sufficient conditions for the asymptotic stability of interval matrices jiang 1987 gave a sufficient condition for the asymptotic stability of interval matrices we shall show here that his results can be derived in a trivial way using the lyapunov equation an extension of his results and a similar result for discrete systems is stated

between and within cluster covariate effects in the analysis of clustered data standard methods for the regression analysis of clustered data postulate models relating covariates to the response without regard to between and within cluster covariate effects implicit in these analyses is the assumption that these effects are identical example data show that this is frequently not the case and that analyses that ignore differential between and within cluster covariate effects can be misleading consideration of between and within cluster effects also helps to explain observed and theoretical differences between mixture model analyses and those based on conditional likelihood methods in particular we show that conditional likelihood methods estimate purely within cluster covariate effects whereas mixture model approaches estimate a weighted average of between and within cluster covariate effects

some new results on unsymmetric successive overrelaxation method the unsymmetric successive overrelaxation ussor iterative method is applied to the solution of the system of linear equationsa x b wherea is annxn nonsingular matrix we find the values of the relaxation parameters and bar omega for which the ussor iterative method converges then we characterize those matrices which are equimodular toa and for which the ussor iterative method converges

application of gee procedures for sample size calculations in repeated measures experiments derivation of the minimum sample size is an important consideration in an applied research effort when the outcome is measured at a single time point sample size procedures are well known and widely applied the corresponding situation for longitudinal designs however is less well developed in this paper we adapt the generalized estimating equation gee approach of liang and zeger to sample size calculations for discrete and continuous outcome variables the non central version of the wald 2 test is considered we use the damped exponential family of correlation structures described in munoz et al for the working correlation matrix among the repeated measures we present a table of minimum sample sizes for binary outcomes and discuss extensions that account for unequal allocation staggered entry and loss to follow up 1998 john wiley sons ltd

within subject variation in bold fmri signal changes across repeated measurements quantification and implications for sample size functional magnetic resonance imaging fmri can be used to detect experimental effects on brain activity across measurements the success of such studies depends on the size of the experimental effect the reliability of the measurements and the number of subjects here we report on the stability of fmri measurements and provide sample size estimations needed for repeated measurement studies stability was quantified in terms of the within subject standard deviation w of bold signal changes across measurements in contrast to correlation measures of stability this statistic does not depend on the between subjects variance in the sampled group sample sizes required for repeated measurements of the same subjects were calculated using this w ten healthy subjects performed a motor task on three occasions separated by one week while being scanned in order to exclude training effects on fmri stability all subjects were trained extensively on the task task performance spatial activation pattern and group wise bold signal changes were highly stable over sessions in contrast we found substantial fluctuations up to half the size of the group mean activation level in individual activation levels both in rois and in voxels given this large degree of instability over sessions and the fact that the amount of within subject variation plays a crucial role in determining the success of an fmri study with repeated measurements improving stability is essential in order to guide future studies sample sizes are provided for a range of experimental effects and levels of stability obtaining estimates of these latter two variables is essential for selecting an appropriate number of subjects

gaussian particle filtering sequential bayesian estimation for nonlinear dynamic state space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations this paper introduces a new filter called the gaussian particle filter it is based on the particle filtering concept and it approximates the posterior distributions by single gaussians similar to gaussian filters like the extended kalman filter and its variants it is shown that under the gaussianity assumption the gaussian particle filter is asymptotically optimal in the number of particles and hence has much improved performance and versatility over other gaussian filters especially when nontrivial nonlinearities are present simulation results are presented to demonstrate the versatility and improved performance of the gaussian particle filter over conventional gaussian filters and the lower complexity than known particle filters

on the convergence of the symmetric sor method for matrices with red black ordering we prove that if the matrixa has the structure which results from the so called red black ordering and ifa is anh matrix then the symmetric sor method called the ssor method is convergent for 0 2 in the special case thata is even anm matrix we show that the symmetric single step method cannot be accelerated by the ssor method symmetry of the matrixa is not assumed

