on the finite escape phenomena for matrix riccati equations we show a necessary and sufficient condition for the solution of riccati differential equations to escape to the infinity in finite time this implies that we obtain a necessary and sufficient condition for the existence of the solution of all time t geq 0 this condition is given as a rank condition of the matrix which we refer to as the escape criterion matrix this matrix consists of the equation matrices and an equilibrium point of riccati differential equation

brief paper root mean square gains of switched linear systems a variational approach we consider the problem of computing the root mean square rms gain of switched linear systems we develop a new approach which is based on an attempt to characterize the worst case switching law wcsl that is the switching law that yields the maximal possible gain our main result provides a sufficient condition guaranteeing that the wcsl can be characterized explicitly using the differential riccati equations dres corresponding to the linear subsystems this condition automatically holds for first order siso systems so we obtain a complete solution to the rms gain problem in this case

solution of the h sub infinity optimal linear filtering problem for discrete time systems the solution of l sub 2 minimum variance and h sub infinity estimation problems is considered using a polynomial systems approach the results for the l sub 2 filtering problem which corresponds with wiener or kalman filtering prediction are first presented in polynomial matrix form attention then turns to the solution of the h sub infinity estimation problem for scalar systems numerous examples are presented to illustrate the computational procedures the two types of estimator are appropriate to very different estimation problems and the new h sub infinity devices should be valuable in certain application areas

a general framework for updating belief distributions we propose a framework for general bayesian inference we argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function which is recovered as a special case modern application areas make it increasingly challenging for bayesians to attempt to model the true data generating mechanism for instance when the object of interest is low dimensional such as a mean or median it is cumbersome to have to achieve this via a complete model for the whole data distribution more importantly there are settings where the parameter of interest does not directly index a family of density functions and thus the bayesian approach to learning about such parameters is currently regarded as problematic our framework uses loss functions to connect information in the data to functionals of interest the updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions importantly the procedure coincides with bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings connections to other inference frameworks are highlighted

thermodynamic versus statistical nonequivalence of ensembles for the mean field blume emery griffiths model abstract we illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean field blume emery griffiths beg model as a test model the novel characterization takes effect at the level of the microcanonical and canonical equilibrium distributions of states for this reason it may be viewed as a statistical characterization of nonequivalent ensembles which extends and complements the common thermodynamic characterization of nonequivalent ensembles based on nonconcave anomalies of the microcanonical entropy by computing numerically both the microcanonical and canonical sets of equilibrium distributions of states of the beg model we show that for values of the mean energy where the microcanonical entropy is nonconcave the microcanonical distributions of states are nowhere realized in the canonical ensemble moreover we show that for values of the mean energy where the microcanonical entropy is strictly concave the equilibrium microcanonical distributions of states can be put in one to one correspondence with equivalent canonical equilibrium distributions of states our numerical computations illustrate general results relating thermodynamic and statistical equivalence and nonequivalence of ensembles proved by ellis et al j stat phys 101 2000 999

a simple and exploratory way to determine the mean variance relationship in generalized linear models this paper introduces an exploratory way to determine how variance relates to the mean in generalized linear models this novel method employs the robust likelihood technique introduced by royall and tsou a urinary data set collected by ginsberg et al and the fabric data set analysed by lee and nelder are considered to demonstrate the applicability and simplicity of the proposed technique application of the proposed method could easily reveal a mean variance relationship that would generally be left unnoticed or that would require more complex modelling to detect copyright 2006 john wiley sons ltd

complete analysis of phase transitions and ensemble equivalence for the curie weiss potts model using the theory of large deviations we analyze the phase transition structure of the curie weiss potts spin model which is a mean field approximation to the nearest neighbor potts model it is equivalent to the potts model on the complete graph on n vertices the analysis is carried out both for the canonical ensemble and the microcanonical ensemble besides giving explicit formulas for the microcanonical entropy and for the equilibrium macrostates with respect to the two ensembles we analyze ensemble equivalence and nonequivalence at the level of equilibrium macrostates relating these to concavity and support properties of the microcanonical entropy the curie weiss potts model is the first statistical mechanical model for which such a detailed and rigorous analysis has been carried out

