analysis we use asymptotic approximations to posterior expectations in deriving diagnostics for case influence and prior sensitivity we obtain an easily interpreted expression for the change in posterior expectation following perturbation of the problem which also produces a useful interpretation of the likelihood displacement discussed by cook weisberg in addition we propose two simple diagnostics of posterior nonnormality the leukaemia data analysed by feigl zelen are used to illustrate the diagnostic measures we discuss

local model influence abstract this article develops a general method for assessing the influence of model assumptions in a bayesian analysis we assume that model choices are indexed by a hyperparameter with some given initial choice we use the term model to encompass both the sampling model and the prior distribution we wish to assess the effect of changing the hyperparameter away from the initial choice we are performing a sensitivity analysis with the hyperparameter defining our perturbations we use the kullback leibler divergence to measure the difference between posteriors corresponding to different choices of the hyperparameter we also measure the change in priors if small changes in the priors lead to large changes in posteriors the choice of hyperparameter is influential the second order difference in the kullback leibler divergence is expressed by fisher information matrices the relative change in posteriors compared with priors may be summarized by the relative eigenvalue of the posterior and prior fishe

a converse lyapunov theorem for non uniform in time global exponential robust stability abstract lyapunov like characterizations are established for the concepts of non uniform in time global exponential robust stability and input to state stability for time varying control systems

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

renormalization group operator product expansion and anomalous scaling in models of turbulent advection recent progress on the anomalous scaling in models of turbulent heat and mass transport is reviewed with the emphasis on the approach based on the field theoretic renormalization group rg and operator product expansion ope in that approach the anomalous scaling is established as a consequence of the existence in the corresponding field theoretic models of an infinite number of dangerous composite fields operators with negative critical dimensions which are identified with the anomalous exponents this allows one to calculate the exponents in a systematic perturbation expansion similar to the e expansion in the theory of critical phenomena the rg and ope approach is presented in a self contained way for the example of a passive scalar field temperature concentration of an impurity etc advected by a self similar gaussian velocity ensemble with vanishing correlation time the so called kraichnan s rapid change model where the anomalous exponents are known up to order o e3 effects of anisotropy compressibility and the correlation time of the velocity field are discussed passive advection by non gaussian velocity field governed by the stochastic navier stokes equation and passively advected vector e g magnetic fields are considered

influence measures for logistic regression another point of view summary several measures of influence for logistic regression have been suggested these measures have been developed for the purpose of identifying observations which are influential relative to the estimation of the regression coefficients vector and the deviance we propose measures for detecting influence relative to the determination of probabilities and the classification of future observations the relationships among measures are indicated

scaling structure of the velocity statistics in atmospheric boundary layers the statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model they contain contributions from various two and three dimensional aspects and from the superposition of inhomogeneous and anisotropic contributions we employ the recently introduced decomposition of statistical tensor objects into irreducible representations of the so 3 symmetry group characterized by j and m indices where j5 0 2 j m j to disentangle some of these contributions separating the universal and the asymptotic from the specific aspects of the flow the different j contributions transform differently under rotations and so form a complete basis in which to represent the tensor objects under study the experimental data are recorded with hot wire probes placed at various heights in the atmospheric surface layer time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of different contributions to the second order statistical objects characterized by j 50 1 and 2 the analysis shows the need to make a careful distinction between long lived quasi twodimensional turbulent motions close to the ground and relatively short lived three dimensional motions we demonstrate that the leading scaling exponents in the three leading sectors j50 1 and 2 appear to be different but universal independent of the positions of the probe the tensorial component considered and the large scale properties the measured values of the scaling exponent are z 2 j50 50 6860 01 z 2 j51 51 0 60 15 and z 2 j52 51 3860 10 we present theoretical arguments for the values of these exponents using the clebsch representation of the euler equations neglecting anomalous corrections the values obtained are 2 3 1 and 4 3 respectively some enigmas and questions for the future are sketched

input output to state stability this work explores lyapunov characterizations of the input output to state stability ioss property for nonlinear systems the notion of ioss is a natural generalization of the standard zero detectability property used in the linear case the main contribution of this work is to establish a complete equivalence between the ioss property and the existence of a certain type of smooth lyapunov function as corollaries one shows the existence of norm estimators and obtains characterizations of nonlinear detectability in terms of relative stability and of finite energy estimates

