an upwinding embedded boundary method for maxwell s equations in media with material interfaces 2d case we propose a new upwinding embedded boundary method to solve time dependent maxwell s equations in media with material interfaces a global second order finite difference method is obtained by combining central difference schemes away from the interfaces and upwinding technique with jump conditions near the interfaces the proposed finite difference method allows time step based on a uniform mesh independent of the locations and shapes of the interfaces moreover the scheme is simple to implement in multidimensional cases numerical tests of wave equations with various types of material interfaces and electromagnetic scattering of 2d cylinders confirm the stability uniform accuracy and ease of implementation of the method

order restricted score parameters in association models for contingency tables abstract the row effects and column effects models for two way contingency tables have parameters for the row and column categories pertaining to the association between the variables for classifications having ordered categories it is often reasonable to assume that the association parameters have a corresponding ordering this article proposes order restricted estimates of the association parameters in these models the maximum likelihood solution can be determined by the solution of a simple isotonic regression of some of the model sufficient statistics the models are primarily log linear in form and can be expressed in terms of odds ratios for 2 2 subtables consisting of adjacent rows and adjacent columns for the order restricted solution these local log odds ratios have uniform sign goodness of fit statistics for this solution are related to corresponding statistics for collapsed tables and to statistics for testing equality of sets of the parameters the row effects model discussed in this art

association models and the bivariate normal for contingency tables with ordered categories summary association models considered by goodman 1979 for contingency tables with ordered categories are presented here in a somewhat different form to facilitate comparison with the bivariate normal association models can be applied when an underlying bivariate normal is assumed and also under more general conditions and they provide alternatives to tetrachoric and polychoric correlation these models agree more closely with the bivariate normal than does plackett s model 1965 when the row and column classifications arise from underlying univariate normal distributions the general utility of the association models is illustrated here

the use of a canonical form in the construction of locally optimal designs for non linear problems optimal experimental designs for non linear problems depend on the values of the underlying undknown parameters in the model for various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters this paper shows that for a certain class of generalized linear models the problem can be reduced to a canonical form this simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments

a d optimality based sensitivity test sensitivity tests are often used to estimate the parameters associated with latent continuous variables that cannot be measured for example each explosive specimen has a threshold the specimen will detonate if and only if an applied shock exceeds this value since there is no way to determine the threshold of an individual specimens are tested at various levels to determine parameters of the population a new test described here produces efficient estimates of the parameters of the distribution even with limited prior knowledge this test efficiently characterizes the entire distribution and desired percentiles of any population

designs for generalized linear models with several variables and model uncertainty standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model for example for describing a binary response in terms of several variables a method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function the linear predictor or the model parameters together with a design search designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models exact designs are investigated for two applications and their advantages over factorial and central composite designs are demonstrated

a note on n estimators for the binomial distribution abstract consider k success counts from a binomial distribution with unknown n and success probability p we examine the problem of estimating n by integrating the likelihood for n and p over a beta density for p we obtain the beta binomial distribution resulting in stable and reasonably efficient estimators of n which compare favorably with and are often better than the estimates introduced by olkin et al 1981

testing dependence among serially correlated multicategory variables the contingency table literature on tests for dependence among discrete multicategory variables is extensive standard tests assume however that draws are independent and only limited results exist on the effect of serial dependency a problem that is important in areas such as economics finance medical trials and meteorology this article proposes new tests of independence based on canonical correlations from dynamically augmented reduced rank regressions the tests allow for an arbitrary number of categories as well as multiway tables of arbitrary dimension and are robust in the presence of serial dependencies that take the form of finite order markov processes for three way or higher order tables we propose new tests of joint and marginal independence monte carlo experiments show that the proposed tests have good finite sample properties an empirical application to microeconomic survey data on firms forecasts of changes to their production and prices demonstrates the importance of correcting fo

