block partitioned solvers for coupled poromechanics a unified framework abstract coupled poromechanical problems appear in a variety of disciplines from reservoir engineering to biomedical applications this work focuses on efficient strategies for solving the matrix systems that result from discretization and linearization of the governing equations these systems have an inherent block structure due to the coupled nature of the mass and momentum balance equations recently several iterative solution schemes have been proposed that exhibit stable and rapid convergence to the coupled solution these schemes appear distinct but a unifying feature is that they exploit the block partitioned nature of the problem to accelerate convergence this paper analyzes several of these schemes and highlights the fundamental connections that underlie their effectiveness we begin by focusing on two specific methods a fully implicit and a sequential implicit scheme in the first approach the system matrix is treated monolithically and a krylov iteration is used to update pressure and displacement unknowns simultaneously to accelerate convergence a preconditioning operator is introduced based on an approximate block factorization of the linear system next we analyze a sequential implicit scheme based on the fixed stress split in this method one iterates back and forth between updating displacement and pressure unknowns separately until convergence to the coupled solution is reached we re interpret this scheme as a block preconditioned richardson iteration and we show that the preconditioning operator is identical to that used within the fully implicit approach rapid convergence in both the richardson and krylov based methods results from a particular choice for a sparse schur complement approximation this analysis leads to a unified framework for developing solution schemes based on approximate block factorizations many classic fully implicit and sequential implicit schemes are simple sub cases the analysis also highlights several new approaches that have not been previously explored for illustration we directly compare the performance and robustness of several variants on a benchmark problem

saddlepoint expansions in finite population problems summary saddlepoint approximations are derived for the sample mean in the case where samples are obtained randomly without replacement from a finite population asymptotic properties are investigated the great accuracy is demonstrated by numerical examples extensions to more general statistics are discussed

saddlepoint approximations for estimating equations summary the saddlepoint method is used to approximate to the distribution of an estimator defined by an estimating equation two different approaches are available one of which is shown to be equivalent to the technique of field hampel 1982 two recent formulae for the tail probability due to lugannani rice 1980 and to robinson 1982 respectively which are uniformly accurate over the whole range of the estimator are compared numerically with the exact results and those computed by field hampel they are found to be of comparable accuracy while avoiding the use of numerical integration the most accurate is that of lugannani rice hampel 1974 introduced a new technique for approximating to the probability density of an estimator defined by an estimating equation it is an example of what he called small sample asymptotics where high accuracy is achieved for quite small sample sizes n even down to single figures in the original version it gave an approximation to the logarithmic derivative of the density function which was integrated numerically to get the density the distribution function was obtained by a second numerical integration which could then be used to renormalize both the density and the distribution function field hampel 1982 develop the technique in detail and compare its performance with that of other approximation methods as hampel had pointed out his approach is closely related to the saddlepoint method of daniels 1954 which was applied to sample means and ratios of means following the private communication referred to by field hampel 1982 p 31 it was realized that the first numerical integration was unnecessary and that hampel s approach could be shortened to give a direct approximation to the density which is in fact a saddlepoint approximation the purpose of the present paper is to extend the use of the saddlepoint method to estimating equations there are two distinct ways of doing this which lead to different approximations of similar accuracy one appears to be more convenient for approxi mating to tail probabilities by numerical integration and was used to compute the saddlepoint approximations quoted in field hampel s tables 1 and 2 the other gives the density directly in a form equivalent to their equation 4 3 which is then integrated

randomization distributions and saddlepoint approximations in generalized linear models various randomization distributions are shown to arise as conditional distributions in the setting of generalized linear models these conditional distributions admit saddlepoint approximations which can obviate the need to simulate the randomization distributions they approximate examples include multinominal and dirichlet bootstraps the jackknife and permutation distributions the double saddlepoint approximation in a regular exponential family is shown to be equivalent to conditional use of a single saddlepoint approximation when the exponential family admits to a cut

on inverting permutation tests abstract polynomial time algorithms are presented for inverting permutation tests the one sample permutation test is inverted to make confidence statements about a location parameter and the two sample permutation test is inverted to make confidence statements concerning a shift in location or scale these algorithms require polynomial time as opposed to complete enumeration algorithms which require exponential time a computational method for the inversion of rank tests is also suggested the algorithms extend to stratified experiments

