additive conjoint isotonic probabilistic models adisop the isop model or model of twodimensional or bi isotonicity scheiblechner 1995 postulates that the probabilities of ordered response categories increase isotonically in the order of subject ability and item easiness adding a conventional cancellation axiom for the factors of subjects and items gives the adisop model where the c d f s of response categories are functions of an additive item and subject parameter and an ordinal category parameter extending cancellation to the interactions of subjects and categories as well as of items and categories independence axiom of the category factor from the subject and item factor gives the cadisop model completely additive model in which the parallel c d f s are functions of the sum of subject item and category parameters the cadisop model is very close to the unidimensional version of the polytomous rasch model with the logistic item category characteristic s replaced by nonparametric axioms and statistics the axioms representation theorems and algorithms for model fitting of the additive models are presented

the optimal p version approximation of singularities on polyhedra in the boundary element method we consider elliptic boundary value problems on three dimensional polyhedral domains we describe the three types of singular components that arise in the solution edge vertex and edge vertex singularities we analyze the approximation of the traces of each of each of these different types of singularities by polynomial subspaces on the boundary as the polynomial degree p tends to infinity the p version we establish asymptotic rates of convergence that are optimal in the h t norm over the boundary for 0 leq t leq 1 we apply these results to a galerkin boundary element method bem formulation for a model neumann problem obtaining the optimal convergence rate for the p version bem over polyhedral domains

a nonparametric approach for assessing latent trait unidimensionality assuming a nonparametric family of item response theory models a theory based procedure for testing the hypothesis of unidimensionality of the latent space is proposed the asymptotic distribution of the test statistic is derived assuming unidimensionality thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait based upon a new notion of dimensionality the test is shown to have asymptotic power 1 a 6300 trial monte carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice

the p version of the boundary element method for weakly singular operators on piecewise plane open surfaces we study piecewise polynomial approximations in negative order sobolev norms of singularities which are inherent to neumann data of elliptic problems of second order in polyhedral domains the worst case of exterior crack problems in three dimensions is included as an application we prove an optimal a priori error estimate for the p version of the bem with weakly singular operators on polyhedral lipschitz surfaces and piecewise plane open screens

exponential convergence of the hp version for the boundary element method on open surfaces we analyze the boundary element galerkin method for weakly singular and hypersingular integral equations of the first kind on open surfaces we show that the hp version of the galerkin method with geometrically refined meshes converges exponentially fast for both integral equations the proof of this fast convergence is based on the special structure of the solutions of the integral equations which possess specific singularities at the corners and the edges of the surface we show that these singularities can be efficiently approximated by piecewise tensor products of splines of different degrees on geometrically graded meshes numerical experiments supporting these results are presented

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

assessing the correspondence of one or more vectors to a symmetric matrix using ordinal regression a statistical model for interpreting psychological scaling research based on the heuristic work of reynolds 1983 is developed this new approach has certain advantages over the standard property fitting approach chang and carroll 1969 currently used to interpret multidimensional scaling spaces shepard 1962 torgerson 1965 these advantages are a the ability to directly assess the correspondence of a descriptor vector s to a symmetric matrix and b to provide a method in which only ordinal properties of such descriptors are required thus standard rating ranking or sorting data collection methods can be used as the basis to interpret the multidimensional space resulting from the distance data

the optimal rate of convergence of the p version of the boundary element method in two dimensions we introduce the jacobi weighted besov and sobolev spaces in the one dimensional setting in the framework of these spaces we analyze lower and upper bounds for approximation errors in the p version of the boundary element method for hypersingular and weakly singular integral operators on polygons we prove the optimal rate of convergence for the p version in the energy norms of and respectively

the effect of correlation in false discovery rate estimation the objective of this paper is to quantify the effect of correlation in false discovery rate analysis specifically we derive approximations for the mean variance distribution and quantiles of the standard false discovery rate estimator for arbitrarily correlated data this is achieved using a negative binomial model for the number of false discoveries where the parameters are found empirically from the data we show that correlation may increase the bias and variance of the estimator substantially with respect to the independent case and that in some cases such as an exchangeable correlation structure the estimator fails to be consistent as the number of tests becomes large

the optimal convergence rate of the p version of the finite element method optimal error estimates for the p version of the finite element method in two dimensions are proven for the case when u in h k omega or u has singularities induced by the corners of the domain the case of nonhomogenous essential boundary conditions is also analyzed