regression analysis of overdispersed correlated count data with subject specific covariates a robust likelihood approach for the analysis of overdispersed correlated count data that takes into account cluster varying covariates is proposed we emphasise two characteristics of the proposed method that the correlation structure satisfies the constraints on the second moments and that the estimation of the correlation structure guarantees consistent estimates of the regression coefficients in addition we extend the mean specification to include within and between cluster effects the method is illustrated through the analysis of data from two studies in the first study cross sectional count data from a randomised controlled trial are analysed to evaluate the efficacy of a communication skills training programme the second study involves longitudinal count data which represent counts of damaged hand joints in patients with psoriatic arthritis motivated by this study we generalize our model to accommodate for a subpopulation of patients who are not susceptible to the development of damaged hand joints

objective priors for the bivariate normal model summary objective bayesian inference for the multivariate normal distribution is illustrated using dieren t types of formal objective priors jereys invariant reference and matching dieren t modes of inference bayesian and frequentist and dieren t criteria involved in selecting optimal objective priors ease of computation frequentist performance marginalization paradoxes and decision theoretic evaluation in the course of the investigation of the bivariate normal model in berger and sun 2006 a variety of surprising results were found including the availability of objective priors that yield exact frequentist inferences for many functions of the bivariate normal parameters such as the correlation coecien t certain of these results are generalized to the multivariate normal situation the prior that most frequently yields exact frequentist inference is the righthaar prior which unfortunately is not unique two natural proposals are studied for dealing with this non uniqueness rst mixing over the right haar priors second choosing the empirical bayes right haar prior that which maximizes the marginal likelihood of the data quite surprisingly we show that neither of these possibilities yields a good solution this is disturbing and sobering it is yet another indication that improper priors do not behave as do proper priors and that it can be dangerous to apply understandings from the world of proper priors to the world of improper priors

on asymptotic normality of limiting density functions with bayesian implications walker 1969 presented a straightforward approach to asymptotic normality of posterior distributions based on independent and identically distributed i i d observations dawid 1970 extended this work by providing a weaker set of conditions to cover some distributions whose ranges depend on the parameters of interest more recently heyde and johnstone 1979 simplified walker s conditions for stochastic processes in this paper we introduce three basic normality conditions for limiting density functions in the bayesian context our approach is data determined and is nonprobabilistic in nature nevertheless the results thus obtained can be easily converted to probabilistic ones when compared with those given by other investigators it is shown that our conditions as a whole have a greater generality and flexibility than those previously assumed either by dawid or heyde and johnstone in particular for the i i d case the commonly assumed wald type uniform boundedness condition for tail behaviours is shown to be unnecessary for asymptotic normality section 3 3 the advantage of our approach is further exemplified by a simple proof of the asymptotic normality of distributions conjugate to the exponential family

the theory of large deviations from boltzmann s 1877 calculation to equilibrium macrostates in 2d turbulence abstract after presenting some basic ideas in the theory of large deviations this paper applies the theory to a number of problems in statistical mechanics these include deriving the form of the gibbs state for a discrete ideal gas describing probabilistically the phase transition in the curie weiss model of a ferromagnet and deriving variational formulas that describe the equilibrium macrostates in models of two dimensional turbulence a general approach to the large deviation analysis of models in statistical mechanics is also formulated

empirical null and false discovery rate analysis in neuroimaging current strategies for thresholding statistical parametric maps in neuroimaging include control of the family wise error rate control of the false discovery rate fdr and thresholding of the posterior probability of a voxel being active given the data the latter derived from a mixture model of active and inactive voxels correct inference using any of these criteria depends crucially on the specification of the null distribution of the test statistics in this article we show examples from fmri and dti data where the theoretical null distribution does not match well the observed distribution of the test statistics as a solution we introduce the use of an empirical null a null distribution empirically estimated from the data itself allowing for global corrections of theoretical null assumptions the theoretical null distributions considered are normal t chi 2 and f all commonly encountered in neuroimaging the empirical null estimate is accompanied by an estimate of the proportion of non active voxels in the data based on the two class mixture model we present the equivalence between the strategies of controlling fdr and thresholding posterior probabilities in the context of neuroimaging and show that the fdr estimates derived from the empirical null can be seen as empirical bayes estimates