high order fdtd methods via derivative matching for maxwell s equations with material interfaces this paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high order finite difference time domain fdtd schemes of computational electromagnetics cem with material interfaces in one 1d and two spatial dimensions 2d by making use of fictitious points systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage to arbitrarily high orders of accuracy in principle while often limited by numerical instability orders up to 16 and 12 are achieved respectively in 1d and 2d detailed stability analyses are presented for the present approach to examine the upper limit in constructing embedded fdtd methods as natural generalizations of the high order fdtd schemes the proposed derivative matching methods automatically reduce to the standard fdtd schemes when the material interfaces are absent an interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code another feature of the present approach is that it can be robustly implemented with other high accuracy time domain approaches such as the multiresolution time domain method and the local spectral time domain method to cope with material interfaces numerical experiments on both 1d and 2d problems are carried out to test the convergence examine the stability access the efficiency and explore the limitation of the proposed methods it is found that operating at their best capacity the proposed high order schemes could be over 2000 times more efficient than their fourth order versions in 2d in conclusion the present work indicates that the proposed hierarchical derivative matching methods might lead to practical high order schemes for numerical solution of time domain maxwell s equations with material interfaces

fast computation of designs robust to parameter uncertainty for nonlinear settings experimental design in nonlinear settings is complicated by the fact that the efficiency of a design depends on the unknown parameter values thus good designs need to be efficient over a range of likely parameter values bayesian design criteria provide a natural framework for achieving such robustness by averaging local design criteria over a prior distribution on the parameters a major drawback to the use of such criteria is the heavy computational burden that they impose we present a clever quadrature scheme that greatly improves the feasibility of using bayesian design criteria we illustrate the method on some designed experiments

perturbation theory for anisotropic dielectric interfaces and application to subpixel smoothing of discretized numerical methods we derive a correct first order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted most previous perturbative methods give incorrect results for this case even to lowest order because of the complicated discontinuous boundary conditions on the electric field at such an interface our final expression is simply a surface integral over the material interface of the continuous field components from the unperturbed structure the derivation is based on a localized coordinate transformation technique which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking the limit in which the coordinate perturbation is infinitesimally localized around the boundary not only is our result potentially useful in evaluating boundary perturbations e g from fabrication imperfections in highly anisotropic media such as many metamaterials but it also has a direct application in numerical electromagnetism in particular we show how it leads to a subpixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes

efficient robbins monro procedure for binary data summary the robbins monro procedure does not perform well in the estimation of extreme quantiles because the procedure is implemented using asymptotic results which are not suitable for binary data here we propose a modification of the robbins monro procedure and derive the optimal procedure for binary data under some reasonable approximations the improvement obtained by using the optimal procedure for the estimation of extreme quantiles is substantial

models for the analysis of association in multivariate contingency tables abstract the present work describes a family of models that can be used for the analysis of association in multiway cross classifications the models are complementary to the usual i e the so called hierarchical log linear models an advantage of this family of models is that it is frequently possible to give a more parsimonious description of the association than is possible with the usual log linear models approach the models will be especially useful when some or all of the variables are ordinal the models are derived from a reparameterization of the saturated model based on singular value decompositions of interaction terms in the log linear parameterization multivariate association models given in goodman 1979 1986 clogg 1982a b agresti and kezouh 1983 gilula and haberman 1988 and becker and clogg 1989 are obtained as special cases the utility of the models developed in this article is demonstrated with the analysis of two examples the first example a cross classification of

optimal designs for binary data abstract this article is concerned with the problem of selecting the values of the explanatory variable in logistic regression to obtain likelihood based confidence regions of minimum area one way of finding analytic solutions is by replacing the log likelihood by a quadratic surface around the maximum approximating in this way the likelihood regions by ellipses the optimal allocation for this local approximation is derived without unnecessary restrictions since the implementation of the optimal allocation requires accurate initial estimates a two stage procedure that uses the second stage to complement the first is recommended an alternative approach is to deal directly with the likelihood regions in this case the identification of the globally optimal allocation calls for numerical integration and optimization the results presented here attempt to strengthen those introduced by abdelbasit and plackett 1983 who derived optimal allocation for the local criterion under the restriction of symmet