why small low powered studies are worse than large high powered studies and how to protect against trivial findings in research comment on friston 2012 it is sometimes argued that small studies provide better evidence for reported effects because they are less likely to report findings with small and trivial effect sizes friston 2012 but larger studies are actually better at protecting against inferences from trivial effect sizes if researchers just make use of effect sizes and confidence intervals poor statistical power also comes at a cost of inflated proportion of false positive findings less power to confirm true effects and bias in reported inflated effect sizes small studies n 16 lack the precision to reliably distinguish small and medium to large effect sizes r 50 from random noise 05 that larger studies n 100 does with high level of confidence r 50 p 00000012 the present paper presents the arguments needed for researchers to refute the claim that small low powered studies have a higher degree of scientific evidence than large high powered studies

a sufficient condition for the stability of interval matrix polynomials the root location of sets of scalar polynomials whose coefficients are confined to intervals and the associated extension to eigenvalues of sets of constant matrices whose coefficients are contained in intervals are reviewed a central result for complex scalar interval polynomials is a theorem developed by v l kharatonov 1978 which states that each member of a set of such polynomials is stable if and only if eight special polynomials from the set are stable the case of interval matrix polynomials is examined and a kharitonov like result for their strong stability is provided this in turn yields a sufficient condition for stability of a set of interval matrix polynomials

on power and sample size calculations for likelihood ratio tests in generalized linear models summary a direct extension of the approach described in self mauritsen and ohara 1992 biometrics 48 31 39 for power and sample size calculations in generalized linear models is presented the major feature of the proposed approach is that the modification accommodates both a finite and an infinite number of covariate configurations furthermore for the approximation of the noncentrality of the noncentral chi square distribution for the likelihood ratio statistic a simplification is provided that not only reduces substantial computation but also maintains the accuracy simulation studies are conducted to assess the accuracy for various model configurations and covariate distributions

a parametric family of correlation structures for the analysis of longitudinal data in epidemiological settings we are often faced with numerous short time series and a parsimonious parametrization of the correlation structure is desired in order to optimize the efficiency of the estimation procedure we propose a damped exponential correlation structure for modeling multivariate gaussian outcomes the correlation between two observations separated by s units of time is modeled as gamma s theta where gamma is the correlation between elements separated by one s unit and theta is a damping parameter for theta 0 theta 1 and theta infinity the correlation structures of compound symmetry first order autoregressive and first order moving average processes are obtained although the ar 2 dependency structure and the combination of random effects and ar 1 errors are not special cases of the proposed parametric family these structures can be well approximated within the family for short time series maximum likelihood methods for parameter estimation and interpretations of intermediate models 0 less than theta less than 1 are discussed in the context of modeling pulmonary function in an adult population in the netherlands and t cell subsets in homosexual men infected with human immunodeficiency virus type i

planning group sizes in clinical trials with a continuous outcome and repeated measures simple formulae have been derived for the accurate computation of sample sizes when the two sample t test is used required sample sizes may be reduced by taking repeated measures especially if correlations are about equal in a trial with two parallel groups repeated measures may be summarized by a pre treatment mean and a post treatment mean in a cross over trial measures may be repeated within each treatment period in case the difference between two independent groups increases in time individual slopes may be used if the correlation between two measures hardly depends on distance in time between these measures however it may be more efficient to use only the first and last measure in the statistical test if correlations strongly depend on time distance

simulation study of power and sample size for repeated measures with multinomial outcomes an application to sound direction identification experiments sdie this study focuses on sample size determination in repeated measures studies with multinomial outcomes from multiple factors in settings where multiple factors have repeated measures a single subject could have hundreds of observations sample size selection may then refer to the number of subjects the number of levels within a factor or the number of repetitions within the level we simulate multinomial data through a generalized linear mixed model glmm with and without overdispersion compute the empirical power of detecting group difference for several analytical methods and contrast their performance in group comparison studies with repeated multinomial data we use four spatial functions to model the spatial correlation structures among observations we evaluate the factors affecting the power under various scenarios we also present a dataset typical in hearing studies for sound localization in which a spatially distributed array of audio loudspeakers plays multiple sounds in order to compare two programming schemes for a hearing aid device