on separability of bi hamiltonian chain with degenerated poisson structures separability of bi hamiltonian finite dimensional chains with two degenerated poisson tensors which have pfaffian quasi bi hamiltonian representation is proved

scalable algorithms for three field mixed finite element coupled poromechanics abstract we introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three field formulation the use of a displacement velocity pressure mixed finite element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 3 unsymmetric and indefinite block matrix the preconditioners are obtained by approximating the two level schur complement with the aid of physically based arguments that can be also generalized in a purely algebraic approach a theoretical and experimental analysis is presented that provides evidence of the robustness efficiency and scalability of the proposed algorithm the performance is also assessed for a real world challenging consolidation experiment of a shallow formation

approximately exact inference for the common odds ratio in several 2 2 tables abstract the conditional maximum likelihood estimator mle of the common odds ratio in a sequence of independent 2 2 tables is known to be superior to the mantel haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known however a long standing barrier to the widespread use of this estimator has been computational intractability in particular the calculation of significance levels confidence sets and power based on the exact distribution requires fast and efficient algorithms an important class of such algorithms form the basis of statxact a software package able to solve various aspects of the exact inference problem for a sequence of several 2 2 tables in real time we provide an alternative methodology by developing several useful saddlepoint approximations to the exact distribution of the conditional mle the approximations are derived from an interesting representation for hypergeometric random variables as a sum of independent

longitudinal and repeated cross sectional cluster randomization designs using mixed effects regression for binary outcomes bias and coverage of frequentist and bayesian methods as medical applications for cluster randomization designs become more common investigators look for guidance on optimal methods for estimating the effect of group based interventions over time this study examines two distinct cluster randomization designs 1 the repeated cross sectional design in which centres are followed over time but patients change and 2 the longitudinal design in which individual patients are followed over time within treatment clusters simulations of each study design stipulated a multiplicative treatment effect on the log odds scale between 5 and 15 clusters in each of two treatment arms and followed over two time periods estimation options included linear mixed effects models using restricted maximum likelihood reml generalized estimating equations gee mixed effects logistic regression using both penalized quasi likelihood pql and numerical integration and bayesian monte carlo analysis for the repeated cross sectional designs most methods performed well in terms of bias and coverage when clusters were numerous 30 and variability across clusters of baseline risk and treatment effect was modest with few clusters two groups of five and higher variability only the bayesian methods maintained coverage in the longitudinal designs the common methods of reml gee or pql performed poorly when compared to numerical integration while bayesian methods demonstrated less bias and better coverage for estimates of both log odds ratios and risk differences the performance of common statistical tools for the analysis of cluster randomization designs depends heavily on the precise design the number of clusters and the variability of baseline outcomes and treatment effects across centres

saddlepoint approximations as smoothers reference stat article 2002 001doi 10 1093 biomet 89 4 933view record in web of science record created on 2006 04 21 modified on 2017 05 12

efficient solvers for hybridized three field mixed finite element coupled poromechanics abstract we consider a mixed hybrid finite element formulation for coupled poromechanics a stabilization strategy based on a macro element approach is advanced to eliminate the spurious pressure modes appearing in undrained incompressible conditions the efficient solution of the stabilized mixed hybrid block system is addressed by developing a class of block triangular preconditioners based on a schur complement approximation strategy robustness computational efficiency and scalability of the proposed approach are theoretically discussed and tested using challenging benchmark problems on massively parallel architectures

