confidence intervals for an effect size measure based on the mann whitney statistic part 1 general issues and tail area based methods for two random variables x and y pr y x pr y x is advocated as a general measure of effect size to characterize the degree of separation of their distributions it is estimated by u mn a generalization of the mann whitney u statistic derived by dividing u by the product of the two sample sizes it is equivalent to the area under the receiver operating characteristic curve it is readily visualized in terms of two gaussian distributions with appropriately separated peaks the effect of discretization of a continuous variable is explored tail area based confidence interval methods are developed which can be applied to very small samples or extreme outcomes copyright 2005 john wiley sons ltd

a constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric abstract the article presents a constitutive framework of large strain elastoplasticity in both the lagrangian and the eulerian geometric setting which takes into account anisotropic material response in summary the key ingredients of this framework are i the introduction of a plastic metric which is assumed to describe locally the history dependent inelastic material response in the sense of an internal variable formulation ii the definition of a convex elastic domain in the space of the local stress like variable conjugate to the plastic metric denoted as the plastic force iii an equivalent lagrangian and eulerian representation of all constitutive functions as isotropic tensor functions in terms of an extended set of arguments denoted as anisotropy variables iv the set up of normality rules for the evolution of the plastic metric and the anisotropy variables yielding a canonical symmetric form of the elastoplastic tangent moduli v a geometrically exact decomposition of the set of constitutive equations into possibly decoupled volumetric and isochoric contributions applications of the constitutive framework are demonstrated by means of several conceptual model problems which cover isotropic initial anisotropic and induced anisotropic elastoplastic response

confidence intervals for probabilities and tolerance regions based on a generalization of the mann whitney statistic abstract inference procedures are proposed for any specified function of two random variables f x y assuming that independent random samples from the x and y populations are available a generalization of the mann whitney statistic is used to obtain point and interval estimates for the probability that f x y falls in a given interval one proposed confidence interval is a modification and improvement to the approach of halperin gilbert and lachin 1987 for estimating pr x y a thorough review is made of the literature on nonparametric confidence bounds for pr x y with emphasis on methods based on the central limit theorem in addition to the improvement of halperin et al s method bounds analogous to the clopper pearson confidence interval for a binomial parameter are proposed simulation results show the performance of the alternative procedures approximate nonparametric tolerance limits for f x y are also proposed the article closes by constructing a two sided tolerance interval for

confidence regions for the multinomial parameter with small sample size consider the observation of n iid realizations of an experiment with d 2 possible outcomes which corresponds to a single observation of a multinomial distribution d n p where p is an unknown discrete distribution on 1 d in many applications the construction of a confidence region for p when n is small is crucial this challenging concrete problem has a long history it is well known that the confidence regions built from asymptotic statistics do not have good coverage when n is small on the other hand most available methods providing nonasymptotic regions with controlled coverage are limited to the binomial case d 2 here we propose a new method valid for any d 2 that provides confidence regions with controlled coverage and small volume the method involves inversion of the covering collection associated with level sets of the likelihood the behavior when d n tends to infinity remains an interesting open problem beyond the scope of this work

confidence intervals for a binomial proportion and asymptotic expansions p z 2n 1 2 p 1 p 1 2 is currently in near universal use we first show that the coverage properties of the wald interval are persistently poor and defy virtually all conventional wisdom we then proceed to a theoretical comparison of the standard interval and four additional alternative intervals by asymptotic expansions of their coverage probabilities and expected lengths the four additional interval methods we study in detail are the score test interval wilson the likelihood ratio test interval a jeffreys prior bayesian interval and an interval suggested by agresti and coull the asymptotic expansions for coverage show that the first three of these alternative methods have coverages that fluctuate about the nominal value while the agresti coull interval has a somewhat larger and more nearly conservative coverage function for the five interval methods we also investigate asymptotically their average coverage relative to distributions for p supported within 0 1 in terms of expected length asymptotic expansions show that the agresti coull interval is always the longest of these the remaining three are rather comparable and are shorter than the wald interval except for p near 0 or 1 these analytical calculations support and complement the findings and the recommendations in brown cai and dasgupta statist sci 2001 16 101 133

an automata theoretic approach to constraint ltl we consider an extension of linear time temporal logic ltl with constraints interpreted over a concrete domain we use a new automata theoretic technique to show pspace decidability of the logic for the constraint systems z and n along the way we give an automata theoretic proof of a result of balbiani and condotta when the constraint system satisfies the completion property our decision procedures extend easily to handle extensions of the logic with past time operators and constants as well as an extension of the temporal language itself to monadic second order logic finally we show that the logic becomes undecidable when one considers constraint systems that allow a counting mechanism

continuous time temporal logic with counting we add to the standard temporal logic tl u s a sequence of counting modalities for each n the modality c n x which says that x will be true at least at n points in the next unit of time and its dual c n which says that x has happened n times in the last unit of time we show that this temporal logic is expressively complete for the metric predicate logic q2mlo which is expressive decidable and easy to use in particular the pnueli modalities p n x 1 x n there is an increasing sequence t 1 t n of points in the unit interval ahead such that t i satisfies x i are definable in tl u s with the counting modalities