optimum performance levels for minimax filters predictors and smoothers abstract for both discrete and continuous time linear time varying systems we obtain the achievable performance levels for minimax filters predictors and smoothers in terms of the finite escape times of some related discrete and continuous time riccati equations our game theoretic approach also yields an alternative derivation for the corresponding minimax estimators which were first obtained in 1 they are all bayes estimators with respect to particular gaussian distributions and admit recursive structures

interpolation approach to h estimation and its interconnection to loop transfer recovery abstract this paper proposes to solve the h optimal estimation problem via interpolation theory the advantages of this approach are the following i direct and simple solutions can be obtained for the optimal estimators ii frequency weightings on estimation error and disturbance can be easily incorporated and iii unnecessary high observer gains can be avoided we also show the interconnection between the h optimal estimation problem and the optimal loop transfer recovery problem the interpolation approach applies to both continuous time and discrete time systems

a geometric dynamical approach to thermodynamics we present a geometric and dynamical approach to the micro canonical ensemble of classical hamiltonian systems we generalize the arguments in rugh 1997 phys rev lett 78 772 4 and show that the energy derivative of a micro canonical average is itself micro canonically observable in particular temperature specific heat and higher order derivatives of the entropy can be observed dynamically we give perturbative asymptotic formulae by which the canonical ensemble itself can be reconstructed from micro canonical measurements only using our geometrical tools we rederive formulae by lebowitz et al and pearson et al relating for example specific heat to fluctuations in the kinetic energy we show that under natural assumptions on the fluctuations in the kinetic energy the micro canonical temperature is asymptotically equivalent to the standard canonical definition using the kinetic energy

h sub spl infin differential riccati equations convergence properties and finite escape phenomena the paper studies the transient and asymptotic behavior of the solution of the sign indefinite differential riccati equation dre arising in finite horizon h sub spl infin filtering and control problems differently from the sign definite h sub spl infin dre the solution of the h sub spl infin dre can have finite escape times even for nonnegative initial conditions sufficient and necessary conditions for boundedness and convergence are derived in correspondence to a fixed value of the h sub spl infin norm attenuation level spl gamma finally a stepwise spl gamma switching strategy is devised to guarantee boundedness as well as asymptotic performance

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

a robust adjustment of the profile likelihood under mild misspecifications of model assumptions maximum likelihood estimates often remain consistent and asymptotically normal asymptotic normality will often hold for the signed root of the likelihood ratio statistic and the score statistic as well however standard estimates of asymptotic variance are usually inconsistent this occurs when bartlett s second identity fails in the manner of mccullagh and tibshirani a variance correction may be used to adjust the profile likelihood so this identity obtains the resulting likelihood yields the robust versions of the signed root wald and score statistic suggested by kent and royall assuming model correctness asymptotic expansions for the first three cumulants of each robust statistic are derived it is seen that bias and skewness are not severely affected by using a robust statistic an invariant expression derived for the asymptotic relative efficiency of a robust method allows assessment in numerous examples considered even for moderately large sample sizes losses in efficiency are significant making the misuse of a robust variance estimate potentially costly computer algebra is used in many of the calculations reported in this paper

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

a structure preserving algorithm for the minimum h norm computation of finite time state feedback control problem the algorithm being developed here is based on the generating function approach for finite time h control and application of canonical transformation of linear hamiltonian system first an equivalent finite time h control law in terms of the third type generating function is derived then by using symplectic structure of the hamiltonian system s state transition matrix a group of matrix recursive formulae are deduced for the evaluation of the finite time h control law combining with a matrix singularity testing procedure this recursive algorithm verifies the existence condition of sub optimal h controllers and gives the minimum h norm of finite time control systems inherited from the canonical transformation the matrix recursive formulae have a standard symplectic form this structure preserving property helps facilitate reliable and effective computation numerical results show the effectiveness of the proposed algorithm

inference for clustered data using the independence loglikelihood we use the properties of independence estimating equations to adjust the independence loglikelihood function in the presence of clustering the proposed adjustment relies on the robust sandwich estimator of the parameter covariance matrix which is easily calculated the methodology competes favourably with established techniques based on independence estimating equations we provide some insight as to why this is so the adjustment is applied to examples relating to the modelling of wind speed in europe and annual maximum temperatures in the u k

on the existence of solutions of the riccati differential equation abstract we generalize a technique given in c martin 1 to obtain a characterization of finite escape times for time varying riccati equations which also apply to the non definite case