adaptive asynchronous time stepping stopping criteria and a posteriori error estimates for fixed stress iterative schemes for coupled poromechanics problems abstract in this paper we develop adaptive iterative coupling schemes for the biot system modeling coupled poromechanics problems we particularly consider the space time formulation of the fixed stress iterative scheme in which we first solve the problem of flow over the whole space time interval then exploiting the space time information for solving the mechanics two common discretizations of this algorithm are then introduced based on two coupled mixed finite element methods in space and the backward euler scheme in time therefrom adaptive fixed stress algorithms are build on conforming reconstructions of the pressure and displacement together with equilibrated flux and stresses reconstructions these ingredients are used to derive a posteriori error estimates for the fixed stress algorithms distinguishing the different error components namely the spatial discretization the temporal discretization and the fixed stress iteration components precisely at the iteration k 1 of the adaptive algorithm we prove that our estimate gives a guaranteed and fully computable upper bound on the energy type error measuring the difference between the exact and approximate pressure and displacement these error components are efficiently used to design adaptive asynchronous time stepping and adaptive stopping criteria for the fixed stress algorithms numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive iterative coupling algorithms

practical use of higher order asymptotics for multiparameter exponential families recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families especially in generalized linear models the aim here is to clarify and explore these attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family excellent approximations to exact conditional inferences are often available in terms of simple adjustments to the signed square root of the likelihood ratio statistic

on distributions of ratios a large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables if the denominator variable is positive then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random variables if in addition the joint characteristic function of numerator and denominator is known then standard fourier inversion techniques can be used to reconstruct the distribution function from it most research in this field has been based on this correspondence but which breaks down when both numerator and denominator are supported on the entire real line the present manuscript derives inversion formulae and saddlepoint approximations that remain valid in this case and reduce to known results when the denominator is almost surely positive applications include the iv est imator of a structural parameter in a just identified equation

improvements of jackknife confidence limit methods summary edgeworth expansion is applied to studentized parameter estimates when the standard error has been computed by a jackknife method adjustments to the usual jackknife confidence limit formulae are obtained this approach is contrasted with a bootstrap approach in numerical illustrations for estimation of a ratio jackknife methods are nonparametric methods for estimating the bias and standard error of an estimate t approximate confidence limits for the estimand can be found by using a large sample normal approximation for t somewhat curiously little is known about possible improvements to the normal approximation in this context although improvements based on edgeworth expansions are familiar in other problems in this paper we show that edgeworth expansion methods can be applied in the jackknife context numerical results for a particular application raise the possibility that the resulting improvements of jackknife methods can be matched by a suitable use of bootstrap methods efron 1982

guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the biot problem abstract the paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi static linear biot equations the system is decoupled by employing the fixed stress split scheme which leads to an iteratively solved semi discrete system the error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations the estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method they are fully computable do not contain mesh dependent constants and provide reliable global estimates of the error measured in the energy norm moreover they suggest efficient error indicators for the distribution of local errors and can be used in adaptive procedures

presymplectic representation of bi hamiltonian chains liouville integrable systems which have bi hamiltonian representation of the gel fand zakharevich type are considered bi presymplectic representation of one casimir bi hamiltonian chains and weakly bi presymplectic representation of multi casimir bi hamiltonian chains are constructed the reduction procedure for poisson and presymplectic structures is presented

a weighted bootstrap approach to bootstrap iteration the operation of resampling from a bootstrap resample encountered in applications of the double bootstrap may be viewed as resampling directly from the sample but using probability weights that are proportional to the numbers of times that sample values appear in the resample this suggests an approximate approach to double bootstrap monte carlo simulation where weighted bootstrap methods are used to circumvent much of the labour involved in compounded monte carlo approximation in the case of distribution estimation or equivalently confidence interval calibration the new method may be used to reduce the computational labour moreover the method produces the same order of magnitude of coverage error for confidence intervals or level error for hypothesis tests as a full application of the double bootstrap

randomization matching and propensity scores in the design and analysis of experimental studies with measured baseline covariates in many experimental situations researchers have information on a number of covariates prior to randomization this information can be used to balance treatment assignment with respect to these covariates as well as in the analysis of the outcome data in this paper we investigate the use of propensity scores in both of these roles we also introduce a randomization procedure in which the balance of all measured covariates is approximately indexed by the variance of the empirical propensity scores and randomization is restricted to those permutations with the least variable propensity scores this procedure is compared with recently proposed methods in terms of resulting covariate balance and estimation efficiency properties of the estimators resulting from each procedure are compared with estimates which incorporate the propensity score in the analysis stage simulation results show that analytical adjustment for the propensity score yields results on par with those obtained through restricted randomization procedures and can be used in conjunction with such procedures to further improve inferential efficiency