a response model for multiple choice items in the mid 1960s samejima initiated the development of item response models that involve separate response functions for all of the alternatives in the multiple choice and likert type formats her work in this area began at the educational testing service and continued during a visit to the l l thurstone psychometric laboratory at the university of north carolina both samejima s 1969 this volume original model for graded item responses and bock s 1972 this volume model for nominal responses were originally intended to produce response functions for all of the alternatives of multiple choice items for various reasons neither model has proved entirely satisfactory for that purpose although both have been applied in other contexts using a combination of ideas suggested by bock 1972 and samejima 1968 1979 a multiple choice model was developed that produces response functions that fit unidimensional multiple choice tests better thissen and steinberg 1984 that model is the subject of this chapter

ordinal consistency and ordinal true scores this paper argues that test data are ordinal that latent trait scores are only determined ordinally and that test data are used largely for ordinal purposes therefore it is desirable to develop a test theory based only on ordinal assumptions a set of ordinal assumptions is presented including an ordinal version of local independence from these assumptions it is first shown that the gamma correlation between two tests is the product of their gamma correlations with the true latent order the theory is generalized to allow for heterogeneous tests by defining a weighted average local independence the tau correlations between total score and the latent order can be found in both homogeneous and heterogeneous cases and a system of differential item weighting to maximize the tau correlation between weighted items and the latent order is provided thus a purely ordinal test theory seems possible

variance of the number of false discoveries summary in high throughput genomic work a very large number d of hypotheses are tested based on n d data samples the large number of tests necessitates an adjustment for false discoveries in which a true null hypothesis was rejected the expected number of false discoveries is easy to obtain dependences between the hypothesis tests greatly affect the variance of the number of false discoveries assuming that the tests are independent gives an inadequate variance formula the paper presents a variance formula that takes account of the correlations between test statistics that formula involves o d2 correlations and so a naive implementation has cost o nd2 a method based on sampling pairs of tests allows the variance to be approximated at a cost that is independent of d

analysis of particle interaction in particle swarm optimization in this paper we analyze the behavior of particle swarm optimization pso on the facet of particle interaction we firstly propose a statistical interpretation of particle swarm optimization in order to capture the stochastic behavior of the entire swarm based on the statistical interpretation we investigate the effect of particle interaction by focusing on the social only model and derive the upper and lower bounds of the expected particle norm accordingly the lower and upper bounds of the expected progress rate on the sphere function are also obtained furthermore the sufficient and necessary condition for the swarm to converge is derived to demonstrate the pso convergence caused by the effect of particle interaction

on the dirichlet problem in elasticity for a domain exterior to an arc abstract we consider here a dirichlet problem for the two dimensional linear elasticity equations in the domain exterior to an open arc in the plane it is shown that the problem can be reduced to a system of boundary integral equations with the unknown density function being the jump of stresses across the arc existence uniqueness as well as regularity results for the solution to the boundary integral equations are established in appropriate sobolev spaces in particular asymptotic expansions concerning the singular behavior for the solution near the tips of the arc are obtained by adding special singular elements to the regular splines as test and trial functions an augmented galerkin procedure is used for the corresponding boundary integral equations to obtain a quasi optimal rate of convergence for the approximate solutions

the dutch identity a new tool for the study of item response models the dutch identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions irfs and the latent trait distribution the identity may be exploited in several ways for example a to suggest how item response models behave for large numbers of items they are approximate submodels of second order loglinear models for 2 j tables b to suggest new ways to assess the dimensionality of the latent trait principle components analysis of matrices composed of second order interactions from loglinear models c to give insight into the structure of latent class models and d to illuminate the problem of identifying the irfs and the latent trait distribution from sample data

isotonic ordinal probabilistic models isop the concept of an ordinal instrumental probabilistic comparison is introduced it relies on an ordinal scale given a priori and on the concept of stochastic dominance it is used to define a weakly independently ordered system or isotonic ordinal probabilistic isop model which allows the construction of separate sample free ordinal scales on a set of subjects and a set of items the isop model is a common nonparametric theoretical structure for unidimensional models for quantitative ordinal and dichotomous variables

discrete dispersion relation for hp version finite element approximation at high wave number the dispersive properties of high order finite element schemes are analyzed in the setting of the helmholtz equation and an explicit form of the discrete dispersion relation is obtained for elements of arbitrary order it is shown that the numerical dispersion displays three different types of behavior depending on the size of the order of the method relative to the mesh size and the wave number quantitative estimates are obtained for the behavior and rates of decay of the dispersion error in the differing regimes all estimates are fully explicit and are shown to be sharp limits are obtained where transitions between the different regimes occur and used to provide guidelines for the selection of the mesh size and the polynomial order in terms of the wave number so that the dispersion error is controlled