a stable fdtd algorithm for non diagonal anisotropic dielectrics a stable fdtd algorithm is developed for simulating maxwell s equations in anisotropic dielectric materials with principal axes not aligned with the grid the algorithm is stable because the finite difference operator that converts d to e is symmetric and positive semidefinite for contrast a previously developed asymmetric algorithm is shown to suffer from late time instabilities the presented algorithm has second order error for continuous dielectric materials and the error can be reduced to third order by richardson extrapolation applied to dielectrics with sharp interfaces the algorithm has first order error even when averaging the dielectric within partially filled grid cells however averaging the dielectric permits richardson extrapolation to obtain second order error

bayesian analyses for a multiple capture recapture model summary in multiple capture recapture surveys the probability of capture can vary between sampling occasions the model accounting for this variation is known as at bayes empirical bayes and bayes empirical bayes solutions are given to the problems of interval estimation decision making and point estimation of the population size n when the number of sampling occasions is small to moderate and the number of recaptured units observed on each sampling occasion is moderate estimates obtained from empirical bayes and bayes empirical bayes methods compare closely to bayesian methods using a reference prior distribution for the capture probabilities however when the number of sampling occasions is large and the number of recaptured units observed on each sampling occasion is small inferences obtained using different reference priors can differ considerably

second order procedure for modeling dielectric material interfaces in structured nonorthogonal finite difference discretizations of maxwell s equations structured nonorthogonal finite difference discretizations of maxwell s equations are often employed to incorporate curved dielectric material interfaces as part of this process it is necessary to employ an adequate procedure to enforce the tangential field continuity conditions at the locations of the interfaces where the components of the permittivity tensor are discontinuous this contribution proposes a second order domain splitting procedure that can accomplish this task without assuming that the permittivity tensor components are piecewise constant or diagonal as explained this feature is needed to exploit the full geometrical flexibility of structured grid generation the proposed domain splitting procedure consistently yields a global error that is second order accurate even in extreme cases where the components of the permittivity tensor have a change of sign or a sharp jump

nonlinear experiments optimal design and inference based on likelihood abstract nonlinear experiments involve response and regressors that are connected through a nonlinear regression type structure examples of nonlinear models include standard nonlinear regression logistic regression probit regression poisson regression gamma regression inverse gaussian regression and so on the fisher information associated with a nonlinear experiment is typically a complex nonlinear function of the unknown parameter of interest as a result we face an awkward situation designing an efficient experiment will require knowledge of the parameter but the purpose of the experiment is to generate data to yield parameter estimates our principal objective here is to investigate proper designing of nonlinear experiments that will let us construct efficient estimates of parameters we focus our attention on a very general nonlinear setup that includes many models commonly encountered in practice the experiments considered have two fundamental stages a static design in the initial stage

diagnostics in categorical data analysis diagnostics as measures of model deviations and of the influence of particular data sets are used extensively in modern regression analysis for contingency tables and more generally for the parametric multinomial distribution it is not the influence of individual observations which is of interest but rather the contribution to a lack of model fit or to the values of the parameter estimates from a single cell in the table which must be evaluated hence diagnostics for contingency tables take somewhat different forms

inadmissibility of the maximum likelihood estimator in the sequential estimation of the size of a population summary for the sequential estimation of the size of a finite population the maximum likelihood estimator is a commonly used estimator but has no explicit expression in this paper it is shown that the maximum likelihood estimator is inadmissible an estimator which is simple in form and dominates the maximum likelihood estimator asymptotically is proposed to study the optimality property of the estimator for the stopping rule sb from a decision theoretical approach we investigate the admissibility of the estimator under a general weighted squared error loss function although the maximum likelihood estimator and its risk have no closed form expression the estimator will be shown to be inadmissible by means of a general theorem that we establish later as theorem 2 1 in this paper we only consider the simple capture capture model discussed by samuel 1968 more complex and realistic capture recapture models have been developed subsequently pollack otto 1983 pickands raghavachari 1987 bonett woodward bentler 1987 cormack 1989 huggins 1989 we conjecture that many of the