dirac reduction of dual poisson presymplectic pairs a new notion of a dual poisson presymplectic pair is introduced and its properties are examined the procedure of dirac reduction of poisson operators onto submanifolds proposed by dirac is in this paper embedded in a geometric procedure of reduction of dual poisson presymplectic pairs the method presented generalizes those introduced by j marsden and t ratiu for reductions of poisson manifolds two examples are given

conditional bootstrap methods in the mean shift model summary bootstrap methods are not inherently conditional but they can be made so by appropri ate stratification of the simulated samples which bootstrap produces we show how stratification can work in a bootstrap analysis of mean shift in nile river flow data the results are compared with both parametric and semiparametric likelihood analyses the paper ends with some general remarks on conditional bootstraps bootstrap methods efron 1982 are simulation methods for assessing frequency properties of statistical analyses the simulation model being that which is fitted to the actual data often the simulation involves monte carlo rather than theoretical evaluation unfortunately the bootstrap as usually described is inherently unconditional rubin s 1981 discussion bears on this point however if the bootstrap simulation results can be properly stratified then it is possible to estimate relevant conditional probabilities stratification can sometimes be effected in the model itself as when fixing the values of sample sizes or explanatory variables otherwise one must run the unconditional bootstrap and stratify its output in the present paper we illustrate the latter situation in the analysis of a mean shift model section 2 describes the application and its analysis by parametric methods sections 3 and 4 produce alternative bootstrap analyses the first of which uses the stratification of an unconditional monte carlo simulation the second bootstrap analysis involves estimation of a likelihood function the final section contains some brief general remarks about conditional bootstraps

saddlepoint approximations in resampling methods summary saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications examples include mean estimation ratio estimation two sample comparisons and autoregressive estimation

improved exact inference about conditional association in three way contingency tables abstract we propose modified exact inferential methods for contingency tables ordinary exact inference is conservative because of the discreteness for estimating a common odds ratio in several 2 2 tables two modifications of the ordinary exact confidence interval maintain at least a fixed confidence level but tend to be much narrower one approach inverts results of a test with a modified p value utilizing the test statistic and table probabilities the second approach inverts one two sided test rather than two one sided tests this approach is much less conservative when the true odds ratio is relatively small or large we also generalize results of cohen and sackrowitz and relate modified p values to construction of exact unbiased and admissible tests for an ordinal alternative to conditional independence

stability and monotonicity for some discretizations of the biot s consolidation model abstract we consider finite element discretizations of the biot s consolidation model in poroelasticity with mini and stabilized p1 p1 elements we analyze the convergence of the fully discrete model based on spatial discretization with these types of finite elements and implicit euler method in time we also address the issue related to the presence of non physical oscillations in the pressure approximation for low permeabilities and or small time steps we show that even in 1d a stokes stable finite element pair fails to provide a monotone discretization for the pressure in such regimes we then introduce a stabilization term which removes the oscillations we present numerical results confirming the monotone behavior of the stabilized schemes

stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium abstract we consider single rate and multirate explicit schemes for the biot system modeling coupled flow and geomechanics in a poro elastic medium these schemes are widely used in practice that follows a sequential procedure in which the flow and mechanics problems are fully decoupled in such a scheme the flow problem is solved first with time lagging the displacement term followed by the mechanics solve the multirate explicit coupling scheme exploits the different time scales for the mechanics and flow problems by taking multiple finer time steps for flow within one coarse mechanics time step we provide fully discrete schemes for both the single and multirate approaches that use backward euler time discretization and mixed spaces for flow and conformal galerkin for mechanics we perform a rigorous stability analysis and derive the conditions on reservoir parameters and the number of finer flow solves to ensure stability for both schemes furthermore we investigate the computational time savings for explicit coupling schemes against iterative coupling schemes