iss property for time varying systems and application to partial static feedback stabilization and asymptotic tracking a concept of input to state stability iss for time varying control systems is introduced that constitutes extension of the well known notion concerning the autonomous case we use this concept to derive sufficient conditions for global stabilization of triangular systems by means of a time varying smooth feedback and to achieve asymptotic tracking of unbounded signals

backstepping design for time varying nonlinear systems with unknown parameters abstract a simple backstepping design procedure is proposed and sufficient conditions for global partial state and dynamic feedback stabilization for a class of triangular systems with unknown time varying parameters are derived

an expected utility approach to influence diagnostics abstract we consider the problem of defining the influence of a set of observations in a parametric modeling framework an expected utility approach motivated by the amount of information to be gained from an experiment is developed with regard to the parameter of interest in some linear model cases simple closed form expressions for our criterion may be found in more complicated settings an adaptive monte carlo integration technique known as the gibbs sampler provides a natural framework for evaluating the influence diagnostic we demonstrate that the influence diagnostic obtained performs well in flagging aberrant subsets of the data exemplified in the cases of a two stage linear model a hierarchical model and a nonlinear michaelis menten model

a characterization of integral input to state stability the notion of input to state stability iss is now recognized as a central concept in nonlinear systems analysis it provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite l sup 2 gains it plays a central role in recursive design coprime factorizations controllers for nonminimum phase systems and many other areas in this paper a newer notion that of integral input to state stability iiss is studied the notion of iiss generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states in that sense generalizing the linear h sup 2 theory it allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance we obtain several necessary and sufficient characterizations of the iiss property expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations

predictive likelihood inference with applications summary conditional and marginal predictive likelihood are defined and used in predicting un observed or missing data a distinction is made between predictive and estimative goals of a data analysis such methodology and distinctions are illustrated in the context of outlier theory and mixed model ano va the prediction of unobserved or missing data is considered from a likelihood perspective a general predictive likelihood is proposed for such purposes and contrasted with parametric likelihood the resulting maximum likelihood predictor is also compared with the limiting imputation from the em algorithm the new methodology is illustrated and contrasted with estimative likelihood analysis in the context of outlier theory and mixed model ano va predictions are proposed that are based on conditional and marginal predictive likelihoods for the unobserved data which are predictive adaptations of the methods developed by kalbfleisch and sprott 1970 1973 these authors were concerned with the elimination of nuisance parameters in order to make inference about another set of structural parameters prediction in the frame work of parametric distributions involves the elimination of all parameters in such a way that inference about the unobserved data is possible therefore in the predictive setting all para meters are nuisance parameters and the unobserved data now play a role similar to that of the structural parameters various predictive approaches to statistical inference have been advocated principally by geisser 1971 1975 stone 1974 aitchison and dunsmore 1975 and guttman 1970 a survey is provided by geisser 1980 and a brief overview in a parametric setting is presented in the next section following this a conditional likelihood approach is developed and shown to be closely related to the lauritzen 1974 hinkley 1979 likelihood method but specified in a manner allowing for a wider range of applicability a marginal predictive likelihood procedure is also specified which when applicable essentially agrees with the conditional likelihood procedure for the examples considered for a general account of likelihood based inference see fraser

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

on zero input stability inheritance for time varying systems with decaying to zero input power abstract stability results for time varying systems with inputs are relatively scarce as opposed to the abundant literature available for time invariant systems this paper extends to time varying systems existing results that ensure that if the input converges to zero in some specific sense then the state trajectory will inherit stability properties from the corresponding zero input system this extension is non trivial in the sense that the proof technique is completely novel and allows to recover the existing results under weaker assumptions in a unifying way

vortices circumfluence symmetry groups and darboux transformations of the 2 1 dimensional euler equation the euler equation ee is one of the basic equations in many physical fields such as fluids plasmas condensed matter astrophysics and oceanic and atmospheric dynamics a symmetry group theorem of the 2 1 dimensional ee is obtained via a simple direct method which is thus utilized to find exact analytical vortex and circumfluence solutions a weak darboux transformation theorem of the 2 1 dimensional ee can be obtained for an arbitrary spectral parameter from the general symmetry group theorem possible applications of the vortex and circumfluence solutions to tropical cyclones especially hurricane katrina 2005 are demonstrated

a characterization of integral iss for switched and time varying systems most of the existing characterizations of the integral input to state stability iiss property are not valid for time varying or switched systems in cases where converse lyapunov theorems for stability are not available this paper provides a characterization that is valid for switched and time varying systems and shows that natural extensions of some of the existing characterizations result in only sufficient but not necessary conditions the results provided also pinpoint suitable iiss gains and relate these to supply functions and bounds on the function defining the system dynamics