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

a formulation of finite elastoplasticity based on dual co and contra variant eigenvector triads normalized with respect to a plastic metric the article presents a new formulation of isotropic elastoplasticity at large strains in both the lagrangian and the eulerian geometric setting and addresses aspects of its numerical implementation the key ingredients on the theoretical side are the introduction of a plastic metric for the description of the local history dependent inelastic material response the definition of a convex elastic domain in the space of the local stress like variable conjugate to the plastic metric denoted as the plastic force and a fully equivalent lagrangian and eulerian representation of all constitutive functions in spectral form for general non cartesian coordinate charts in terms of dual co and contra variant eigenvector triads which are normalized with respect to the plastic metric on the numerical side we propose a stress update algorithm for general non associative isotropic elasto visco plastic response with an arbitrary number of scalar internal variables the algorithm is based on an exponential map integrator and is recast into a general return mapping scheme methodically organized with tensorial pre and postprocessing and a constitutive box in the eigenvalue space furthermore we propose a new perturbation stabilization technique which dramatically enhances the convergence of the general return algorithm the theoretical and numerical developments are applied to a constitutive model problem with large elastic and large plastic strains the von mises tresca type associative plastic flow in ogden type large strain elastic materials

interval estimation for a difference between intraclass kappa statistics summary model based inference procedures for the kappa statistic have developed rapidly over the last decade however no method has yet been developed for constructing a confidence interval about a difference between independent kappa statistics that is valid in samples of small to moderate size in this article we propose and evaluate two such methods based on an idea proposed by newcombe 1998 statistics in medicine 17 873 890 for constructing a confidence interval for a difference between independent proportions the methods are shown to provide very satisfactory results in sample sizes as small as 25 subjects per group sample size requirements that achieve a prespecified expected width for a confidence interval about a difference of kappa statistic are also presented

on the superiority of the negative binomial test over the binomial test for estimating the bit error rate this paper examines the binomial and negative binomial tests for estimating the bit error rate using monte carlo simulations whereas the estimator error variances and simulation times do not recommend one test over the other confidence interval analysis and test design criteria recommend the negative binomial test for estimating a small bit error rate based on a limited number of error events the clopper pearson interval length is much more consistent for the negative binomial test in the small bit error rate case the logarithmically centered confidence interval is introduced and analyzed for a given confidence interval length and confidence probability the negative binomial test requires fewer error events than the binomial test the asymptotic analyses of the clopper pearson and logarithmically centered confidence intervals yield useful design criteria for the negative binomial test in a way that is not possible for the binomial test

improved confidence intervals for the difference between binomial proportions based on paired data existing methods for setting confidence intervals for the difference theta between binomial proportions based on paired data perform inadequately the asymptotic method can produce limits outside the range of validity the exact conditional method can yield an interval which is effectively only one sided both these methods also have poor coverage properties better methods are described based on the profile likelihood obtained by conditionally maximizing the proportion of discordant pairs a refinement methods 5 and 6 which aligns 1 alpha with an aggregate of tail areas produces appropriate coverage properties a computationally simpler method based on the score interval for the single proportion also performs well method 10

mid p confidence intervals for the poisson expectation conventionally a confidence interval ci for the standardized mortality ratio is set using the conservative ci for a poisson expectation mu employing the mid p argument we present alternative cis that are shorter than the conventional ones the mid p intervals do not guarantee the nominal confidence level but the true coverage probability is only lower than the nominal level for a few short ranges of mu the implications for mid p confidence intervals of various proposed definitions of two sided tests for discrete data are discussed