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

a simple method for the adjustment of profile likelihoods summary we propose a simple adjustment for profile likelihoods the aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods such as bias inconsistency and overoptimistic variance estimates the adjustment is applied to the profile loglikelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function for cases in which explicit calculation of the adjustments is difficult we give two methods to simplify their computation an automatic simulation method that requires as input only the profile loglikelihood and its first few derivatives first order asymptotic expressions some examples are provided and a comparison is made with the conditional profile log likelihood of cox and reid

local model uncertainty and incomplete data bias with discussion problems of the analysis of data with incomplete observations are all too familiar in statistics they are doubly difficult if we are also uncertain about the choice of model we propose a general formulation for the discussion of such problems and develop approximations to the resulting bias of maximum likelihood estimates on the assumption that model departures are small loss of efficiency in parameter estimation due to incompleteness in the data has a dual interpretation the increase in variance when an assumed model is correct the bias in estimation when the model is incorrect examples include non ignorable missing data hidden confounders in observational studies and publication bias in meta analysis doubling variances before calculating confidence intervals or test statistics is suggested as a crude way of addressing the possibility of undetectably small departures from the model the problem of assessing the risk of lung cancer from passive smoking is used as a motivating example

phase portrait of the matrix riccati equation the matrix riccati equation which arises from optimal control and filtering problems is a quadratic differential equation on the space of real symmetric n times n matrices it is closely related via compactification of the phase space to the differential equations on the grassmann manifold and the lagrange grassmann manifold whose flows are generated by the action of one parameter subgroups of the general linear group and of the symplectic group respectively we determine the complete phase portraits of the riccati equations on all three spaces the asymptotic behavior of every solution is described the phase portraits are characterized topologically as well as set theoretically although the riccati equation is not generally a morse smale vector field we are able to show that it possesses suitable generalizations of many of the important properties of morse smale vector fields in particular the riccati equation satisfies a generalized version of the morse inequalities for a morse smale dynamica

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

posterior probability maps and spms this technical note describes the construction of posterior probability maps that enable conditional or bayesian inferences about regionally specific effects in neuroimaging posterior probability maps are images of the probability or confidence that an activation exceeds some specified threshold given the data posterior probability maps ppms represent a complementary alternative to statistical parametric maps spms that are used to make classical inferences however a key problem in bayesian inference is the specification of appropriate priors this problem can be finessed using empirical bayes in which prior variances are estimated from the data under some simple assumptions about their form empirical bayes requires a hierarchical observation model in which higher levels can be regarded as providing prior constraints on lower levels in neuroimaging observations of the same effect over voxels provide a natural two level hierarchy that enables an empirical bayesian approach in this note we present a brief motivation and the operational details of a simple empirical bayesian method for computing posterior probability maps we then compare bayesian and classical inference through the equivalent ppms and spms testing for the same effect in the same data

on the probability of observing misleading statistical evidence abstract the law of likelihood explains how to interpret statistical data as evidence specifically it gives to the discipline of statistics a precise and objective measure of the strength of statistical evidence supporting one probability distribution vis a vis another that measure is the likelihood ratio but evidence even when properly interpreted can be misleading observations can truly constitute strong evidence supporting one distribution when the other is true what makes statistical evidence valuable to science is that this cannot occur very often here we examine two bounds on the probability of observing strong misleading evidence one is a universal bound applicable to every pair of probability distributions the other bound much smaller applies to all pairs of distributions within fixed dimensional parametric models in large samples the second bound comes from examining how the probability of strong misleading evidence varies as a function of the alternative value of the parameter we

multiplicity adjustments in testing for bioequivalence bioequivalence of two drugs is usually demonstrated by rejecting two one sided null hypotheses using the two one sided tests for pharmacokinetic parameters area under the concentration time curve auc and maximum concentration cmax by virtue of the intersection union test there is no need for multiplicity adjustment in testing the two one sided null hypotheses within each parameter however the decision rule for bioequivalence often requires equivalence to be achieved simultaneously on both parameters that contain four one sided null hypotheses together without adjusting for multiplicity the family wise error rate fwer could fail to be controlled at the nominal type i error rate the multiplicity issue for bioequivalence in this regard is scarcely discussed in the literature to address this issue we propose two approaches including a closed test procedure that controls fwer for the simultaneous auc and cmax bioequivalence and requires no adjustment of the type i error and an alpha adaptive sequential testing aast that controls fwer by pre specifying the significance level on auc 1 and obtaining it for cmax 2 adaptively after testing of auc while both methods control fwer the closed test requires testing of eight intersection null hypotheses each at and aast is at times accomplished through a slight deduction in 1 and no deduction in 2 relative to the latter considers equivalence reached in auc a higher importance than that in cmax illustrated with published data the two approaches although operate differently can lead to the same substantive conclusion and are better than a traditional method like bonferroni adjustment copyright 2014 john wiley sons ltd

