survival analysis using a scale change random effects model abstract frailty models are effective in broadening the class of survival models and inducing dependence in multivariate survival distributions in proportional hazards the random effect multiplies the hazard function the scale change model incorporates unobserved heterogeneity through a random effect that enters the baseline hazard function to change the time scale we interpret this random effect as frailty or other unobserved risks that create heterogeneity in the population this model produces a wide range of shapes for univariate survival and hazard functions we extend this model to multivariate survival data by assuming that members of a group share a common random effect this structure induces association among the survival times in a group and provides alternative association structures to the proportional hazards frailty model we present parametric and semiparametric estimation techniques and illustrate these methods with an example

semiparametric inference in a model for association in bivanate survival data summary clayton s 1978 model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem that is a problem where inference about a parameter is required in the presence of nuisance functions we derive the asymptotic variance of clayton s estimator obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship some comparisons are made with results derived by oakes 1982 for other estimators within this model in the absence of censoring the exact null variance of the score statistic corresponding to clayton s estimator is derived and compared with that of the locally most powerful rank test given by cuzick 1982

local dependence functions for some families of bivariate distributions and total positivity the purpose of this paper is to investigate a very useful application of a certain local dependence function c f x y which was considered recently by holland and wang 20 an interesting property of c f x y is that the underlying joint density f x y is tp 2 that is totally positive of order 2 if and only if c f x y 0 this gives an elegant way to investigate the tp 2 property of any bivariate distribution for the saramanov family the ali mikhail haq family of bivariate distributions and the family of bivariate elliptical distributions we derive the local dependence function and obtain conditions for f x y to be tp 2 these families are quite rich and include many other large classes of bivariate distributions as their special cases similar conditions are obtained for bivariate distributions with exponential conditionals and bivariate distributions with pareto conditionals

inferring a possibility distribution from empirical data several transformations from probabilities to possibilities have been proposed in particular dubois and prade s procedure produces the most specific possibility distribution among the ones dominating a given probability distribution in this paper this method is generalized to the case where the probabilities are unknown the only information being a data sample represented by a histogram it is proposed to characterize the probabilities of the different classes by simultaneous confidence intervals with a given confidence level email protected from this imprecise specification a procedure for constructing a possibility distribution is described insuring that the resulting possibility distribution will dominate the true probability distribution in at least 100 email protected of the cases finally a simple efficient algorithm is given which makes the computations tractable even if the number of classes is high

nonparametric estimation of the concordance correlation coefficient under univariate censoring assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects lin s 1989 biometrics 45 255 268 concordance correlation coefficient ccc has become a popular measure of agreement for correlated continuous outcomes however commonly used estimation methods for the ccc do not accommodate censored observations and are therefore not applicable for survival outcomes in this article we estimate the ccc nonparametrically through the bivariate survival function the proposed estimator of the ccc is proven to be strongly consistent and asymptotically normal with a consistent bootstrap variance estimator furthermore we propose a time dependent agreement coefficient as an extension of lin s 1989 ccc for measuring the agreement between survival times among subjects who survive beyond a specified time point a nonparametric estimator is developed for the time dependent agreement coefficient as well it has the same asymptotic properties as the estimator of the ccc simulation studies are conducted to evaluate the performance of the proposed estimators a real data example from a prostate cancer study is used to illustrate the method

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

on the concept of possibility probability consistency both probability and possibility may be seen as information about an experiment it is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once in this paper some aspects of the concept of possibility probability consistency are studied the consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information we analyse several measures of the degree of consistency and introduce an axiomatic to characterize them