complexity of metric temporal logics with counting and the pnueli modalities the common metric temporal logics for continuous time were shown to be insufficient when it was proved in hirshfeld and rabinovich 1999 2007 7 12 that they cannot express a modality suggested by pnueli moreover no temporal logic with a finite set of modalities can express all the natural generalizations of this modality the temporal logic with counting modalities tlc is the extension of until since temporal logic tl u s by counting modalities c n x and email protected n email protected n for each n the modality c n x says that x will be true at least at n points in the next unit of time and its dual email protected n x says that x has happened n times in the last unit of time in hirshfeld and rabinovich 2006 11 it was proved that this temporal logic is expressively complete for a natural decidable metric predicate logic in particular the pnueli modalities pn k x 1 x k there is an increasing sequence t 1 t k of points in the unit interval ahead such that x i holds at t i are definable in tlc in this paper we investigate the complexity of the satisfiability problem for tlc and show that the problem is pspace complete when the index of c n is coded in unary and expspace complete when the index is coded in binary we also show that the satisfiability problem for the until since temporal logic extended by the pnueli modalities is pspace complete

binomial confidence intervals abstract for x with binomial n p distribution section 1 gives a one page table of 95 and 99 confidence intervals for p for n 1 2 30 this interval is equivariant under x n x and p 1 p has approximately equal probability tails is approximately unbiased has crow s property of minimizing the sum of the n 1 possible lengths and each of its ends is increasing in x and decreasing in n with about as regular steps as possible sections 2 and 3 consider the usual approximate confidence intervals calculations and asymptotic results show the need for the continuity correction in these even when n is large because of the nonuniformity of the binomial normal convergence as p 0 these intervals fail to have their stated asymptotic confidence coefficients simple corrections are given for this in the approximate interval x n c n x n 1 x n 1 2n it is shown that the factor c n should be replaced by c n c 2 2c n 1 n

finite sample pointwise confidence intervals for a survival distribution with right censored data we review and develop pointwise confidence intervals for a survival distribution with right censored data for small samples assuming only independence of censoring and survival when there is no censoring at each fixed time point the problem reduces to making inferences about a binomial parameter in this case the recently developed beta product confidence procedure bpcp gives the standard exact central binomial confidence intervals of clopper and pearson additionally the bpcp has been shown to be exact gives guaranteed coverage at the nominal level for progressive type ii censoring and has been shown by simulation to be exact for general independent right censoring in this paper we modify the bpcp to create a mid p version which reduces to the mid p confidence interval for a binomial parameter when there is no censoring we perform extensive simulations on both the standard and mid p bpcp using a method of moments implementation that enforces monotonicity over time all simulated scenarios suggest that the standard bpcp is exact the mid p bpcp like other mid p confidence intervals has simulated coverage closer to the nominal level but may not be exact for all survival times especially in very low censoring scenarios in contrast the two asymptotically based approximations have lower than nominal coverage in many scenarios this poor coverage is due to the extreme inflation of the lower error rates although the upper limits are very conservative both the standard and the mid p bpcp methods are available in our bpcp r package published 2016 this article is us government work and is in the public domain in the usa

quantitative temporal logics over the reals pspace and below in many cases the addition of metric operators to qualitative temporal logics tls increases the complexity of satisfiability by at least one exponential while common qualitative tls are complete for np or pspace their metric extensions are often expspace complete or even undecidable in this paper we exhibit several metric extensions of qualitative tls of the real line that are at most pspace complete and analyze the transition from np to pspace for such logics our first result is that the logic obtained by extending since until logic of the real line with the operators sometime within n time units in the past future is still pspace complete in contrast to existing results we also capture the case where n is coded in binary and the finite variability assumption is not made to establish containment in pspace we use a novel reduction technique that can also be used to prove tight upper complexity bounds for many other metric tls in which the numerical parameters to metric operators are coded in binary we then consider metric tls of the reals that do not offer any qualitative temporal operators in such languages the complexity turns out to depend on whether binary or unary coding of parameters is assumed satisfiability is still pspace complete under binary coding but only np complete under unary coding

coupled thermoviscoplasticity of glassy polymers in the logarithmic strain space based on the free volume theory the paper outlines a constitutive model for finite thermo visco plastic behavior of amorphous glassy polymers and considers details of its numerical implementation in contrast to existing kinematical approaches to finite plasticity of glassy polymers the formulation applies a plastic metric theory based on an additive split of lagrangian hencky type strains into elastic and plastic parts the analogy between the proposed formulation in the logarithmic strain space and the geometrically linear theory of plasticity makes this constitutive framework very transparent and attractive with regard to its numerical formulation the characteristic strain hardening of the model is derived from a polymer network model we consider the particularly simple eight chain model but also comment on the recently developed microsphere model the viscoplastic flow rule in the logarithmic strain space uses structures of the free volume flow theory which provides a highly predictive modeling capacity at the onset of viscoplastic flow the integration of this micromechanically motivated approach into a three dimensional computational model is a key concern of this work we outline details of the numerical implementation of this model including elements such as geometric pre and post transformations to from the logarithmic strain space a thermomechanical operator split algorithm consisting of an isothermal mechanical predictor followed by a heat conduction corrector and finally the consistent linearization of the local update algorithm for the dissipative variables as well as its relationship to the global tangent operator the performance of the proposed formulation is demonstrated by means of a spectrum of numerical examples which we compare with our experimental findings