auxiliary signal design for robust multimodel identification under the assumption that one of two given linear models is the real underlying model of the system a proper auxiliary signal is defined as an input signal that allows the selection of the correct model under the assumption that model noises have bounded energy the separability index is defined as the inverse of the energy of the proper auxiliary signal of least energy a method for the computation of this index and the construction of the auxiliary signal is presented finally an efficient procedure for online identification called the hyperplane test is developed

a robust effect size index effect size indices are useful tools in study design and reporting because they are unitless measures of association strength that do not depend on sample size existing effect size indices are developed for particular parametric models or population parameters here we propose a robust effect size index based on m estimators this approach yields an index that is very generalizable because it is unitless across a wide range of models we demonstrate that the new index is a function of cohen s d formula see text and standardized log odds ratio when each of the parametric models is correctly specified we show that existing effect size estimators are biased when the parametric models are incorrect e g under unknown heteroskedasticity we provide simple formulas to compute power and sample size and use simulations to assess the bias and standard error of the effect size estimator in finite samples because the new index is invariant across models it has the potential to make communication and comprehension of effect size uniform across the behavioral sciences

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

parametric robust inferences for correlated ordinal data the aim of this article is to provide asymptotically valid likelihood inferences about regression parameters for correlated ordinal response variables the legitimacy of this novel approach requires no knowledge of the underlying joint distributions so long as their second moments exist the efficacy of the proposed parametric approach is demonstrated via simulations and the analyses of two real data sets

on global existence of solutions to coupled matrix riccati equations in closed loop nash games presents comparison and global existence results for solutions of coupled matrix riccati differential equations appearing in closed loop nash games and in mixed h sub 2 h sub spl infin type problems convergence of solutions is established for the diagonal case solutions of the corresponding algebraic equations are discussed using numerical examples

assigning a value to a power likelihood in a general bayesian model summarybayesian robustness under model misspecification is a current area of active research among recent ideas is that of raising the likelihood function to a power in this paper we discuss the choice of appropriate power and provide examples

large deviation techniques applied to systems with long range interactions we discuss a method to solve models with long range interactions in the microcanonical and canonical ensemble the method closely follows the one introduced by r s ellis physica d 133 106 1999 which uses large deviation techniques we show how it can be adapted to obtain the solution of a large class of simple models which can show ensemble inequivalence the model hamiltonian can have both discrete ising potts and continuous hmf free electron laser state variables this latter extension gives access to the comparison with dynamics and to the study of non equilibrium effects we treat both infinite range and slowly decreasing interactions and in particular we present the solution of the ising model in one dimension with 0 1

finite horizon h sup infinity control problems with terminal penalties the standard h sup infinity control problem is generalized to the finite horizon case with two possibly singular terminal penalties at the initial and final times the major objective of the generalization is to increase flexibility of h sup infinity controls transients in the finite horizon and the terminal penalties are taken into account within the framework of h sup infinity control problems a complete solution a necessary and sufficient condition and a parameterization to the finite horizon h sup infinity control problem are given the solution is a natural extension of the riccati equation solution in the special case when all the terminal penalties vanish the solution is reduced to the existing one and to the finite horizon standard h sup infinity control problem this approach to the problem is based on completing the square argument of a particular quadratic form which is at least technically different from the previous ones

tests for 2 x k contingency tables with clustered ordered categorical data ordered categorical data summarized in a 2 x k table usually consist of two sample multinomial or k sample binomial observations in analysing these data we usually assign scores to the k columns and perform a testing for the equality of two multinomial distributions in the former case and no trend among k binomial proportions in the latter case among the most popular score tests are the wilcoxon rank sum test and the armitage s linear trend test in this paper we extend the score tests to be used for clustered data under diverse study designs our methods do not require correct specification of the dependence structure within clusters the proposed tests are based on the asymptotic normality for large number of clusters and are a generalization of the standard tests used for independent data simulation studies are conducted to investigate the finite sample performance of the new methods the proposed methods are applied to real life data