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

dealing with uncertainties in engineering problems using only available data abstract this paper is the second in the series of three addressing the problem of how to deal with uncertainties in the modelings of engineering problems using only available data the problem of the heat exchanger was selected as the example because it is sufficiently complex but still simple so that the difficulties and ideas will be apparent there are various theories on how to treat the uncertainties in the first paper in the series we use only the fuzzy set respectively the possibility theory in this paper we use the fuzzy approach for some model parameters and the probability approach for the others the third paper will use the bayesian theory

second order convected particle domain interpolation cpdi2 with enrichment for weak discontinuities at material interfaces summary convected particle domain interpolation cpdi is a recently developed extension of the material point method in which the shape functions on the overlay grid are replaced with alternative shape functions which by coupling with the underlying particle topology facilitate efficient and algorithmically straightforward evaluation of grid node integrals in the weak formulation of the governing equations in the original cpdi algorithm herein called cpdi1 particle domains are tracked as parallelograms in 2 d or parallelepipeds in 3 d in this paper the cpdi method is enhanced to more accurately track particle domains as quadrilaterals in 2 d hexahedra in 3 d this enhancement will be referred to as cpdi2 not only does this minor revision remove overlaps or gaps between particle domains it also provides flexibility in choosing particle domain shape in the initial configuration and sets a convenient conceptual framework for enrichment of the fields to accurately solve weak discontinuities in the displacement field across a material interface that passes through the interior of a grid cell the new cpdi2 method is demonstrated with and without enrichment using one dimensional and two dimensional examples copyright 2013 john wiley sons ltd

quantile association for bivariate survival data bivariate survival data arise frequently in familial association studies of chronic disease onset as well as in clinical trials and observational studies with multiple time to event endpoints the association between two event times is often scientifically important in this article we examine the association via a novel quantile association measure which describes the dynamic association as a function of the quantile levels the quantile association measure is free of marginal distributions allowing direct evaluation of the underlying association pattern at different locations of the event times we propose a nonparametric estimator for quantile association as well as a semiparametric estimator that is superior in smoothness and efficiency the proposed methods possess desirable asymptotic properties including uniform consistency and root n convergence they demonstrate satisfactory numerical performances under a range of dependence structures an application of our methods suggests interesting association patterns between time to myocardial infarction and time to stroke in an atherosclerosis study

a particle method for history dependent materials abstract a broad class of engineering problems including penetration impact and large rotations of solid bodies causes severe numerical problems for these problems the constitutive equations are history dependent so material points must be followed this is difficult to implement in a eulerian scheme on the other hand purely lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables a process which can introduce errors proposed here is an extension of the particle in cell method in which particles are interpreted to be material points that are followed through the complete loading process a fixed eulerian grid provides the means for determining a spatial gradient because the grid can also be interpreted as an updated lagrangian frame the usual convection term in the acceleration associated with eulerian formulations does not appear with the use of maps between material points and the grid the advantages of both eulerian and lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced also it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity

constructing membership functions using statistical data abstract determination of the membership functions is vital in practical applications of the fuzzy set theory this paper presents a guideline to construct the membership functions for fuzzy sets whose elements have a defining feature with a known probability density function pdf in the universe of discourse the method finds the smallest fuzzy set which assigns high average membership values to those objects with the defining features distributed according to the given pdf it is show that for any pdf the method is capable of generating membership functions in accordance with the possibility probability consistency principle membership functions derived from some of the well known pdfs and an application in solving noise contaminated linear system of equations are presented

some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates abstract recurrent event time data are common in medical research examples include infections in aids patients and seizures in epilepsy patients in this context as well as in the more usual context of a single failure time variable time dependent covariates are frequently of interest we suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time dependent covariate is of interest estimators of these functions are provided along with two sample test statistics a new approach to regression modeling of these data is suggested and contrasted with existing methods our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual this is in line with the currently popular generalized estimating equation approach to longitudinal data if the nature of such associations is known or is of particular interest then alternative methods may be appropriate

a copula based mixed poisson model for bivariate recurrent events under event dependent censoring in many chronic disease processes subjects are at risk of two or more types of events we describe a bivariate mixed poisson model in which a copula function is used to model the association between two gamma distributed random effects the resulting model is a bivariate negative binomial process in which each type of event arises from a negative binomial process methods for parameter estimation are described for parametric and semiparametric models based on an em algorithm we also consider the issue of event dependent censoring based on one type of event which arises when one event is sufficiently serious that its occurence may influence the decision of whether to withdraw a patient from a study the asymptotic biases of estimators of rate and mean functions from naive marginal analyses are discussed as well as associated treatment effects because the joint model is fit based on a likelihood consistent estimates are obtained simulation studies are carried out to evaluate the empirical performance of the proposed estimators with independent and event dependent censoring and applications to a trial of breast cancer patients with skeletal metastases and a study of patients with chronic obstructive pulmonary disease illustrate the approach