aspects of the formulation and finite element implementation of large strain isotropic elasticity the paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation on the theoretical side an eulerian setting of isotropic elasticity is discussed exclusively in terms of the finger tensor as a strain measure noval aspects are a direct representation of the eulerian elastic moduli in terms of the finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the finger tensor into spherical and unimodular parts the isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the finger tensor a constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity on the computational side the implementation of the constitutive model in three possible finite element formulations is discussed after pointing out algorithmic techniques for the treatment of incompressible elasticity several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity

exact inference for categorical data recent advances and continuing controversies methods for exact small sample analyses with categorical data have been increasingly well developed in recent years a variety of exact methods exist primarily using the approach that eliminates unknown parameters by conditioning on their sufficient statistics in addition a variety of algorithms now exist for implementing the methods this paper briefly summarizes the exact approaches and describes recent developments controversy continues about the appropriateness of some exact methods primarily relating to their conservative nature because of discreteness this issue is examined for two simple problems in which discreteness can be severe interval estimation of a proportion and the odds ratio in general adjusted exact methods based on the mid p value seem a reasonable way of reducing the severity of this problem

constrained group balancing why does it work abstract we consider a problem where a set of objects possessing multiple attributes must be partitioned into a certain number of groups so that the groups are as balanced as possible with respect to the number of objects possessing each attribute this multi criteria decision problem arises in a variety of practical applications ranging from assigning students to study groups to designing level schedules for jit assembly lines a direct approach enforcing balance through hard constraints may lead to infeasibility but works well in practice we analyze this phenomenon from the worst case and empirical perspectives as well as through an in depth analysis of one representative practical application the design of student groups at the rotman school of management university of toronto the goals of the analysis are to understand what classes of balancing problems may contain infeasible instances and how prevalent such instances are within these classes as well as to synthesize practical managerial insights that a decision maker could follow in order to increase the chances that balanced groups can be found

recommended tests and confidence intervals for paired binomial proportions we describe evaluate and recommend statistical methods for the analysis of paired binomial proportions a total of 24 methods are considered the best tests for association include the asymptotic mcnemar test and the mcnemar mid p test for the difference between proportions we recommend two simple confidence intervals with closed form expressions and the asymptotic score interval the asymptotic score interval is also recommended for the ratio of proportions as is an interval with closed form expression based on combining two wilson score intervals for the single proportion for the odds ratio we recommend a transformation of the wilson score interval and a transformation of the clopper pearson mid p interval we illustrate the practical application of the methods using data from a recently published study of airway reactivity in children before and after stem cell transplantation and a matched case control study of the association between floppy eyelid syndrome and obstructive sleep apnea hypopnea syndrome

anisotropic elastic plastic analysis of shells at large strains a comparison of multiplicative and additive approaches to enhanced finite element design and constitutive modelling the article presents new aspects of large strain anisotropic elastoplastic analyses of shells on the side of computational shell analysis we focus on recently developed brick type mixed finite shell elements based on trilinear displacement interpolations equipped with enhanced strain modes and shell typical assumed strain modifications here we compare two classes of this shell element design based on a multiplicative and an additive definition of an enhanced strain measure respectively furthermore for both types of continuum based shell elements we outline unified interfaces to strain driven constitutive stress update algorithms of anisotropic finite plasticity on the side of computational plasticity we investigate two classes of constitutive models suitable for the description of anisotropic elastoplastic response at finite strains the first framework uses a multiplicative definition of an elastic strain measure based on a plastic map the second an additively defined elastic strain measure based on a plastic metric both constitutive frameworks use hencky type logarithmic strain measures and are specified to a model problem of orthotropic elastic plastic response of a standard material the algorithmic treatment of the two constitutive models is based on an incremental variational formulation that defines the stresses and consistent tangent moduli in terms of a function evaluation we compare the performances of the two finite element formulations and the two constitutive models by means of numerical simulations of sheet drawing processes for the range of metal plasticity at moderate strains it is shown that results obtained with the different approaches are close to each other while the additive approaches provide simpler and more efficient settings copyright 2004 john wiley sons ltd