approximate marginal densities of nonlinear functions this paper presents an asymptotic approximation for the marginal density of a nonlinear function g 0 that is applicable when the joint density of 0 is dominated by a single mode and the jacobian of g is of full rank near that mode the approximation is based on laplace s method and its asymptotic properties are similar to those of the saddlepoint approximation the approximation is applied to the computation of a marginal posterior density a marginal sampling density and a marginal density based on a multivariate saddlepoint approximation to a joint density

bayesian influence analysis a geometric approach in this paper we develop a general framework of bayesian influence analysis for assessing various perturbation schemes to the data the prior and the sampling distribution for a class of statistical models we introduce a perturbation model to characterize these various perturbation schemes we develop a geometric framework called the bayesian perturbation manifold and use its associated geometric quantities including the metric tensor and geodesic to characterize the intrinsic structure of the perturbation model we develop intrinsic influence measures and local influence measures based on the bayesian perturbation manifold to quantify the effect of various perturbations to statistical models theoretical and numerical examples are examined to highlight the broad spectrum of applications of this local influence method in a formal bayesian analysis

fluctuating hydrodynamics and turbulence in a rotating fluid universal properties we analyze the statistical properties of three dimensional 3d turbulence in a rotating fluid to this end we introduce a generating functional to study the statistical properties of the velocity field mathbit v we obtain the master equation from the navier stokes equation in a rotating frame and thence a set of exact hierarchical equations for the velocity structure functions for arbitrary angular velocity mathbit ensuremath omega in particular we obtain the differential forms for the analogs of the well known von karman howarth relation for 3d fluid turbulence we examine their behavior in the limit of large rotation our results clearly suggest dissimilar statistical behavior and scaling along directions parallel and perpendicular to mathbit ensuremath omega the hierarchical relations yield strong evidence that the nature of the flows for large rotation is not identical to pure two dimensional flows to complement these results by using an effective model in the small ensuremath omega limit within a one loop approximation we show that the equal time correlation of the velocity components parallel to mathbit ensuremath omega displays kolmogorov scaling q ensuremath 5 3 wherein as for all other components the equal time correlators scale as q ensuremath 3 in the inertial range where mathbit q is a wave vector in 3d our results are generally testable in experiments and or direct numerical simulations of the navier stokes equation in a rotating frame

assessing the accuracy of normal approximations abstract the widespread applicability and use of normal approximations creates a need for methods for assessing their accuracy in an operational fashion in this article two new methods are proposed and exemplified these new methods are based on a comparison of the level curves of an exact likelihood with the level curves of the usual normal approximation to it and on a comparison of selected line integrals of an exact density and a normal approximation to it the operational usefulness of these methods is compared with the operational usefulness of two well known existing approaches to assessing the accuracy of approximations namely convergence rates and the curvature methods of bates and watts 1980 as an example the second method is applied to the lee geisser 1972 1975 approximation to the predictive distribution of dental measurements on girls at the ages of 8 10 12 and 14 years in this application the method shows that the 50 central predictive probability region has actual predicti

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

discontinuous control of high order generalized chained systems the stabilization problem for nonlinear systems in a generalized high order chained form is solved by means of discontinuous state feedback control laws the proposed controllers yield exponential convergence of the states to the origin moreover the design does not require the precise knowledge of the system parameters the method is applied to an underactuated surface vessel and a mobile robot moving on an uneven surface and its effectiveness is demonstrated through simulations

a bayesian segmentation methodology for parametric image models region based image segmentation methods require some criterion for determining when to merge regions this paper presents a novel approach by introducing a bayesian probability of homogeneity in a general statistical context the authors approach does not require parameter estimation and is therefore particularly beneficial for cases in which estimation based methods are most prone to error when little information is contained in some of the regions and therefore parameter estimates are unreliable the authors apply this formulation to three distinct parametric model families that have been used in past segmentation schemes implicit polynomial surfaces parametric polynomial surfaces and gaussian markov random fields the authors present results on a variety of real range and intensity images

bayes factors for outlier models using the device of imaginary observations abstract suppose we think that most observations in a sample have been generated from a distribution with density f x but we fear that a few outliers from a distribution with density g x may have contaminated our sample in many situations we might assume that f x is a density depending on a parameter and that g x is of the same form as f but with parameter or a number of bayesian models for this problem when f is normal have been discussed by freeman he points out that with a vague improper prior for contaminating parameters most posterior weight is put on the model allowing for the largest number of outliers he therefore confines attention to proper priors when trying to answer the question of how many outliers however in many situations we do not have very certain information on the contaminating parameters and would like to make inferences about outliers when using improper priors for the parameters of the model in this article we apply the ideas of spiegelhalter and smith to