different approaches for state filtering in nonlinear systems with uncertain observations this paper addresses the least squares filtering problem for nonlinear systems with uncertain observations when random interruptions in the observation process are modelled by a sequence of independent bernoulli random variables we propose four filtering algorithms which are based on different approximations of the first and second order statistics of a nonlinear transformation of random vectors perturbed by additive and multiplicative noises these algorithms generalize the extended and unscented kalman filters to the case in which there is a positive probability that the observation in each time consists of noise alone and hence does not contain the signal to be estimated the accuracy of the different approximations is also analyzed and the performance of the proposed algorithms is compared in a numerical simulation example

robust kalman filtering for discrete time varying uncertain systems with multiplicative noises in this paper a robust finite horizon kalman filter is designed for discrete time varying uncertain systems with both additive and multiplicative noises the system under consideration is subject to both deterministic and stochastic uncertainties sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete riccati difference equations a numerical example is given to show the applicability of the presented method

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

least squares νth order polynomial estimation of signals from observations affected by non independent uncertainty abstract the least squares th order polynomial filtering and fixed point smoothing problems of uncertainly observed discrete time signals are considered when the variables describing the uncertainty in the observations are non independent by defining suitable augmented signal and observation vectors the polynomial estimation problem of the signal is reduced to the linear estimation problem of the augmented signal the proposed estimators do not require the knowledge of the state space model generating the signal but only the probability that the signal exists in the observations the 2 2 element of the conditional probability matrices of the sequence describing the uncertainty and the moments up to the 2 th ones of the signal and the observation noise

power and sample size calculations for longitudinal studies comparing rates of change with a time varying exposure existing study design formulas for longitudinal studies have assumed that the exposure is time invariant we derived sample size formulas for studies comparing rates of change by exposure when the exposure varies with time within a subject focusing on observational studies where this variation is not controlled by the investigator two scenarios are considered one assuming that the effect of exposure on the response is acute and the other assuming that it is cumulative we show that accurate calculations can often be obtained by providing the intraclass correlation of exposure and the exposure prevalence at each time point when comparing rates of change studies with a time varying exposure are in general less efficient than studies with a time invariant one we provide a public access program to perform the calculations described in the paper http www hsph harvard edu faculty spiegelman optitxs html copyright 2009 john wiley sons ltd

power for studies with random group sizes in any study it is essential to select the sample size carefully to ensure adequate power for many studies this is simple recruit a desired number of subjects within each group conduct measurements and perform the statistical test in some studies e g observational studies however the group membership is unknown at recruitment in this paper we examine the effect of random group sizes on power additionally we consider the situation when the group proportions are unknown and specified by a prior distribution the problem that initially motivated this research is presented power for a 2 by 2 table as are examples using continuous outcomes we find that standard estimates of power using expected group sizes can over or underestimate power sas macros are available at http www phs wfubmc edu public wambrosi randompower

on the convergence of the unsymmetric successive overrelaxation ussor method abstract given a linear system with an h matrix a splitting of varga s type is considered and a convergence theorem for the unsymmetric successive overrelaxation ussor method is obtained our results extend the known area of the convergence

necessary and sufficient conditions for componentwise stability of interval matrix systems in the asymptotic stability as analysis of interval matrix systems some results are available that operate only as sufficient conditions based on a unique test matrix adequately built from the interval matrix our note reveals the complete role of this test matrix for fully characterizing the componentwise asymptotic stability cwas of interval matrix systems cwas is a special type of as which ensures the flow invariance of certain time dependent sets with respect to the state space trajectories hence the sufficient conditions for as get a new and deeper meaning by their reformulation as necessary and sufficient conditions with respect to the stronger property of cwas

an evolution strategy method for computing eigenvalue bounds of interval matrices in this paper a modified method by means of an evolution strategy es is introduced for computing eigenvalue bounds of interval matrices then a sufficient condition theorem of the evolutionary strategy is presented which guarantees the convergence in probability of the method the numerical examples show the method can effectively yield accurate bounds for interval eigenvalues

nonlinear inexact uzawa algorithms for linear and nonlinear saddle point problems this paper proposes some nonlinear uzawa methods for solving linear and nonlinear saddle point problems a nonlinear inexact uzawa algorithm is first introduced for linear saddle point problems two different pcg techniques are allowed in the inner and outer iterations of the algorithm this algorithm is then extended for a class of nonlinear saddle point problems arising from some convex optimization problems with linear constraints for this extension some pcg method used in the inner iteration needs to be carefully constructed so that it converges in a certain energy norm instead of the usual l 2 norm it is shown that the new algorithm converges under some practical conditions and there is no need for any a priori estimates on the minimal and maximal eigenvalues of the two local preconditioned systems involved the two new methods perform more efficiently than the existing methods in the cases where no good preconditioners are available for the schur complements