a method for designing nonlinear univariate calibration a method is proposed for designing nonlinear univariate calibration of measuring instruments the problem addressed is how to select a set of design points standards or calibrators to minimize the errors in the inverse predictions the curve parameters are assumed to vary randomly between calibrations with known expected value and known covariance matrix a design criterion is suggested for analytical procedures according to which the coefficient of variation and the area under the precision profile are minimized

inference for the binomial n parameter a hierarchical bayes approach summary a hierarchical bayes approach to the problem of estimating n in the binomial distribution is presented this provides a simple and flexible way of specifying prior information and also allows a convenient representation of vague prior knowledge it yields solutions to the problems of interval estimation prediction and decision making as well as that of point estimation the bayes estimator compares favourably with the best previously proposed point estimators in the literature unknown parameters n and 0 most of the literature about statistical analysis of this model has focused on point estimation of n while interval estimation prediction and decision making have been little considered see 2 i adopt a hierarchical bayes approach this provides a simple way of specifying prior information and also allows a convenient representation of vague prior knowledge using limiting improper prior forms it leads to solutions of the problems of interval estimation prediction and decision making as well as that of point estimation a difficulty with bayesian analysis of this problem has been the absence of a sufficiently flexible and tractable family of prior distributions mainly due to the fact that n is an integer the present approach gets around this by first assuming that n has a poisson distribution the resulting hyperparameters are then continuous valued and one may use existing results about conjugate and vague priors in better understood settings

a survey of models for repeated ordered categorical response data we survey models for analysing repeated observations on an ordered categorical response variable the models presented are univariate models that permit correlation among repeated measurements the models describe simultaneously the dependence of marginal response distributions on values of explanatory variables and on the occasion of response we present models for three transformations of the response distribution cumulative logits adjacent category logits and the mean for scores assigned to response categories we discuss three methods for fitting the models maximum likelihood weighted least squares and semi parametric weighted least squares is easily implemented with sas as illustrated with a study designed to compare a drug with a placebo for the treatment of insomnia

robust designs for binary data this article is concerned with experimental design of statistical models for binary data since in most commonly used models for binary data the information matrix depends on the unknown parameters the standard optimality criteria used in regression cannot be used what is typically done to avoid this problem is to assume good initial parameter estimates the main purpose of this article is to introduce a minimax procedure for obtaining designs that are robust to poor initial parameter estimates the procedure yields designs with more design points and larger spread if precise knowledge of the parameters is unavailable d optimality and fieller and confidence intervals for the median response dose are used to construct optimality functions for the procedure

analysis of sets of two way contingency tables using association models abstract a class of models is introduced for the analysis of group differences in the association between two discrete variables the rc m association model for two way tables is reviewed and alternative weighting systems for identifying interaction parameters are presented this model is generalized for the setting where a two way contingency table is available for two or more groups various restricted models can be used to examine possible sources of intergroup heterogeneity in the association these sources pertain to heterogeneity in the intrinsic association and or in the scores for the row and column variables the importance of weights used to identify the row and column scores is emphasized a classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here

experimental design for binary data abstract models for binary data are usually such that the information matrix depends on the unknown parameters thus the standard criteria for optimality in regression experiments cannot be applied without modification methods of going around this difficulty include the use of initial point estimates sequential methods and bayesian analysis this article is mainly concerned with the robustness and the number of design points for methods involving initial estimates and for sequential methods in a small number of stages a final section discusses the criterion of constant information for models involving one or two parameters and summarizes recent results in this field