confidence intervals for the relative frequency of responding cells in limiting dilution assays summary confidence intervals for the relative frequency of responding cells in limiting dilution assays ldas have not been examined closely generally confidence intervals are calculated by using the normal approximation sometimes preceded by a log transform we evaluate and compare with analytical approaches the normal approximation the log transform and two binomial methods the quadratic approximation and a modification of the clopper pearson exact method we evaluate these confidence interval methods for use with the maximum likelihood and jackknife estimators of the relative frequency our results show that confidence interval construction with maximum likelihood point estimates is more accurate than construction with jackknife estimates when using maximum likelihood estimates the normal approximation produces acceptable two sided confidence intervals with the smallest length at a 05 at a 01 the normal approximation is anticonservative in all cases the normal approximation is unable to produce adequate one sided confidence intervals the log transform and both binomial confidence interval methods are shown to be generally superior to

confidence intervals for a binomial proportion thirteen methods for computing binomial confidence intervals are compared based on their coverage properties widths and errors relative to exact limits the use of the standard textbook method x n 1 96 square root of x n 1 x n n or its continuity corrected version is strongly discouraged a commonly cited rule of thumb stating that alternatives to exact methods may be used when the estimated proportion p is such that np and n 1 p both exceed 5 does not ensure adequate accuracy score limits are easily calculated from closed form solutions to quadratic equations and can be used at all times based on coverage functions the continuity corrected score method is recommended over exact methods its conservative nature should be kept in mind as should the wider fluctuation of actual coverage that accompanies omission of the continuity correction

confidence intervals for the binomial parameter some new considerations several methods have been proposed to construct confidence intervals for the binomial parameter some recent papers introduced the mean coverage criterion to evaluate the performance of confidence intervals and suggested that exact methods because of their conservatism are less useful than asymptotic ones in these studies however exact intervals were always represented by the clopper pearson interval c p now we focus on sterne s interval which is also exact and known to be better than the c p in the two sided case introducing a computer intensive level adjustment procedure which allows constructing intervals that are exact in terms of mean coverage we demonstrate that sterne s interval performs better than the best asymptotic intervals even in the mean coverage context level adjustment improves the c p as well which with an appropriate level adjustment becomes equivalent to the mid p interval finally we show that the asymptotic behaviour of the mid p method is far poorer than is generally expected

confidence intervals for an effect size measure based on the mann whitney statistic part 2 asymptotic methods and evaluation several asymptotic confidence interval methods for u mn the mann whitney u statistic divided by the product of the two sample sizes are developed and evaluated alongside published methods novel methods derived from gaussian and beta models perform well though overall a modification of the hanley mcneil approach method 5 in this evaluation performed better and is recommended for calculating confidence intervals for u mn for continuously distributed data

approximate binomial confidence limits abstract this article examines the accuracy of normal approximations to confidence limits for the binomial n p parameter p the method of getting exact values from an f table is too slow for practical use and useless for large n the two usual approximations have unsatisfactory accuracy both for small n and asymptotically and the simpler one lacks an invariance property of the confidence limit hall s 1982 approximation also lacks invariance and even when symmetrized has unsatisfactory accuracy pratt s 1968 approximation has excellent accuracy for all n inversion of a molenaar 1973 normal approximation to the binomial gives better asymptotic accuracy than pratt s approximation but poor values for observations close to n

confidence intervals for the mean of a variable taking the values 0 1 and 2 the problem of setting a confidence interval for the mean of a variable on 0 1 2 arises in three contexts paired organ procedure rates estimation of gene frequency and three point likert scales an effective approach to its estimation may be based on a good interval for a paired difference of proportions four good methods due to newcombe and tango are shown to have much better performance than more naive methods over regions of the parameter space corresponding to the above applications

estimation of aquifer scale proportion using equal area grids assessment of regional scale groundwater quality 1 the proportion of an aquifer with constituent concentrations above a specified threshold high concentrations is taken as a nondimensional measure of regional scale water quality if computed on the basis of area it can be referred to as the aquifer scale proportion a spatially unbiased estimate of aquifer scale proportion and a confidence interval for that estimate are obtained through the use of equal area grids and the binomial distribution traditionally the confidence interval for a binomial proportion is computed using either the standard interval or the exact interval research from the statistics literature has shown that the standard interval should not be used and that the exact interval is overly conservative on the basis of coverage probability and interval width the jeffreys interval is preferred if more than one sample per cell is available cell declustering is used to estimate the aquifer scale proportion and kish s design effect may be useful for estimating an effective number of samples the binomial distribution is also used to quantify the adequacy of a grid with a given number of cells for identifying a small target defined as a constituent that is present at high concentrations in a small proportion of the aquifer case studies illustrate a consistency between approaches that use one well per grid cell and many wells per cell the methods presented in this paper provide a quantitative basis for designing a sampling program and for utilizing existing data