linearly divergent treatment effects in clinical trials with repeated measures efficient analysis using summary statistics in many randomized clinical trials with repeated measures of a response variable one anticipates a linear divergence over time in the difference between treatments this paper explores how to make an efficient choice of analysis based on individual patient summary statistics with the objective of estimating the mean rate of treatment divergence the simplest choice of summary statistic is the regression coefficient of response on time for each subject slope the gains in statistical efficiency imposed by adjusting for the observed pre treatment levels or even better the estimated intercepts are clarified in the process we develop the optimal linear summary statistic for any repeated measures design with assumed known covariance structure and shape of true mean treatment difference over time statistical power considerations are explored and an example from an asthma trial is used to illustrate the main points

optimal combination of number of participants and number of repeated measurements in longitudinal studies with time varying exposure in the context of observational longitudinal studies we explored the values of the number of participants and the number of repeated measurements that maximize the power to detect the hypothesized effect given the total cost of the study we considered two different models one that assumes a transient effect of exposure and one that assumes a cumulative effect results were derived for a continuous response variable whose covariance structure was assumed to be damped exponential and a binary time varying exposure under certain assumptions we derived simple formulas for the approximate solution to the problem in the particular case in which the response covariance structure is assumed to be compound symmetry results showed the importance of the exposure intraclass correlation in determining the optimal combination of the number of participants and the number of repeated measurements and therefore the optimized power thus incorrectly assuming a time invariant exposure leads to inefficient designs we also analyzed the sensitivity of results to dropout mis specification of the response correlation structure allowing a time varying exposure prevalence and potential confounding impact we illustrated some of these results in a real study in addition we provide software to perform all the calculations required to explore the combination of the number of participants and the number of repeated measurements

sample size calculations based on slopes and other summary statistics sample size calculations based on two sample comparisons of slopes have been reported by many this paper extends such discussions to include summary statistics other than slopes such as post baseline means change scores and final observations specifically sample size formulas for analyses based on a broad class of summary statistics are presented with modifications proposed to allow for missing data caused by staggered entry and random dropouts the formulas developed are used to illustrate how required sample size is affected by summary statistic choice variance parameters the type of treatment difference of interest and the manner in which incomplete observations are used in the analysis an example based on longitudinal data from the muscatine study is presented

estimating intraclass correlation for binary data summary this paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study some of the estimators are very specific while others result from general methods such as pseudo likelihood and extended quasi likelihood estimation the simulation study identifies several useful estimators one of which does not seem to have been considered previously for binary data estimators based on extended quasi likelihood are found to have a substantial bias in some circumstances

formulae and tables for the determination of sample sizes and power in clinical trials for testing differences in proportions for the two sample design a review this paper is a compendium of exact and asymptotic formulae and tables for estimating the sample size in a clinical trial with two treatment groups and a dichotomous outcome the paper provides separate formulae for equal and unequal treatment group sizes formulae for the calculation of power given the sample size and complete references for all formulae and tables cited

on the application of a hybrid ellipsoidal rectangular interval arithmetic algorithm to interval kalman filtering for state estimation of uncertain systems modelling uncertainty is a key limitation to the applicability of the classical kalman filter for state estimation of dynamic systems for such systems with bounded modelling uncertainty the interval kalman filter ikf is a direct extension of the former to interval systems however its usage is not yet widespread owing to the over conservatism of interval arithmetic bounds in this paper the ikf equations are adapted to use an ellipsoidal arithmetic that in some cases provides tighter bounds than direct rectangular interval arithmetic in order for the ikf to be useful it must be able to provide reasonable enclosures under all circumstances to this end a hybrid ellipsoidal rectangular enclosure algorithm is proposed and its robustness is evidenced by its application to two characteristically different systems for which it provides stable estimate bounds whereas the rectangular and ellipsoidal approaches fail to accomplish this in either one or the other case

linear estimation for discrete time systems in the presence of time correlated disturbances and uncertain observations this note considers optimum linear recursive estimation for linear discrete time systems with uncertain observations in cases where state and measurement noises are correlated the different kinds of estimation problems treated include one stage prediction and filtering

some new results on the convergence of the ssor and ussor methods we obtain conditions for the convergence of ssor and ussor methods when the matrix a has a special form so called red black ordering using some vectorial norms we give characterizations for the h matrix with respect to the ussor iteration matrix our results extend the work of alefeld and krishna