towards a nonperturbative theory of hydrodynamic turbulence fusion rules exact bridge relations and anomalous viscous scaling functions in this paper we address nonperturbative aspects of the analytic theory of hydrodynamic turbulence of paramount importance for this theory are the fusion rules that describe the asymptotic properties of n point correlation functions when some of the coordinates tend toward one other we first derive here on the basis of two fundamental assumptions a set of fusion rules for correlations of velocity differences when all the separations are in the inertial interval using this set of fusion rules we consider the standard hierarchy of equations relating the n mathrm th order correlations originating from the viscous term in the navier stokes equations to n 1 mathrm th order originating from the nonlinear term and demonstrate that for fully unfused correlations the viscous term is negligible consequently the hierarchic chain of equations is decoupled in the sense that the correlations of n 1 mathrm th order satisfy a homogeneous equation that may exhibit anomalous scaling solutions using the same hierarchy of equations when some separations go to zero we derive on the basis of the navier stokes equations a second set of fusion rules for correlations with differences in the viscous range the latter includes gradient fields we demonstrate that every n mathrm th order correlation function of velocity differences mathcal f n r 1 r 2 dots exhibits its own crossover length ensuremath eta n to dissipative behavior as a function of say r 1 this length depends on n and on the remaining separations r 2 r 3 dots when all these separations are of the same order r this length scales as ensuremath eta n r ensuremath sim ensuremath eta frac r l x n with x n frac ensuremath zeta n ensuremath ensuremath zeta n 1 ensuremath zeta 3 ensuremath ensuremath zeta 2 2 ensuremath ensuremath zeta 2 with ensuremath zeta n being the scaling exponent of the n mathrm th order structure function we derive a class of exact scaling relations bridging the exponents of correlations of gradient fields to the exponents ensuremath zeta n of the n mathrm th order structure functions one of these relations is the well known bridge relation for the scaling exponent of dissipation fluctuations ensuremath mu 2 ensuremath ensuremath zeta 6

local sensitivity of posterior expectations we investigate the degree to which posterior expectations are sensitive to prior distributions using a local method based on functional differentiation invariance considerations suggest a family of norms which can be used to measure perturbations to the prior the sensitivity measure is seen to depend heavily on the choice of norm asymptotic results suggest which norm will yield the most useful results in practice we find that to maintain asymptotically sensible behaviour it is necessary to reduce the richness of the class of prior perturbations as the dimension of the parameter space increases jeffreys prior is characterized as the prior to which inference is least sensitive

forward completeness unboundedness observability and their lyapunov characterizations a finite dimensional continuous time system is forward complete if solutions exist globally for positive time this paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities moreover a version of this fact is also proved for systems with inputs and a generalization is also provided for systems with outputs and a notion unboundedness observability of relative completeness we apply these results to obtain a bound on reachable states in terms of energy like estimates of inputs

a framework for bayesian and likelihood approximations in statistics summary regular bayesian and frequentist approximations in statistics are studied within a unified framework in particular it is shown how some higher order likelihood based approximations arise from their bayesian counterparts via an unsmoothing argument this approach serves to shed new light on these formulae and to clarify relationships between bayesian and frequentist inferences for example bayesian interpretations of higher order approximations can give insights into the acceptability or otherwise of these approximations from the point of view of relevance to the actual data observed furthermore this approach is a very natural one for the study of more general nonregular problems models for dependent data and approximate conditional inference for ease of exposition the development is in terms of a single real parameter the main analytic development proceeds in terms of signed roots of log density ratios

nonuniform in time input to state stability and the small gain theorem for time varying control systems various equivalent characterizations of the nonuniform in time input to state stability iss property are established these characterizations enable us to derive sufficient conditions for nonuniform in time iss concerning composite time varying systems our main result generalizes the well known small gain theorem due to jiang teel praly for autonomous systems under the presence of uniform in time iss