prediction of deformation behavior of glassy polymers based on molecular chain network model abstract in order to develop a constitutive equation for polymeric materials covering a wide class of deformation processes a three dimensional nonaffine model has been developed by adopting the non gaussian network theory with the generalized argon double kink model of intermolecular resistance a phenomenological relation between the non gaussian molecular chain network structure and entanglement of chains is formulated and a simple evolutional equation of the number of entanglements of chains during the deformation process is developed the validity of the proposed constitutive equation has been proven through comparison between the predicted results and experimental results furthermore its application to the deformation analysis of circular polymeric bars under tension has been discussed

a logical characterization of timed regular languages cltloc constraint ltl over clocks is a quantifier free extension of ltl allowing variables behaving like clocks over real numbers cltloc is in pspace 1 and its satisfiability can polynomially be reduced to a satisfiability modulo theories smt problem allowing a feasible implementation of a decision procedure we used cltloc to capture the semantics of metric temporal logics over continuous time such as metric interval temporal logic mitl resulting in the first successful implementation of a tool for checking mitl satisfiability 2 3 in this paper we assess the expressive power of cltloc by comparing it with various temporal formalisms over dense time we restrict the analysis to well initialized models of formulae where the value of all clocks in the origin is either 0 or equal to a positive real constant under this assumption when interpreted over timed words the class of timed languages defined by cltloc formulae coincides with the class defined by timed automata we also define a timed monadic first order logic of order extending the one introduced by kamp which is expressively equivalent to cltloc for the class of timed languages that are defined by well initialized models

on small sample confidence intervals for parameters in discrete distributions summary the traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level in constructing such intervals for parameters in discrete distributions less conservative behavior results from inverting a single two sided test than inverting two separate one sided tests of half the nominal level each we illustrate for a variety of discrete problems including interval estimation of a binomial parameter the difference and the ratio of two binomial parameters for independent samples and the odds ratio

plane strain neck propagation abstract quasi static neck propagation in polymers cold drawing is studied for the case of plane strain tension for a j 2 deformation theory material nonlinear elastic jump conditions across the neck provide a simple steady state solution for a j 2 flow theory material a finite element solution characterizes the complete development of a neck in an initially smooth specimen the numerical results include the overall load deflection curve details of deformation states and the triaxial stress distribution the solution algorithm is based on a convected coordinate description of the governing equations lagrangian in character with both newton equilibrium iterations and a stress integration algorithm to improve accuracy

an smt based approach to satisfiability checking of mitl we present a satisfiability preserving reduction from mitl interpreted over finitely variable continuous behaviors to constraint ltl over clocks a variant of cltl that is decidable and for which an smt based bounded satisfiability checker is available the result is a new complete and effective decision procedure for mitl although decision procedures for mitl already exist the automata based techniques they employ appear to be very difficult to realize in practice and to the best of our knowledge no implementation currently exists for them a prototype tool for mitl based on the encoding presented here has instead been implemented and is publicly available

exact one sided confidence limits for the difference between two correlated proportions we construct exact and optimal one sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well established optimality theory of buehler starting with five different approximate lower and upper limits we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use

interval estimation of the density of organisms using a serial dilution experiment summary the serial dilution assay is a standard microbiological method for estimating the density of organisms in a solution the commonly used interval estimation procedures of woodward and deman are described and compared a new method for the calculation of two sided confidence intervals which is superior to the standard procedures is presented the computations are illustrated for a decimal dilution assay with three samples at each of three dilutions

comparative analysis of two rates in this paper we examine comparative analysis of rates with a view to each of the usual comparative parameters rate difference rd rate ratio rr and odds ratio or and with particular reference to first principles for rd and rr we show the prevailing statistical practices to be rather poor we stress the need for restricted estimation of variance in the chi square function underlying interval estimation and also point estimation and hypothesis testing for rr analysis we propose a chi square formulation analogous to that for rd and thus one which obviates the present practice of log transformation and its associated use of taylor series approximation of the variance as for or analysis we emphasize that the chi square function introduced by cornfield for unstratified data and extended by gart to the case of stratified analysis is based on the efficient score and thus embodies its optimality properties we provide simulation results to evince the better performance of the proposed parameter constrained procedures over the traditional ones