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

optimal estimates for lower and upper bounds of approximation errors in the p version of the finite element method in two dimensions this paper will analyze the lower and upper error bounds of the finite element solution of the p version for linear elliptic problems in polygonal domains the optimal rate of convergence is rigorously proved based on the sharp estimates of lower and upper bounds of the approximation error

a stochastic process approach to false discovery control this paper extends the theory of false discovery rates fdr pioneered by benjamini and hochberg j roy statist soc ser b 57 1995 289 300 we develop a framework in which the false discovery proportion fdp the number of false rejections divided by the number of rejections is treated as a stochastic process after obtaining the limiting distribution of the process we demonstrate the validity of a class of procedures for controlling the false discovery rate the expected fdp we construct a confidence envelope for the whole fdp process from these envelopes we derive confidence thresholds for controlling the quantiles of the distribution of the fdp as well as controlling the number of false discoveries we also investigate methods for estimating the p value distribution

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

a new item response theory modeling approach with applications to unidimensionality assessment and ability estimation using an infinite item test framework it is argued that the usual assumption of local independence be replaced by a weaker assumption essential independence a fortiori the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriatestatistically testable assumption of essential unidimennsionality essential unidimennsionnality implies the existence of a unique unidimensional latent ability essential unidimensionality is equivalent to the consistent estimation of this latnet ability in an ordinal scaling sense using anybalanced empirical scaling a variation of this estimation approach allows consistent estimation of ability on the given latent ability scale

some standard errors in item response theory the mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for some common situations it is shown that the maximum likelihood estimation of a lower asymptote can wreak havoc with the accuracy of estimation of a location parameter indicating that if one needs to have accurate estimates of location parameters say for purposes of test linking equating or computerized adaptive testing the sample sizes required for acceptable accuracy may be unattainable in most applications it is suggested that other estimation methods be used if the three parameter model is applied in these situations

ordinal test fidelity estimated by an item sampling model a test theory using only ordinal assumptions is presented it is based on the idea that the test items are a sample from a universe of items the sum across items of the ordinal relations for a pair of persons on the universe items is analogous to a true score using concepts from ordinal multiple regression it is possible to estimate the tau correlations of test items with the universe order from the taus among the test items these in turn permit the estimation of the tau of total score with the universe it is also possible to estimate the odds that the direction of a given observed score difference is the same as that of the true score difference the estimates of the correlations between items and universe and between total score and universe are found to agree well with the actual values in both real and artificial data

on the convergence of the p version of the boundary element galerkin method abstract the authors consider various physical problems which may be formulated in terms of integral equations of the first kind including the two dimensional screen neumann and dirichlet problems in acoustics and crack problems in elasticity sharp regularity results for the solutions are available for these problems proven is the convergence of the p version for some galerkin boundary element schemes based on the integral equation formulations it is shown that the rate of convergence obtained by our method is twice that for the usual h version

radial basis functions for the solution of hypersingular operators on open surfaces we analyze the approximation by radial basis functions of a hypersingular integral equation on an open surface in order to accommodate the homogeneous essential boundary condition along the surface boundary scaled radial basis functions on an extended surface and lagrangian multipliers on the extension are used we prove that our method converges quasi optimally approximation results for scaled radial basis functions indicate that for highly regular radial basis functions the achieved convergence rates are close to the one of low order conforming boundary element schemes numerical experiments confirm our conclusions

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

new global optima results for the kauffman nk model handling dependency the kauffman nk model has been used in theoretical biology physics and business organizations to model complex systems with interacting components this paper presents new global optima results for the nk model by developing tools for handling dependency in the cases where k grows with n this generalizes the previous work that focused on the analysis of the independent case k n 1 a dependency graph is defined and studied to handle dependencies among underlying random variables in the nk model order statistics with dependencies and the expected value of the global optima e n k are bounded using equitable coloring of the dependency graph these bounds convert the problem of bounding order statistics of dependent random variables into that of independent random variables while incorporating quantitative information about the mutual dependencies between the underlying random variables an alternative upper bound on e n k using direct arguments is also proposed a detailed analysis of e n k for k close to n k n and k n z 0 1 is given for underlying uniform and normal distributions finally for bounded underlying distributions the global optima is shown to be concentrated around its mean e n k

gaussian estimation for correlated binomial data summary the mean variance structure of correlated binomial data is discussed and whittle s 1961 gaussian estimation is suggested as a useful general method in this context comparisons are made with other monrent methods in current use