on global uniform asymptotic stability of nonlinear time varying systems in cascade abstract in this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade in particular we give sufficient conditions to guarantee that i a globally uniformly stable gus nonlinear time varying nltv system remains gus when it is perturbed by the output of a globally uniformly asymptotically stable guas nltv system under the assumption that the perturbing signal is absolutely integrable ii if in addition the perturbed system is guas it remains guas under the cascaded interconnection iii two guas systems yield a guas cascaded system under some growth restrictions over the lyapunov function our proofs rely on the second method of lyapunov roughly speaking on a e stability analysis

temporal surrogates of spatial turbulent statistics the taylor hypothesis revisited the taylor hypothesis which allows surrogating spatial measurements requiring many experimental probes by time series from one or two probes is examined on the basis of a simple analytic model of turbulent statistics the main points are as follows i the taylor hypothesis introduces systematic errors in the evaluation of scaling exponents ii when the mean wind v 0 is not infinitely larger than the root mean square longitudinal turbulent fluctuations v mathrm t the effective taylor advection velocity v mathrm ad should take the latter into account iii when two or more probes are employed the application of the taylor hypothesis and the optimal choice of the effective advecting wind v mathrm ad need extra care we present practical considerations for minimizing the errors incurred in experiments using one or two probes iv analysis of the taylor hypothesis when different probes experience different mean winds is offered

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

decision theoretic measures of influence in regression the identification of influential observations is a crucial phase of fitting a model because such observations have a strong impact on inferences or decisions based on the fit an aberrant influential observation should be excluded from the data used to fit the model on the other hand if an influential observation arises from the same model underlying the rest of the data it ought to be included we address the characterization of influence measures justified by the principles of decision theory texts by belsley kuh and welsch 1980 and by cook and weisberg 1982 develop many measures of influence and survey others which have appeared in the literature most measures are motivated in a frequentist perspective but several bayesian measures have also been developed see for example pettit and smith 1985 and johnson and geisser 1982 armed with the ability to compute these measures one can generate reams of computer output when fitting a regression model to even a small data set apart from the discussion in section 4 4 of cook and weisberg 1982 comparing four types of influence diagnostics little has been said about the relative merits of different measures consequently data analysts lack practical guidance in parsimoniously choosing appropriate influence measures when fitting a regression model to data we use a bayesian decision theoretic framework to develop measures of influence in section 2 the regression fitting problem is set up as a formal decision problem complete with action space loss function and a prior distribution for the unknown parameters we then define influence measures in section 3 based on the change in bayes risk resulting from an observation s inclusion in or exclusion from the analysis to express regression fitting as a decision problem it must be simplified perhaps to an unrealistic extent still our study provides insight for defining influence measures in ideal settings an observation s influence will depend on the purpose and context of the regression fitting as characterized by the loss function and the prior distribution two examples are presented for some cases of the loss and prior these measures are equivalent to ones already proposed in the literature and in other cases new measures result

an approach to bayesian sensitivity analysis this paper describes an approach to bayesian sensitivity analysis that uses an influence statistic and an outlier statistic to assess the sensitivity of a model to perturbations the basic outlier statistic is a bayes factor whereas the influence statistic depends strongly on the purpose of the analysis the task of influence analysis is aided by having an interpretable influence statistic two alternative divergences an l 1 distance and a x 2 divergence are proposed and shown to be interpretable the bayes factor and the proposed influence measures are shown to be summaries of the posterior of a perturbation function

influential observations and outliers in regression statistics offered by cook 1977 and andrews and pregibon 1978 purport to reveal influential observations in a regression analysis detailed examination of these statistics shows that two different types of influence are being measured and this is illustrated with examples derived from a set of data given by mickey dunn and clark 1967 recommendations are given for obtaining the best use of the statistics available

a converse lyapunov theorem for nonuniform in time global asymptotic stability and its application to feedback stabilization lyapunov like characterizations for the concepts of nonuniform in time robust global asymptotic stability and input to state stability for time varying systems are established the main result of our work enables us to derive 1 necessary and sufficient conditions for feedback stabilization for affine in the control systems and 2 sufficient conditions for the propagation of the input to state stability property through integrators

anomalous scaling in anisotropic turbulence abstract we present a short review of the work conducted by our group on the subject of anomalous scaling in anisotropic turbulence the basic idea that unifies all the applications discussed here is that the equations of motion for correlation functions are always linear and invariant to rotations and therefore the solutions foliate into sectors of the symmetry group of all rotations so 3 we have considered models of passive scalar and passive vector advections by a rapidly changing turbulent velocity field kraichnan type models for which we find a discrete spectrum of universal anomalous exponents with a different exponent characterizing the scaling behavior in every sector generically the correlation functions and structure functions appear as sums over all these contributions with nonuniversal amplitudes which are determined by the anisotropic boundary conditions in addition we considered navier stokes turbulence by analyzing simulations and experiments and reached some interesting conclusions regarding the scaling exponents in the anisotropic sectors the theory presented here clarifies questions like the restoration of local isotropy upon decreasing scales we explain when the local isotropy is fully restored and when the lingering effects of the anisotropic forcing appear for arbitrarily small scales