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

a convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations summary a new algorithm is developed to improve the accuracy and efficiency of the material point method for problems involving extremely large tensile deformations and rotations in the proposed procedure particle domains are convected with the material motion more accurately than in the generalized interpolation material point method this feature is crucial to eliminate instability in extension which is a common shortcoming of most particle methods also a novel alternative set of grid basis functions is proposed for efficiently calculating nodal force and consistent mass integrals on the grid specifically by taking advantage of initially parallelogram shaped particle domains and treating the deformation gradient as constant over the particle domain the convected particle domain is a reshaped parallelogram in the deformed configuration accordingly an alternative grid basis function over the particle domain is constructed by a standard 4 node finite element interpolation on the parallelogram effectiveness of the proposed modifications is demonstrated using several large deformation solid mechanics problems copyright 2011 john wiley sons ltd

on data based estimation of possibility distributions abstract in this paper we show how a possibilistic description of uncertainty arises very naturally in statistical data analysis in combination with recent results in inverse uncertainty propagation and the consistent aggregation of marginal possibility distributions this estimation procedure enables a very general approach to possibilistic identification problems in the framework of imprecise probabilities i e the non parametric estimation of possibility distributions of uncertain variables from data with a clear interpretation

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

semiparametric modelling and estimation of covariate adjusted dependence between bivariate recurrent events a time dependent measure termed the rate ratio was proposed to assess the local dependence between two types of recurrent event processes in one sample settings however the one sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received the focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events we propose the covariate adjusted rate ratio a measure of covariate adjusted dependence we propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure we develop a pseudo partial likelihood to estimate the parameters in the proportional rate ratio model we establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies we illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

time dependent association measures for bivariate survival distributions abstract we propose time dependent association measures for application to bivariate survival analysis such association measures provide informative summaries for data on twins ophthalmic and auditory studies and for other matched pair designs we develop several desirable properties of time dependent association measures and study three measures motivated by these properties we examine the measures from a general bivariate survival perspective and for the proportional hazards frailty model we use monozygotic mz and dizygotic dz twin data from the danish twin registry to illustrate how these measures depend on the specification of the proportional hazards frailty model this model consists of two components a baseline hazard function and a frailty distribution we produce gamma and nonparametric maximum likelihood estimates of the frailty distribution and estimate a gompertz baseline hazard function for two of the measures a nonparametric estimate provides a comparison to the model based estim

estimating load sharing properties in a dynamic reliability system an estimator for the load share parameters in an equal load share model is derived based on observing k component parallel systems of identical components that have a continuous distribution function f and failure rate r in an equal load share model after the first of k components fails failure rates for the remaining components change from r t to 1r t then to 2r t after the next failure and so on on the basis of observations on n independent and identical systems a semiparametric estimator of the component baseline cumulative hazard function r log 1 f is presented and its asymptotic limit process is established to be a gaussian process the effect of estimation of the load share parameters is considered in the derivation of the limiting process potential applications can be found in diverse areas including materials testing software reliability and power plant safety assessment

simultaneous confidence intervals and sample size determination for multinomial proportions abstract simultaneous confidence interval procedures for multinomial proportions are used in many areas of science in this article two new simultaneous confidence interval procedures are introduced numerical results are presented to evaluate these procedures and compare their performance with established methods that have been used in statistical literature from the results presented in this article it is evident that the new procedures are more accurate than the established ones where the accuracy of the procedure is measured by the volume of the confidence region corresponding to the nominal coverage probability and the probability of coverage it achieves in the sample size determination problem the new procedures provide a sizable amount of savings as compared to the procedures that have been used in many applications because both procedures performed equally well the procedure that requires the least amount of computing time is recommended

fuzzy sets and statistical data abstract specific features of probability and possibility theories are discussed with emphasis on semantical aspects instead of putting forward the acknowledged usefulness of possibility theory for the non statistical modelling of subjective categories we try to figure out how statistical data and possibility theory could be matched as a result procedures for constructing weak possibilistic substitutes of probability measures and for processing imprecise statistical data are outlined they provide new insights on relationship between fuzzy sets and probability theories