bi presymplectic chains of co rank 1 and related liouville integrable systems bi presymplectic chains of 1 forms of co rank 1 are considered the conditions under which such chains represent some liouville integrable systems and the conditions under which there exist related bi hamiltonian chains of vector fields are derived to present the construction of bi presymplectic chains the notion of a dual poisson presymplectic pair is used and the concept of d compatibility of poisson bivectors and d compatibility of presymplectic forms is introduced it is shown that bi presymplectic representation of a related flow leads directly to the construction of separation coordinates in a purely algorithmic way as an illustration bi presymplectic and bi hamiltonian chains in are considered in detail

performance and robustness of block constraint preconditioners in finite element coupled consolidation problems block constraint preconditioners are a most recent development for the iterative solution to large scale often ill conditioned coupled consolidation problems a major limitation to their practical use however is the somewhat difficult selection of a number of user defined parameters at least 4 in a more or less optimal way the present paper investigates the robustness of three variants of the block constraint preconditioning in relation to the above parameters a theoretical analysis of the eigenspectrum of the preconditioned matrix provides relatively simple bounds of the eigenvalues as a function of these parameters a number of test problems used to validate the theoretical results show that both the mixed constraint preconditioner mcp combined with the symmetric quasi minimal residual sqmr solver and the mcp triangular variant t mcp combined with the bi conjugate gradient stabilized bi cgstab are efficient and robust tools for the solution to difficult finite element discretized coupled consolidation problems moreover the practical selection of the user defined parameters is relatively easy as a stable behavior is observed for a wide range of fill in degree values the theoretical bounds on the eigenspectrum of the preconditioned matrix may help to suggest the most appropriate parameter combination copyright 2009 john wiley sons ltd

novel preconditioners for the iterative solution to fe discretized coupled consolidation equations a major computational issue in the finite element fe integration of coupled consolidation equations is the repeated solution in time of the resulting discretized indefinite system because of ill conditioning the iterative solution which is recommended in large size 3d settings requires the computation of a suitable preconditioner to guarantee convergence in this paper the coupled system is solved by a krylov subspace method preconditioned by an inexact constraint preconditioner icp preserving the same block structure as the native fe matrix the conditioning number of the preconditioned coupled problem depends on the quality of the approximation of the block corresponding to the structural stiffness matrix an efficient algorithm to implement icp into a krylov subspace method is developed numerical tests performed on realistic 3d problems reveal that icp typically outperforms standard ilut preconditioners and proves much more robust in severely ill conditioned problems

a distribution free test for symmetry based on a runs statistic abstract i present a simple test based on a runs statistic for symmetry of a continuous distribution about a known median the statistic has a binomial sampling distribution and desirable invariance properties monte carlo studies demonstrate that for a wide variety of alternative asymmetric distributions the test is more powerful than tests proposed by butler 1969 rothman and woodroofe 1972 or hill and rao 1977

bayesian exponentially tilted empirical likelihood summary while empirical likelihood has been shown to exhibit many of the properties of conven tional parametric likelihoods a formal probabilistic interpretation has so far been lacking we show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric bayesian procedure which places a type of noninformative prior on the space of distributions this prior gives preference to distributions having a small support and among those sharing the same support it favours entropy maximising distributions the resulting nonparametric bayesian procedure admits a computationally convenient representation as an empirical likelihood type likelihood where the probability weights are obtained via exponential tilting the proposed methodology provides an attractive alternative to the bayesian bootstrap as a nonparametric limit of a bayesian procedure for moment condition models

theory of separability of multi hamiltonian chains the theory of separability of one casimir bi hamiltonian chains is extended onto unsplit multi casimir bi hamiltonian chains multi casimir extensions of the known one casimir chains are constructed

space time finite element approximation of the biot poroelasticity system with iterative coupling abstract we analyze an optimized artificial fixed stress iterative scheme for a space time finite element approximation of the biot system modeling fluid flow in deformable porous media the iteration is based on a prescribed constant artificial volumetric mean total stress in the first half step the optimization comes through the adaptation of a numerical stabilization or tuning parameter and aims at an acceleration of the iterations the separated subproblems of fluid flow written as a mixed first order in space system and mechanical deformation are discretized by space time finite element methods of arbitrary order continuous and discontinuous galerkin discretizations of the time variable are encountered the convergence of the iterative schemes is proved for the continuous and fully discrete case the choice of the optimization parameter is identified in the proofs of convergence of the iterations the analyses are illustrated and confirmed by numerical experiments