inference of bioequivalence for log normal distributed data with unspecified variances two drugs are bioequivalent if the ratio of a pharmacokinetic pk parameter of two products falls within equivalence margins the distribution of pk parameters is often assumed to be log normal therefore bioequivalence be is usually assessed on the difference of logarithmically transformed pk parameters in the presence of unspecified variances test procedures such as two one sided tests tost use sample estimates for those variances bayesian models integrate them out in the posterior distribution these methods limit our knowledge on the extent that inference about be is affected by the variability of pk parameters in this paper we propose a likelihood approach that retains the unspecified variances in the model and partitions the entire likelihood function into two components f statistic function for variances and t statistic function for demonstrated with published real life data the proposed method not only produces results that are same as tost and comparable with bayesian method but also helps identify ranges of variances which could make the determination of be more achievable our findings manifest the advantages of the proposed method in making inference about the extent that be is affected by the unspecified variances which cannot be accomplished either by tost or bayesian method

symmetric explicit numerical integrator for molecular dynamics equations of motion with a generalized friction a general mathematical scheme to construct symmetric explicit numerical integrators of newtonian equations of motion endowed with a generalized friction is provided for a molecular dynamics md study the exact integrations are done for all the decomposed vector fields including the one that contains the friction term on the basis of the symmetric composition scheme with the adjoint for the resulting maps integrators with any local order of accuracy can be systematically constructed among them the second order p2s1 integrator gives the least evaluation of atomic force and potential which are most time consuming in md simulations as examples of the friction function three functional types are considered constant laurent polynomial and exponential with respect to the kinetic energy several md equations of motion fall into these categories and the numerical examinations of their integrators using model systems give positive results on the accuracy and efficiency the extended phase space scheme also presents an invariant function which allows us to easily detect numerical errors in the integration process by monitoring the function value

marginal modelling of multivariate categorical data this paper describes likelihood methods of analysis for multivariate categorical data the joint distribution is specified in terms of marginal mean functions and pairwise and higher order association measures for the association the emphasis is on global odds ratios the method allows flexible formulation of a broad class of designs such as repeated measurements longitudinal studies interrater agreement and cross over trials the proposed model can be used for parameter estimation and hypothesis testing simple fitting algorithms are proposed the method is illustrated using a data example

h filtering for linear periodic systems with parameter uncertainty abstract this paper focuses on h filtering for a class of linear periodic systems with a certain type of norm bounded time varying parameter uncertainty which appears in both the state and output matrices the problem addressed is the design of a linear periodic estimator that guarantees both the quadratic stability and and prescribed h performance on infinite horizon for the estimation error for all admissible parameter uncertainties a solution to this problem is obtained via a riccati equation approach

finite horizon h filter and its 2n algorithm a 2n algorithm will double a time or space step in each evaluation for initial value problem the 2n algorithm for the integration of filtering differential equation of the finite horizon h filter is presented in this paper since it is a boundary value problem within a time range a new 2n algorithm is introduced by merging two intervals each time so that the time interval is doubled in each evaluation if one divides the original time range into one million intervals 20 evaluations will complete the whole process owing to the extremely small initial time interval the first few terms of the taylor expansion of the interval matrices are sufficient for very accurate results since the filter gain matrices are the solution of the riccati differential equation and the existence of the solution depends on the induced norm the computation of critical value is reviewed first then according to the result and the prespecified performance index the suitable parameter 2 can be selected and the precise numerical solution of the riccati differential equation and the filtering differential equation can be obtained by using the 2n algorithm although the filtering equation is time varying the 2n algorithm for interval merging is given explicitly copyright 2001 john wiley sons ltd