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

accounting for variability in sample size estimation with applications to nonadherence and estimation of variance and effect size we consider sample size calculations for testing differences in means between two samples and allowing for different variances in the two groups typically the power functions depend on the sample size and a set of parameters assumed known and the sample size needed to obtain a prespecified power is calculated here we account for two sources of variability we allow the sample size in the power function to be a stochastic variable and we consider estimating the parameters from preliminary data an example of the first source of variability is nonadherence noncompliance we assume that the proportion of subjects who will adhere to their treatment regimen is not known before the study but that the proportion is a stochastic variable with a known distribution under this assumption we develop simple closed form sample size calculations based on asymptotic normality the second source of variability is in parameter estimates that are estimated from prior data for example we account for variability in estimating the variance of the normal response from existing data which are assumed to have the same variance as the study for which we are calculating the sample size we show that we can account for the variability of the variance estimate by simply using a slightly larger nominal power in the usual sample size calculation which we call the calibrated power we show that the calculation of the calibrated power depends only on the sample size of the existing data and we give a table of calibrated power by sample size further we consider the calculation of the sample size in the rarer situation where we account for the variability in estimating the standardized effect size from some existing data this latter situation as well as several of the previous ones is motivated by sample size calculations for a phase ii trial of a malaria vaccine candidate

power analyses for longitudinal trials and other clustered designs summary existing methods for power and sample size estimation for longitudinal and other clustered study designs have limited applications in this paper we review and extend existing approaches to improve these limitations in particular we focus on power analysis for the two most popular approaches for clustered

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

polynomial extended kalman filter this work presents a polynomial version of the well known extended kalman filter ekf for the state estimation of nonlinear discrete time stochastic systems the proposed filter denoted polynomial ekf pekf consists in the application of the optimal polynomial filter of a chosen degree spl mu to the carleman approximation of a nonlinear system when spl mu 1 the pekf algorithm coincides with the standard ekf for the filter implementation the moments of the state and output noises up to order 2 spl mu are required numerical simulations compare the performances of the pekf with those of some other existing filters showing significant improvements

analysis of the inexact uzawa algorithm for saddle point problems in this paper we consider the so called inexact uzawa algorithm for iteratively solving linear block saddle point problems such saddle point problems arise for example in finite element and finite difference discretizations of stokes equations the equations of elasticity and mixed finite element discretization of second order problems we consider both the linear and nonlinear variants of the inexact uzawa iteration we show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left hand block in the case of nonlinear iteration the inexact uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left hand block is of sufficient accuracy bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear uzawa algorithm applications to the stokes equations and mixed finite element discretization of second order elliptic problems are discussed and finally the results of numerical experiments involving the algorithms are presented

linear convergence and metric selection for douglas rachford splitting and admm recently several convergence rate results for douglas rachford splitting and the alternating direction method of multipliers admm have been presented in the literature in this paper we show global linear convergence rate bounds for douglas rachford splitting and admm under strong convexity and smoothness assumptions we further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters for problems that satisfy the assumptions we show how to select step size and metric for the algorithm that optimize the derived convergence rate bounds for problems with a similar structure that do not satisfy the assumptions we present heuristic step size and metric selection methods

a monotone skew splitting model for composite monotone inclusions in duality the principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew adjoint operator an algorithmic framework is developed for solving this generic problem in a hilbert space setting new primal dual splitting algorithms are derived from this framework for inclusions involving composite monotone operators and convergence results are established these algorithms draw their simplicity and efficacy from the fact that they operate in a fully decomposed fashion in the sense that the monotone operators and the linear transformations involved are activated separately at each iteration comparisons with existing methods are made and applications to composite variational problems are demonstrated