confidence intervals from randomization tests an efficient method of constructing confidence intervals that correspond to randomization tests is described the method is based on the robbins monro search process and conducts a separate search for each endpoint of the confidence interval each search requires only slightly more permutations than the number needed for a randomization test diagnostics to monitor searches are suggested and the method is illustrated with examples

stability and convergence of sequential methods for coupled flow and geomechanics fixed stress and fixed strain splits abstract we analyze stability and convergence of sequential implicit methods for coupled flow and geomechanics in which the flow problem is solved first we employ the von neumann and energy methods for linear and nonlinear problems respectively we consider two sequential methods with the generalized midpoint rule for tn where is the parameter of time discretization namely the fixed strain and fixed stress splits the von neumann method indicates that the fixed strain split is only conditionally stable and that its stability limit is a coupling strength less than unity if 0 5 on the other hand the fixed stress split is unconditionally stable when 0 5 the amplification factors of the fixed stress split are different from those of the undrained split and are identical to the fully coupled method unconditional stability of the fixed stress split is also obtained from the energy method for poroelastoplasticity we show that the fixed stress split is contractive and b stable when 0 5 we also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward euler method in time from the estimates the fixed strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable the fixed stress split however is convergent for a fixed number of iterations showing better accuracy than the undrained split even when we cannot obtain the exact local bulk modulus or exact rock compressibility at the flow step a priori due to complex boundary conditions or the nonlinearity of the materials the fixed stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus such as the dimension based estimation by which the employed local bulk modulus is less stiff than the exact local bulk modulus we provide numerical examples supporting all the estimates of stability and convergence for the fixed strain and fixed stress splits

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

numerical stabilization of biot s consolidation model by a perturbation on the flow equation in this paper a stabilized finite element scheme for the poroelasticity equations is proposed this method based on the perturbation of the flow equation allows us to use continuous piecewise linear approximation spaces for both displacements and pressure obtaining solutions without oscillations independently of the chosen discretization parameters the perturbation term depends on a parameter which is established in terms of the mesh size and the properties of the material in the one dimensional case this parameter is shown to be optimal some numerical experiments are presented indicating the efficiency of the proposed stabilization technique copyright 2008 john wiley sons ltd

regaining confidence in confidence intervals for the mean treatment effect in many experiments it is necessary to evaluate the effectiveness of a treatment by comparing the responses of two groups of subjects this evaluation is often performed by using a confidence interval for the difference between the population means to compute the limits of this confidence interval researchers usually use the pooled t formulas which are derived by assuming normally distributed errors when the normality assumption does not seem reasonable the researcher may have little confidence in the confidence interval because the actual one sided coverage probability may not be close to the nominal coverage probability this problem can be avoided by using the robbins monro iterative search method to calculate the limits one problem with this iterative procedure is that it is not clear when the procedure produces a sufficiently accurate estimate of a limit in this paper we describe a multiple search method that allows the user to specify the accuracy of the limits we also give guidance concerning the number of iterations that would typically be needed to achieve a specified accuracy this multiple iterative search method will produce limits for one sided and two sided confidence intervals that maintain their coverage probabilities with non normal distributions

resampling procedures to compare two survival distributions in the presence of right censored data summary in this simulation study the accuracy of the size of four classes of test procedures asymptotic normal test permutation test bootstrap hypothesis test and bootstrap interval test were compared using the logrank and prentice wilcoxon two sample test statistics sample sizes of 20 and 50 per group were used twenty observations per group yielded differences in the test procedures when the prentice wilcoxon test statistic was employed the asymptotic test procedure was the most accurate resampling procedures did not improve upon its accuracy using the logrank test statistic the permutation or bootstrap hypothesis testing procedures were closest to the nominal significance level the more popular asymptotic normal logrank test was consistently anticonservative when the number of observations in each group was increased to 50 the test procedures were comparable power comparisons were also examined the test with the greatest power was dependent upon the two survival patterns and the choice of test statistic