entropic thermoelasticity at finite strains aspects of the formulation and numerical implementation abstract this paper presents a formulation of isotropic finite strain thermoelasticity and addresses some aspects of its numerical implementation on the theoretical side a eulerian setting of isotropic thermoelasticity is discussed based on the finger tensor as a strain measure novel aspects are a direct representation of the eulerian thermoelastic moduli in terms of the finger tensor and a rigorous decomposition of the thermoelastic response functions into decoupled volumetric and isochoric contributions based on a multiplicative split of the finger tensor into spherical and unimodular parts an algorithmic procedure for the computation of the stress and thermoelastic moduli based on a representation of the free energy in terms of eigenvalues of the unimodular part of the finger tensor is developed and applied to model problems of strictly entropic and modified entropic thermoelasticity furthermore two algorithms for the solution of the coupled problem are discussed based on operator splits of the global field equations of thermoelasticity the paper concludes with some representative numerical simulations of thermoelastic processes in rubber like materials

interval estimation for the difference between independent proportions comparison of eleven methods several existing unconditional methods for setting confidence intervals for the difference between binomial proportions are evaluated computationally simpler methods are prone to a variety of aberrations and poor coverage properties the closely interrelated methods of mee and miettinen and nurminen perform well but require a computer program two new approaches which also avoid aberrations are developed and evaluated a tail area profile likelihood based method produces the best coverage properties but is difficult to calculate for large denominators a method combining wilson score intervals for the two proportions to be compared also performs well and is readily implemented irrespective of sample size

interval estimation of binomial proportion in clinical trials with a two stage design generally a two stage design is employed in phase ii clinical trials to avoid giving patients an ineffective drug if the number of patients with significant improvement which is a binomial response is greater than a pre specified value at the first stage then another binomial response at the second stage is also observed this paper considers interval estimation of the response probability when the second stage is allowed to continue two asymptotic interval estimators wald and score as well as two exact interval estimators clopper pearson and sterne are constructed according to the two binomial responses from this two stage design where the binomial response at the first stage follows a truncated binomial distribution the mean actual coverage probability and expected interval width are employed to evaluate the performance of these interval estimators according to the comparison results the score interval is recommended for both simon s optimal and minimax designs

optimal and most exact confidence intervals for person parameters in item response theory models the common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter is normally distributed however this approximation is often inadequate for short and medium test lengths as a result the coverage probabilities fall below the given level of significance in many cases and therefore the corresponding intervals are no longer confidence intervals in terms of the actual definition in the present work confidence intervals are defined more precisely by utilizing the relationship between confidence intervals and hypothesis testing two approaches to confidence interval construction are explored that are optimal with respect to criteria of smallness and consistency with the standard approach

score and profile likelihood confidence intervals for contingency table parameters a straightforward approach to computing score and profile likelihood confidence intervals for contingency table parameters is described the computational approach herein avoids two main limitations of existing methods 1 compared with existing methods this paper s approach is applicable to a much broader class of parameters 2 unlike existing methods this paper s approach is not case specific and hence lends itself to a general yet very simple computational algorithm this paper describes the sliding quadratic computational algorithm and illustrates its use on examples that have not been previously considered in the literature a small scale simulation study highlights the advantage of using score and profile likelihood intervals rather than wald intervals

approximate confidence intervals for the parameters of a stationary binary markov chain the power divergence family of test statistics introduced by cressie and read 1984 is used to obtain approximate confidence intervals for the parameters of a stationary first order binary markov chain intervals based on inverting the likelihood ratio pearson and freeman tukey statistics are included in this family small sample comparisons are used to select the best intervals for the different parameters the results show that the best power divergence intervals for the probability of success and in particular the likelihood ratio interval have error rates closer to nominal levels than the sample proportion based intervals suggested by crow 1979 the properties of power divergence joint confidence regions for the transition probabilities are also explored

confidence intervals from the difference between two correlated proportions abstract when data arise as matched binary pairs it is often of interest to test whether or not the probabilities of an odd pair of each type are equal construction of a small sample confidence interval for the difference in these probabilities is more difficult and either approximate or conservative methods need be resorted to two methods are suggested in this article one a natural asymptotic method and the other a more generally applicable conservative method the coverage probability and average width are studied for small and moderate sample sizes