microcanonical solution of the mean field φ 4 model comparison with time averages at finite size abstract we study the mean field 4 model in an external magnetic field in the microcanonical ensemble using two different methods the first one is based on rugh s microcanonical formalism and leads to express macroscopic observables such as temperature specific heat magnetization and susceptibility as time averages of convenient functions of the phase space the approach is applicable for any finite number of particles n the second method uses large deviation techniques and allows us to derive explicit expressions for microcanonical entropy and for macroscopic observables in the n limit assuming ergodicity we evaluate time averages in molecular dynamics simulations and using rugh s approach we determine the value of macroscopic observables at finite n these averages are affected by a slow time evolution often observed in systems with long range interactions we then show how the finite n time averages of macroscopic observables converge to their corresponding n values as n is increased as expected finite size effects scale as n 1

cal h _ infty and dwell time specifications of continuous time switched linear systems this technical note deals with continuous time switched linear systems and addresses the problem of characterizing open loop switching strategies based on dwell time specifications assuring a pre specified root mean square gain rms as a natural consequence of treating general systems of this particular class in terms of order and number of subsystems only sufficient conditions are worked out however as positive features they are expressed through linear matrix inequalities lmi being thus numerically solvable in polynomial time and allow the treatment of stable switched linear systems which do not admit a common lyapunov function the conservativeness of the proposed design method is evaluated by comparison with other results available in the literature by means of two simple illustrative examples

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

difference and differential riccati equations a note on the convergence to the strong solution the convergence of the solutions of the differential difference riccati equations to the strong solution of the corresponding algebraic riccati equation are is addressed detectability only is required in the analysis and no assumption is made on the eigenvalues on the real imaginary axis on the unit circle in the discrete time case in particular from the results it follows that under the sole assumption of detectability a positive definite initial condition guarantees convergence to the strong solution even in the presence of unreachable eigenvalues on the imaginary axis or on the unit circle

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

towards a unification of second order theory for likelihood and marginal composite likelihood an adjustment for marginal composite likelihoods is derived to match the second order theory of the likelihood when inference is for a vector valued parameter in the absence of nuisance components the adjustment overcomes the failure of bartlett identities for marginal composite likelihoods and leads to a bartlett correctable marginal composite likelihood ratio statistic

a note on robust variance estimation for cluster correlated data there is a simple robust variance estimator for cluster correlated data while this estimator is well known it is poorly documented and its wide range of applicability is often not understood the estimator is widely used in sample survey research but the results in the sample survey literature are not easily applied because of complications due to unequal probability sampling this brief note presents a general proof that the estimator is unbiased for cluster correlated data regardless of the setting the result is not new but a simple and general reference is not readily available the use of the method will benefit from a general explanation of its wide applicability

likelihood for statistically equivalent models in likelihood inference we usually assume that the model is fixed and then base inference on the corresponding likelihood function often however the choice of model is rather arbitrary and there may be other models which fit the data equally well we study robustness of likelihood inference over such statistically equivalent models and suggest a simple envelope likelihood to capture this aspect of model uncertainty robustness depends critically on how we specify the parameter of interest some asymptotic theory is presented illustrated by three examples

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

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

comparing several means of dependent populations of count a parametric robust approach we propose a parametric robust procedure for comparing several means of dependent populations of counts the validity of the proposed method requires no knowledge of the true underlying joint distributions so long as they have finite second moments the efficacy of this novel technique is demonstrated by simulations and the analysis of a data set from the taiwan national health insurance research database our new parametric robust method is also compared with the popular semi parametric generalized estimating equations approach

simultaneous control of error rates in fmri data analysis the key idea of statistical hypothesis testing is to fix and thereby control the type i error false positive rate across samples of any size multiple comparisons inflate the global family wise type i error rate and the traditional solution to maintaining control of the error rate is to increase the local comparison wise type ii error false negative rates however in the analysis of human brain imaging data the number of comparisons is so large that this solution breaks down the local type ii error rate ends up being so large that scientifically meaningful analysis is precluded here we propose a novel solution to this problem allow the type i error rate to converge to zero along with the type ii error rate it works because when the type i error rate per comparison is very small the accumulation or global type i error rate is also small this solution is achieved by employing the likelihood paradigm which uses likelihood ratios to measure the strength of evidence on a voxel by voxel basis in this paper we provide theoretical and empirical justification for a likelihood approach to the analysis of human brain imaging data in addition we present extensive simulations that show the likelihood approach is viable leading to cleaner looking brain maps and operational superiority lower average error rate finally we include a case study on cognitive control related activation in the prefrontal cortex of the human brain