controlling the onset of numerical fracture in parallelized implementations of the material point method mpm with convective particle domain interpolation cpdi domain scaling the material point method is well suited for large deformation problems in solid mechanics but requires modification to avoid cell crossing errors as well as extension instabilities that lead to numerical nonphysical fracture a promising solution is convected particle domain interpolation cpdi in which the integration domain used to map data between particles and the background grid deforms with the particle based on the material deformation gradient while eliminating the extension instability can be a benefit it is often desirable to allow material separation to avoid nonphysical stretching additionally large stretches in material points can complicate parallel implementation of cpdi if a single particle domain spans multiple computational patches a straightforward modification to the cpdi algorithm allows a user specified scaling of the particle integration domain to control the numerical fracture response which facilitates parallelization combined with particle splitting the method can accommodate materials with arbitrarily large failure strains used with a smeared damage softening model this approach will prevent nonphysical numerical fracture in situations where the material should remain intact but the effect of a single velocity field on localization may still produce errors in the post failure response details are given for both 2 d and 3 d implementations of the scaling algorithm copyright c 2015 john wiley sons ltd

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

fuzzy numbers from raw discrete data using linear regression this paper focuses on modelling fuzzy numbers with meaningful membership functions more precisely it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data in many applications input information is numerical and therefore particular fuzzy sets such as fuzzy numbers hold great interest and relevance in managing data imprecision and vagueness the proposed technique provides an efficient way to obtain trapezoidal numbers using linear regression the technique is simple fast and effective preliminary tests are performed using different types of input data a gaussian function a sigmoidal function three datasets of synthetic discrete data and an histogram obtained from a colour satellite image

model selection and semiparametric inference for bivariate failure time data abstract we propose model selection procedures for bivariate survival models for censored data generated by the archimedean copula family in route to constructing the selection methodology we develop estimates of some time dependent association measures including estimates of the local and global kendall s tau local odds ratio and other measures defined throughout the literature we propose a goodness of fit based model selection methodology as well as a graphical approach we show that the proposed methods have desirable asymptotic properties and perform well in finite samples

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

power and sample size calculation for paired recurrent events data based on robust nonparametric tests the purpose of this paper is to develop a formula for calculating the required sample size for paired recurrent events data the developed formula is based on robust non parametric tests for comparing the marginal mean function of events between paired samples this calculation can accommodate the associations among a sequence of paired recurrent event times with a specification of correlated gamma frailty variables for a proportional intensity model we evaluate the performance of the proposed method with comprehensive simulations including the impacts of paired correlations homogeneous or nonhomogeneous processes marginal hazard rates censoring rate accrual and follow up times as well as the sensitivity analysis for the assumption of the frailty distribution the use of the formula is also demonstrated using a premature infant study from the neonatal intensive care unit of a tertiary center in southern taiwan copyright 2017 john wiley sons ltd

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

nonparametric analysis of an accelerated failure time model summary survival distributions can be characterized by and compared through their hazard functions tests using a proportional hazards model have good power if the two hazards do not cross but without time dependent covariates can have low power if they do the method contained herein is designed to provide a complement to the proportional hazards model differences in survival distributions are parameterized by a scale change and the log rank statistic is used to generate an estimate of the change and a confidence interval based test this approach is fully efficient for the weibull family with no censoring in general it compares favourably with the proportional hazards approach although neither method dominates

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

finitary coalgebraic multisemilattices and multilattices in this paper we continue the coalgebraization of the structure of multilattice specifically we introduce a coalgebraic characterization of the notion of finitary multi semi lattice a generalization of that of semilattice which arises naturally in several areas of computer science and provides the possibility of handling non determinism

a relationship between probability interval and random sets and its application to linear optimization with uncertainties abstract random sets and probability intervals could be represented as uncertain parameters in a linear program however they are not the same this paper presents a method by which an intersection of random sets provides an approximation of a given probability interval two specific random sets generating this approximation are used to construct probability density mass functions that provide the smallest and the largest expected values with respect to the probability interval uncertainty we show that our construction is computationally more efficient than computing directly from probability intervals these results are applied to linear programs with random set and probability interval uncertainties to obtain optimal solutions with respect to pessimistic optimistic and minimax regret approaches