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

bayesian repulsive gaussian mixture model we develop a general class of bayesian repulsive gaussian mixture models that encourage well separated clusters aiming at reducing potentially redundant components produced by independent priors f

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

frequentist and bayesian bartlett correction of test statistics based on adjusted profile likelihoods summary for inference about a multidimensional parameter b in the presence of nuisance param

a predictive view of the detection and characterization of influential observations in regression analysis abstract assuming a set of observations is available from the general linear model and assuming prior information about parameters we propose a method of assessing the influence of specified subsets of the data when the goal is to predict future observations

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

the conditional predictive ordinate for the normal distribution summary the conditional predictive ordinate cpo is a bayesian diagnostic which detects surprising observations it has been used in a variety of situations such as univariate samples the multivariate normal distribution and regression models results are presented about the most surprising observation which has minimum cpo for the multivariate normal distribution it is shown that the most surprising observation must lie at one of the vertices of the convex hull it is also shown that the observation with maximum mahalanobis distance from the sample mean must lie on the convex hull results are given for the expected number of vertices on the convex hull when the sample is contaminated an alternative closely related diagnostic the ratio ordinate measure is presented a numerical comparison of the two measures is given

measuring the effect of observations on bayes factors summary in this paper we consider a measure of the effect of single observations on a logarithmic bayes factor defined via the difference in the logarithms of the bayes factors conditional first on all the data and then omitting an observation the measure is related to the conditional predictive ordinate the form of the measure and examples of its use are presented for a variety of situations normal samples linear models log linear models and the checking of distributional assumptions

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

non uniform in time robust global asymptotic output stability abstract the notions of non uniform in time robust global asymptotic output stability and robust forward completeness for time varying systems are introduced necessary and sufficient conditions and lyapunov like characterizations are given for these notions

anomalous scaling of a passive scalar advected by the navier stokes velocity field two loop approximation the field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by a non gaussian velocity field with finite correlation time the velocity is governed by the navier stokes equation subject to an external random stirring force with the correlation function proportional to ensuremath delta t ensuremath t ensuremath k 4 ensuremath d ensuremath 2 ensuremath epsilon it is shown that the scalar field is intermittent already for small ensuremath epsilon its structure functions display anomalous scaling behavior and the corresponding exponents can be systematically calculated as series in ensuremath epsilon the practical calculation is accomplished to order ensuremath epsilon 2 two loop approximation including anisotropic sectors as for the well known kraichnan rapid change model the anomalous scaling results from the existence in the model of composite fields operators with negative scaling dimensions identified with the anomalous exponents thus the mechanism of the origin of anomalous scaling appears similar for the gaussian model with zero correlation time and the non gaussian model with finite correlation time it should be emphasized that in contrast to gaussian velocity ensembles with finite correlation time the model and the perturbation theory discussed here are manifestly galilean covariant the relevance of these results for real passive advection and comparison with the gaussian models and experiments are briefly discussed

curvatures for parameter subsets in nonlinear regression on etend les mesures de nonlinearite proposees par bates et watts 1980 a un sous ensemble arbitraire des parametres dans un modele de regression non lineaire normal

an accurate method for approximate conditional and bayesian inference about linear regression models from censored data summary a method to approximate marginal posterior distribution functions of regression coefficients and scale parameters is presented it is based on a general asymptotic formula of diciccio field fraser 1990 for approximating marginal tail probabilities in developing the method it is shown that the accuracy of the approximation of diciccio et al can be substantially increased in certain cases by using a suitable change of variables and a general approach to deriving such transformations is considered

correlation functions in isotropic and anisotropic turbulence the role of the symmetry group the theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state real turbulent flows exhibit the effects of anisotropic forcing the analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations so 3 in this paper we first consider the needed general theory and explain why we expect different universal scaling exponents in the different sectors of the symmetry group we exemplify the theory context of isotropic turbulence for third order tensorial structure functions and in weakly anisotropic turbulence for the second order structure function the utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high reynolds number measurements of turbulence in the atmosphere