prepivoting to reduce level error of confidence sets summary approximate confidence sets for a parameter 0 may be obtained by referring a function of 0 and of the sample to an estimated quantile of that function s sampling distribution we call this function the root of the confidence set either asymptotic theory or bootstrap methods can be used to estimate the desired quantile when the root is not a pivot in the sense of classical statistics the actual level of the approximate confidence set may differ substantially from the intended level prepivoting is the transformation of a confidence set root by its estimated bootstrap cumulative distribution function prepivoting can be iterated bootstrap confidence sets generated from a root prepivoted one or more times have smaller error in level than do confidence sets based on the original root the first prepivoting is nearly equivalent to studentizing when that operation is appropriate further iterations of prepivoting make higher order corrections automatically

bootstrapping survival times in stochastic systems by using saddlepoint approximations summary the single bootstrap is implemented by using a saddlepoint approximation to determine estimates for the survival and hazard functions of first passage times in complicated semi markov processes the double bootstrap is also implemented by resampling saddlepoint inversions and provides bca confidence bands for these functions confidence intervals for the mean and variance of first passage times are easily computed a new characterization of the asymptotic hazard rate for survival times is presented and leads to an indirect method for constructing its bootstrap confidence interval

randomization based interval estimation in randomized clinical trials randomization based interval estimation takes into account the particular randomization procedure in the analysis and preserves the confidence level even in the presence of heterogeneity it is distinguished from population based confidence intervals with respect to three aspects definition computation and interpretation the article contributes to the discussion of how to construct a confidence interval for a treatment difference from randomization tests when analyzing data from randomized clinical trials the discussion covers i the definition of a confidence interval for a treatment difference in randomization based inference ii computational algorithms for efficiently approximating the endpoints of an interval and iii evaluation of statistical properties ie coverage probability and interval length of randomization based and population based confidence intervals under a selected set of randomization procedures when assuming heterogeneity in patient outcomes the method is illustrated with a case study

on the fixed stress split scheme as smoother in multigrid methods for coupling flow and geomechanics the fixed stress split method has been widely used as solution method in the coupling of flow and geomechanics in this work we analyze the behavior of an inexact version of this algorithm as smoother within a geometric multigrid method in order to obtain an efficient monolithic solver for biot s problem this solver combines the advantages of being a fully coupled method with the benefit of decoupling the flow and the mechanics part in the smoothing algorithm moreover the fixed stress split smoother is based on the physics of the problem and therefore all parameters involved in the relaxation are based on the physical properties of the medium and are given a priori a local fourier analysis is applied to study the convergence of the multigrid method and to support the good convergence results obtained the proposed geometric multigrid algorithm is used to solve several tests in semi structured triangular grids in order to show the good behavior of the method and its practical utility

the weighted log rank class of permutation tests p values and confidence intervals using saddlepoint methods test statistics from the weighted log rank class are commonly used to compare treatment with control when there is right censoring this paper uses saddlepoint methods to determine mid p values from the null permutation distributions of tests from the weighted log rank class analytical saddlepoint computations replace the permutation simulations and provide mid p values that are virtually exact for all practical purposes the speed of these saddlepoint computations makes it practicable to invert the weighted log rank tests to determine nominal 95 confidence intervals for the treatment effect with right censored data such analytical inversions lead to permutation confidence intervals that are easily computed and virtually identical to the exact intervals that would normally require massive amounts of simulation

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

separation of variables in quasi potential systems of bi cofactor form we perform variable separation in the quasi potential systems of equations of the form q a 1 k a 1 k w herea and a are killing tensors by embedding these systems into a bi hamiltonian chain and by calculating the corresponding darboux nijenhuis coordinates on the symplectic leaves of one of the hamiltonian structures of the system we also present examples of the corresponding separation coordinates in two and three dimensions