decidable metric logics the common metric temporal logic for continuous time were shown to be insufficient when it was proved that they cannot express a modality suggested by pnueli moreover no finite temporal logic can express all the natural generalizations of this modality it followed that if we look for an optimal decidable metric logic we must accept infinitely many modalities or adopt a different formalism here we identify a fragment of the second order monadic logic of order with the 1 function that expresses all the pnueli modalities and much more its main advantage over the temporal logics is that it enables us to say not just that within prescribed time there is a point where some punctual event will occur but also that within prescribed time some process that starts now or that started before or that will start soon will terminate we prove that this logic is decidable with respect to satisfiability and validity over continuous time the proof depends heavily on the theory of compositionality in particular every temporal logic that has truth tables in this logic is automatically decidable we extend this result by proving that any temporal logic that has all its modalities defined by means more general than truth tables in a logic stronger than the one just described has a decidable satisfiability problem we suggest that this monadic logic can be the framework in which temporal logics can be safely defined with the guarantee that their satisfiability problem is decidable

ensemble confidence intervals for binomial proportions we propose two measures of performance for a confidence interval for a binomial proportion p the root mean squared error and the mean absolute deviation we also devise a confidence interval for p based on the actual coverage function that combines several existing approximate confidence intervals this ensemble confidence interval has improved statistical properties over the constituent confidence intervals software in an r package which can be used in devising and assessing these confidence intervals is available on cran

the accuracy of approximate intervals for a binomial parameter abstract this article considers the uniform convergence of the coverage probabilities of some approximate confidence intervals for the binomial parameter p induced by central limit arguments a uniform upper bound on the coverage probabilities of any such interval obtained by transformation of the sample proportion pcirc n is derived the coverage probability of the interval induced by the arcsine transformation turns out to be very close to the upper bound replacing pcirc n by the bayes estimate x n 2 for some however gives even better uniform asymptotic properties the choice z 2 2 is recommended where z is the 1 th quantile of the standard normal distribution with such numerical results show that this interval is satisfactory even in the uniform sense since it possesses uniform asymptotic coefficients that are very close to the nominal ones furthermore the best k for of the form kz 2 such that the uniform asymptotic coefficient is as close to the nomin

timer formulas and decidable metric temporal logic we define a quantitative temporal logic that is based on a simple modality within the framework of monadic predicate logic its canonical model is the real line and not an w sequence of some type it can be interpreted either by behaviors with finite variability or by unrestricted behaviors for finite variability models it is as expressive as any logic suggested in the literature for unrestricted behaviors our treatment is new in both cases we prove decidability and complexity bounds using general theorems from logic and not from automata theory the technical proof uses a sublanguage of the metric monadic logic of order the language of timer normal form formulas metric formulas are reduced to timer normal form and timer normal form formulas allow elimination of the metric

two sided confidence intervals for the single proportion comparison of seven methods simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals criteria appropriate to the evaluation of various proposed methods include closeness of the achieved coverage probability to its nominal value whether intervals are located too close to or too distant from the middle of the scale expected interval width avoidance of aberrations such as limits outside 0 1 or zero width intervals and ease of use whether by tables software or formulae seven methods for the single proportion are evaluated on 96 000 parameter space points intervals based on tail areas and the simpler score methods are recommended for use in each case methods are available that aim to align either the minimum or the mean coverage with the nominal 1 alpha

anisotropic additive plasticity in the logarithmic strain space modular kinematic formulation and implementation based on incremental minimization principles for standard materials the paper presents a modular formulation and computational implementation of a class of anisotropic plasticity models at finite strains based on incremental minimization principles the modular kinematic setting consists of a constitutive model in the logarithmic strain space that is framed by a purely geometric pre and postprocessing on the theoretical side the point of departure is an a priori six dimensional approach to finite plasticity based on the notion of a plastic metric in a first step a geometric preprocessor defines a total and a plastic logarithmic strain measure obtained from the current and the plastic metrics respectively in a second step these strains enter in an additive format a constitutive model of anisotropic plasticity that may have a structure identical to the geometrically linear theory the model defines the stresses and consistent tangents work conjugate to the logarithmic strain measure in a third step these objects of the logarithmic space are then mapped back to nominal lagrangian or eulerian objects by a geometric postprocessor this geometric three step approach defines a broad class of anisotropic models of finite plasticity directly related to counterparts of the geometrically linear theory it is specified to a model problem of anisotropic metal plasticity on the computational side we develop an incremental variational formulation of the above outlined constitutive structure where a quasi hyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables it is shown that this minimization problem is exclusively restricted to the logarithmic strain space in a structure identical to the small strain theory the minimization problem determines the internal state of the material for finite increments of time we develop a discrete formulation in terms of just one scalar parameter for the amount of incremental flow the existence of the incremental stress potential provides a natural basis for the definition of the geometric postprocessor based on function evaluations furthermore the global initial boundary value problem of the elastic plastic solid appears in the incremental setting as an energy minimization problem numerical examples show that the results obtained are surprisingly close to those obtained by a reference framework of multiplicative plasticity