a transfer function approach to the problems of discrete time systems h sub infinity optimal linear control and filtering a solution is derived to the problems of h sub infinity optimal linear state regulation and filtering the solution method for both problems is based on a transfer function approach which applies standard spectral factorization return difference relations are given which are extensions of the relations associated with the linear quadratic problem

statistical evidence for glm regression parameters a robust likelihood approach when a likelihood ratio is used to measure the strength of evidence for one hypothesis over another its reliability i e how often it produces misleading evidence depends on the specification of the working model when the working model happens to be the true or correct model the probability of observing strong misleading evidence is low and controllable but this is not necessarily the case when the working model is misspecified royall and tsou j r stat soc ser b 2003 65 391 404 show how to adjust working models to make them robust to misspecification likelihood ratios derived from their robust adjusted likelihood are just as reliable asymptotically as if the working model were correctly specified in the first place in this paper we apply and extend these ideas to the generalized linear model glm regression setting we provide several illustrations both from simulated data and real data concerning rates of parasitic infection in philippine adolescents show how the required adjustment factor can be obtained from standard statistical software and draw some connections between this approach and the sandwich estimator for robust standard errors of regression parameters this substantially broadens the availability and the viability of likelihood methods for measuring statistical evidence in regression settings copyright 2007 john wiley sons ltd

the mean field φ 4 model entropy analyticity and configuration space topology a large deviation technique is applied to the mean field model phi4 providing an exact expression for the configurational entropy s v m as a function of the potential energy v and the magnetization m although a continuous phase transition occurs at some critical energy vc the entropy is found to be a real analytic function in both arguments and it is only the maximization over m which gives rise to a nonanalyticity in s v supm s v m this mechanism of nonanalyticity generation by maximization over one variable of a real analytic entropy function is restricted to systems with long range interactions and has for continuous phase transitions the generic occurrence of classical critical exponents as an immediate consequence furthermore this mechanism can provide an explanation why contradictory to the so called topological hypothesis the phase transition in the mean field model need not be accompanied by a topology change in the family of constant energy submanifolds

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

receding horizon revisited an easy way to robustly stabilize an ltv system stabilization schemes are often based on infinite horizon optimization of a non singular cost functional for such schemes to make sense in a time varying context a fairly good knowledge of the system parameters at all times is a prerequisite that is a major disadvantage in adaptive implementations when applicable the receding horizon approach overcomes this difficulty as though it relies on general qualitative long term properties such as controllability it requires quantitative knowledge only of temporally local parameter values work done on receding horizon stabilization during the 1970 s focused on lq h2 optimization criteria looking for a stabilization method which carries also the robustness properties of infinite horizon h design we consider here local minimization of the l2 induced i o norm h optimization as the design objective both state and observation based feedback scheme are derived and relations to finite and infinite horizon optimization are discussed

interpreting statistical evidence by using imperfect models robust adjusted likelihood functions summary the strength of statistical evidence is measured by the likelihood ratio two key performance properties of this measure are the probability of observing strong misleading evidence and the probability of observing weak evidence for the likelihood function associated with a parametric statistical model these probabilities have a simple large sample structure when the model is correct here we examine how that structure changes when the model fails this leads to criteria for determining whether a given likelihood function is robust continuing to perform satisfactorily when the model fails and to a simple technique for adjusting both likelihoods and profile likelihoods to make them robust we prove that the expected information in the robust adjusted likelihood cannot exceed the expected information in the likelihood function from a true model we note that the robust adjusted likelihood is asymptotically fully efficient when the working model is correct and we show that in some important examples this efficiency is retained even when the working model fails in such cases the bayes posterior probability distribution based on the adjusted likelihood is robust remaining correct asymptotically even when the model for the observable random variable does not include the true distribution finally we note a link to standard frequentist methodology in large samples the adjusted likelihood functions provide robust likelihood based confidence intervals

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

new conditions for the convergence of h sub spl infin filters and predictors the finite horizon h sub spl infin filtering and prediction problems in the discrete time case admit solutions only if a suitable difference riccati equation is solved by a matrix sequence satisfying feasibility conditions in this work sufficient conditions ensuring the existence of filters and predictors over an arbitrarily long time interval are derived moreover it is shown that under these conditions finite horizon estimators tend to stable stationary ones as the time horizon increases