higher order sigma point filter a new heuristic for nonlinear time series filtering in this paper we present some new results related to the higher order sigma point filter hospof introduced in 1 for filtering nonlinear multivariate time series this paper makes two distinct contributions firstly we propose a new algorithm to generate a discrete statistical distribution to match exactly a specified mean vector a specified covariance matrix the average of specified marginal skewness and the average of specified marginal kurtosis both the sigma points and the probability weights are given in closed form and no numerical optimization is required combined with hospof this random sigma point generation algorithm provides a new method for generating proposal density which propagates the information about higher order moments a numerical example on nonlinear multivariate time series involving real financial market data demonstrates the utility of this new algorithm secondly we show that hospof achieves a higher order estimation accuracy as compared to ukf for smooth scalar nonlinearities we believe that this new filter provides a new and powerful alternative heuristic to existing filtering algorithms and is useful especially in econometrics and in engineering applications

an interval kalman filtering with minimal conservatism abstract the interval kalman filtering ikf can handle parametric interval uncertainties of the system matrices and it computes the lower and upper boundaries of the estimated states in this paper we propose an alternative form of interval kalman filtering to reduce the conservatism inherent to the existing interval kalman filtering first we address why the existing interval kalman filtering scheme induces conservatism in the boundary estimation then to remove the conservatism we derive noise covariance matrices taking into account of interval uncertainties as well as process and measurement noises following the typical derivation process of the standard kalman filtering a new recursive form of interval kalman filtering is derived through numerical simulations the superiority of the new algorithm over existing ikf is illustrated

new estimates for multilevel algorithms including the v cycle the purpose of this paper is to provide new estimates for certain multilevel algorithms in particular we are concerned with the simple additive multilevel algorithm discussed recently together with j xu and the standard v cycle algorithm with one smoothing step per grid we shall prove that these algorithms have a uniform reduction per iteration independent of the mesh sizes and number of levels even on nonconvex domains which do not provide full elliptic regularity for example the theory applies to the standard multigrid vcycle on the l shaped domain or a domain with a crack and yields a uniform convergence rate we also prove uniform convergence rates for the multigrid v cycle for problems with nonuniformly refined meshes finally we give a new multigrid approach for problems on domains with curved boundaries and prove a uniform rate of convergence for the corresponding multigrid v cycle algorithms

sample sizes for clinical trials with normal data this article gives an overview of sample size calculations for parallel group and cross over studies with normal data sample size derivation is given for trials where the objective is to demonstrate superiority equivalence non inferiority bioequivalence and estimation to a given precision for different types i and ii errors it is demonstrated how the different trial objectives influence the null and alternative hypotheses of the trials and how these hypotheses influence the calculations sample size tables for the different types of trials and worked examples are given copyright 2004 john wiley sons ltd

sample size estimation for gee method for comparing slopes in repeated measurements data sample size calculation is an important component at the design stage of clinical trials controlled clinical trials often use a repeated measurement design in which individuals are randomly assigned to treatment groups and followed up for measurements at intervals across a treatment period of fixed duration in studies with repeated measurements one of the popular primary interests is the comparison of the rates of change in a response variable between groups statistical models for calculating sample sizes for repeated measurement designs often fail to take into account the impact of missing data correctly in this paper we propose to use the generalized estimating equation gee method in comparing the rates of change in repeated measurements and introduce closed form formulae for sample size and power that can be calculated using a scientific calculator since the sample size formula is based on asymptotic theory we investigate the performance of the estimated sample size in practical settings through simulations

ordered group reference priors with application to the multinomial problem summary noninformative priors are developed using the reference prior approach for multiparameter problems in which there may be parameters of interest and nuisance parameters for a given grouping of parameters and ordering of the groups intuitively according to inferential importance an algorithm for determining the associated reference prior is presented the algorithm is illustrated on the multinomial problem with discussion of the variety and success of various groupings and ordering strategies

a general statistical analysis for fmri data we propose a method for the statistical analysis of fmri data that seeks a compromise between efficiency generality validity simplicity and execution speed the main differences between this analysis and previous ones are a simple bias reduction and regularization for voxel wise autoregressive model parameters the combination of effects and their estimated standard deviations across different runs sessions subjects via a hierarchical random effects analysis using the em algorithm overcoming the problem of a small number of runs session subjects using a regularized variance ratio to increase the degrees of freedom