convergence analysis of multirate fixed stress split iterative schemes for coupling flow with geomechanics abstract we consider multirate iterative schemes for the biot system modeling coupled flow and geomechanics in a poro elastic medium the multirate iterative coupling scheme exploits the different time scales for the mechanics and flow problems by taking multiple finer time steps for flow within one coarse mechanics time step we adapt the fixed stress split algorithm that decouples the flow and mechanics equations for the multirate case and perform an iteration between the two problems until convergence we provide a fully discrete scheme that uses backward euler time discretization and mixed spaces for flow and conformal galerkin for mechanics our analysis is based on studying the equations satisfied by the difference of iterates and using banach contraction argument to prove that the corresponding scheme is a fixed point contraction the analysis provides the value of an adjustable coefficient used in the proposed iterative coupling algorithms furthermore we show that the converged quantities satisfy the variational weak form for the coupled discrete system

a partially parallel in time fixed stress splitting method for biot s consolidation model in this work we study the parallel in time iterative solution of coupled flow and geomechanics in porous media modelled by a two field formulation of biot s equations in particular we propose a new version of the fixed stress splitting method which has been widely used as solution method of these problems this new approach forgets about the sequential nature of the temporal variable and considers the time direction as a further direction for parallelization the method is partially parallel in time we present a rigorous convergence analysis of the method and numerical experiments to demonstrate the robust behaviour of the algorithm

small sample confidence intervals abstract in this article we present a technique for constructing one or two sided confidence intervals which are second order correct in terms of coverage for either parametric or nonparametric problems the construction is valid in the presence of nuisance parameters the situation we consider is this there are p parameters and we want a confidence interval for some function of them possibly one of the parameters itself the p parameters are estimated by m estimates which means they are obtained as a solution of a system of equations maximum likelihood estimates are included as a special case the essential intermediate result given in equation 3 4 says that the estimated parameter of interest can be written as a mean up to order o p 1 n the representation 3 4 is attained when is a smooth function of the parameters and is the solution of a well behaved system of equations we avoid the use of pivots and strive to obtain accurate coverage confidence intervals are construc

small sample asymptotic distributions of m estimators of location summary asymptotic formulae for the distribution of m estimators i e maximum likelihood type estimators of location including the arithmetic mean are derived which numerical studies show to give relative errors for densities and tail areas of the order of magnitude of 1 down to sample sizes 3 and 4 even in the extreme tails the paper is the continuation of earlier work by the second author and is also closely related to daniels s work on the saddlepoint approximation the method consists in expanding the derivative of the logarithm of the unstandardized density of the estimator in powers of 1 n at each point using recentring by means of conjugate distributions this method yields a unified point of view for the comparison of other asymptotic methods namely saddlepoint method edgeworth expansion and large deviations approach which are also compared numerically

a conditional saddlepoint approximation for testing problems a saddlepoint approximation is provided for the distribution function of one m statistic conditional on another m statistic many interesting statistics based on dependent quantities e g spacings multinomial frequencies rank differences can be expressed in terms of independent identically distributed random variables conditioned on their sum so that this conditional saddlepoint approximation yields accurate approximations for the distribution of such statistics this saddlepoint approximation can also be used in conditional testing where nuisance parameters are eliminated by conditioning on sufficient statistics

on stability and convergence of finite element approximations of biot s consolidation problem stability and convergence analysis of finite element approximations of biot s equations governing quasistatic consolidation of saturated porous media are discussed a family of decay functions parametrized by the number of time steps is derived for the fully discrete backward euler galerkin formulation showing that the pore pressure oscillations arising from an unstable approximation of the incompressibility constraint on the initial condition decay in time error estimates holding over the unbounded time domain for both semidiscrete and fully discrete formulations are presented and a post processing technique is employed to improve the pore pressure accuracy

variance stabilization for a scalar parameter summary we present a variance stabilizing transformation for inference about a scalar parameter that is estimated by a function of a multivariate m estimator the transformation proposed is automatic computationally simple and can be applied quite generally though it is based on an intuitive notion and entirely empirical the transformation is shown to have an appropriate justification in providing variance stabilization when viewed from both parametric and nonparametric perspectives further the transformation repairs deficiencies of existing methods for variance stabilization the transformation proposed is illustrated in a range of examples and its effectiveness to yield confidence limits having low coverage error is demonstrated in a numerical example

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses

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