aleatory uncertainty and scale effects in computational damage models for failure and fragmentation summary stress concentrations near grain boundaries precipitates and similar micro heterogeneities nucleate instabilities leading to macroscale fracture as it is not practical to model each flaw explicitly their ensemble effect is modeled statistically accounting for this aleatory uncertainty requires smaller specimens e g small finite elements to have generally higher and more variable strengths which is necessary for the initial failure probability of a finite domain to be unaffected by its discretization into elements localization itself which might be attributed to constitutive instability requires realistic numerical perturbations to predict bifurcations such as radial cracking in axisymmetric problems these perturbations stemming from microscale heterogeneity are incorporated in simulations by imposing statistical spatial variability in the parameters of an otherwise conventional deterministic and scale independent damage model this approach is attractive for its algorithmic simplicity and straightforward calibration from standard strength tests in addition it results in virtually no loss of efficiency or robustness relative to deterministic models and accommodates general three dimensional loading despite these advantages some significant challenges remain and are discussed however it is demonstrated that including aleatory uncertainty with associated scale effects significantly improves predictiveness on large scale computational domains where it is impractical to resolve each crack or localization zone copyright 2014 john wiley sons ltd

quick simultaneous confidence intervals for multinomial proportions abstract opinion polls often give an indication of sampling error based on the standard conservative confidence intervals for a single binomial proportion we give a lower bound for the simultaneous coverage probability when such intervals are applied to all of the proportions in a poll this bound is equal to 1 2 for small values of the same result is shown to apply to the standard confidence intervals for changes in proportions between surveys

on the dependence structure of bivariate recurrent event processes inference and estimation bivariate or multivariate recurrent event processes are often encountered in longitudinal studies in which more than one type of event is of interest there has been much research on regression analysis for such data but little has been done to measure the dependence between recurrent event processes we propose a time dependent measure termed the rate ratio to assess the local dependence between two types of recurrent event processes we model the rate ratio as a parametric function of time and leave unspecified all other aspects of the distribution we develop a composite likelihood procedure for model fitting and parameter estimation we show that the proposed estimator is consistent and asymptotically normal its finite sample performance is evaluated by simulation and illustrated by an application to a soft tissue sarcoma study

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided

fuzzy linear least squares for the identification of possibilistic regression models abstract the stochastic approach to regression e g the least squares method is a commonly used technique in a wide range of disciplines as it offers an intuitive and well founded solution to the problem of fitting a set of parameters to existing data specifically in the case where the parameters of meta models are identified the linear least squares formulation receives wide appreciation among engineers due to its simple yet powerful formulation and solution usually this approach provides a reasonable fit depending largely on the quality of the model that is employed however it has two main drawbacks from a statistical point of view the premises justifying its use cannot always be assumed in good faith and most importantly the resulting model will almost certainly fail at correctly predicting the output without falling victim to the effect of over fitting the presented fuzzy regression algorithm originates from a set of different axioms for the solution of the linear least squares problem it is able to provide the worst case optimal parameter variation necessary to cover all of the crisp data points while encoding meaningful information in the membership function this is accomplished by means of a sensible fuzzification procedure of the crisp data points and the application of an exact inverse fuzzy arithmetic for estimating the fuzzy valued parameters of the model in question

generating linear extensions fast one of the most important sets associated with a poset cal p is its set of linear extensions e cal p this paper presents an algorithm to generate all of the linear extensions of a poset in constant amortized time that is in time o e cp where e cp e cp the fastest previously known algorithm for generating the linear extensions of a poset runs in time o n cdot e cp where n is the number of elements of the poset the algorithm presented here is the first constant amortized time algorithm for generating a naturally defined class of combinatorial objects for which the corresponding counting problem is p complete furthermore it is shown that linear extensions can be generated in constant amortized time where each extension differs from its predecessor by one or two adjacent transpositions the algorithm is practical and can be modified to count linear extensions efficiently and to compute p x y for all pairs x y in time o n 2 e cal p