an algorithm to determine linear independence of a set of interval vectors this paper presents an algorithm to determine the linear dependence and independence of a set of interval vectors the algorithm is developed on the basis of a necessary and sufficient condition for linear independence of an arbitrary interval vector relative to other linearly independent interval vectors the necessary and sufficient condition can be checked by a linear programming method then the developed necessary and sufficient condition will be employed to check the linear independence of a set of interval vectors through numerical examples the validity of the developed algorithm is illustrated

preconditioned douglas rachford splitting methods for convex concave saddle point problems we propose a preconditioned version of the douglas rachford splitting method for solving convex concave saddle point problems associated with fenchel rockafellar duality our approach makes it possible to use approximate solvers for the linear subproblem arising in this context we prove weak convergence in hilbert space under minimal assumptions in particular various efficient preconditioners are introduced in this framework for which only a few inner iterations are needed instead of computing an exact solution or controlling the error the method is applied to a discrete total variation denoising problem numerical experiments show that the proposed algorithms with appropriate preconditioners are very competitive with existing fast algorithms including the first order primal dual algorithm for saddle point problems of chambolle and pock

sufficient condition for the asymptotic stability of interval matrices the stability of interval matrices has been studied by bialas 1983 but bialas s main theorem on the stability of interval matrices has been shown to be false by barmish 1984 a new sufficient condition for the asymptotic stability of interval matrices is given in the present paper

exact distributions of intraclass correlation and cronbach s alpha with gaussian data and general covariance intraclass correlation and cronbach s alpha are widely used to describe reliability of tests and measurements even with gaussian data exact distributions are known only for compound symmetric covariance equal variances and equal correlations recently large sample gaussian approximations were derived for the distribution functions new exact results allow calculating the exact distribution function and other properties of intraclass correlation and cronbach s alpha for gaussian data with any covariance pattern not just compound symmetry probabilities are computed in terms of the distribution function of a weighted sum of independent chi square random variables newf approximations for the distribution functions of intraclass correlation and cronbach s alpha are much simpler and faster to compute than the exact forms assuming the covariance matrix is known the approximations typically provide sufficient accuracy even with as few as ten observations either the exact or approximate distributions may be used to create confidence intervals around an estimate of reliability monte carlo simulations led to a number of conclusions correctly assuming that the covariance matrix is compound symmetric leads to accurate confidence intervals as was expected from previously known results however assuming and estimating a general covariance matrix produces somewhat optimistically narrow confidence intervals with 10 observations increasing sample size to 100 gives essentially unbiased coverage incorrectly assuming compound symmetry leads to pessimistically large confidence intervals with pessimism increasing with sample size in contrast incorrectly assuming general covariance introduces only a modest optimistic bias in small samples hence the new methods seem preferable for creating confidence intervals except when compound symmetry definitely holds

an error bound for the ssor and ussor methods abstract we consider the ssor and ussor methods in order to approximate the solution of the linear system ax b we establish a bound for the norm of e n x x n in terms of the norms of n x n x n 1 n 1 and their inner product where x n is the n th iteration vector obtained using the ussor method similar results are given for the ssor method

chandrasekhar type filter for a wide sense stationary signal from uncertain observations using covariance information in this paper the least mean squared error linear filtering problem of a wide sense stationary signal from uncertain observations perturbed by a white noise is approached by means of a chandrasekhar type recursive algorithm in comparison with a riccati type algorithm the proposed algorithm is more advantageous from a computational point of view since it reduces the number of difference equations contained in it and consequently the computation time the algorithm is derived by using covariance information without requiring that the state space model of the signal is completely known

sample size for logistic regression with small response probability abstract the fisher information matrix for the estimated parameters in a multiple logistic regression can be approximated by the augmented hessian matrix of the moment generating function for the covariates the approximation is valid when the probability of response is small with its use one can obtain a simple closed form estimate of the asymptotic covariance matrix of the maximum likelihood parameter estimates and thus approximate sample sizes needed to test hypotheses about the parameters the method is developed for selected distributions of a single covariate and for a class of exponential type distributions of several covariates it is illustrated with an example concerning risk factors for coronary heart disease