a continuation ratio random effects model for repeated ordinal responses this paper presents methods of analysis for ordinal repeated measures we use a generalization of the continuation ratio model with a random effect we handle frailty by using a normal distribution and also a non parametric distribution the methodology is readily implemented in existing software and flexible enough to treat large data sets with uncommon time measurements as well as different numbers of repeated measures for each individual the models are used to investigate how a group of explanatory variables influences the overall condition of patients treated for breast cancer

finite difference time domain modeling of curved surfaces em scattering the finite difference time domain fdtd method is generalized to include the accurate modeling of curved surfaces this generalization the contour path cp method accurately models the illumination of bodies with curved surfaces yet retains the ability to model corners and edges cp modeling of two dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented

a staggered fourth order accurate explicit finite difference scheme for the time domain maxwell s equations abstract we consider a model explicit fourth order staggered finite difference method for the hyperbolic maxwell s equations appropriate fourth order accurate extrapolation and one sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces an eigenvalue analysis of the overall scheme provides a necessary but not sufficient stability condition and indicates long time stability numerical results verify both the stability analysis and the scheme s fourth order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces for a fixed error level we find the fourth order scheme is computationally cheaper in comparison to the yee scheme by more than an order of magnitude some open problems encountered in the application of such high order schemes are also discussed

modeling continuous response variables using ordinal regression we study the application of a widely used ordinal regression model the cumulative probability model cpm for continuous outcomes such models are attractive for the analysis of continuous response variables because they are invariant to any monotonic transformation of the outcome and because they directly model the cumulative distribution function from which summaries such as expectations and quantiles can easily be derived such models can also readily handle mixed type distributions we describe the motivation estimation inference model assumptions and diagnostics we demonstrate that cpms applied to continuous outcomes are semiparametric transformation models extensive simulations are performed to investigate the finite sample performance of these models we find that properly specified cpms generally have good finite sample performance with moderate sample sizes but that bias may occur when the sample size is small cumulative probability models are fairly robust to minor or moderate link function misspecification in our simulations for certain purposes the cpms are more efficient than other models we illustrate their application with model diagnostics in a study of the treatment of hiv cd4 cell count and viral load 6 months after the initiation of antiretroviral therapy are modeled using cpms both variables typically require transformations and viral load has a large proportion of measurements below a detection limit

a more accurate stable fdtd algorithm for electromagnetics in anisotropic dielectrics a more accurate stable finite difference time domain fdtd algorithm is developed for simulating maxwell s equations with isotropic or anisotropic dielectric materials this algorithm is in many cases more accurate than previous algorithms g r werner et al 2007 5 a f oskooi et al 2009 7 and it remedies a defect that causes instability with high dielectric contrast usually for e 10 with either isotropic or anisotropic dielectrics ultimately this algorithm has first order error in the grid cell size when the dielectric boundaries are sharp due to field discontinuities at the dielectric interface accurate treatment of the discontinuities in the limit of infinite wavelength leads to an asymmetric unstable update c a bauer et al 2011 6 but the symmetrized version of the latter is stable and more accurate than other fdtd methods the convergence of field values supports the hypothesis that global first order error can be achieved by second order error in bulk material with zero order error on the surface this latter point is extremely important for any applications measuring surface fields

blocked designs for experiments with correlated non normal response many experiments measure a response that cannot be adequately described by a linear model with normally distributed errors and are often run in blocks of homogeneous experimental units we develop the first general methods of obtaining efficient blocked designs for experiments with an exponential family response described by a marginal model fitted via generalized estimating equations this methodology is appropriate when the blocking factor is a nuisance variable as often occurs in industrial experiments a d optimality criterion is developed for finding designs robust to the values of the marginal model parameters and applied using two strategies unrestricted algorithmic search and blocking of an optimal design for the corresponding generalized linear model glm designs from each strategy are critically compared and shown to be more efficient than use of a random allocation to blocks of the points from an optimal glm design the designs are compared for a range of values of the intra block working c

robust submodular observation selection in many applications one has to actively select among a set of expensive observations before making an informed decision for example in environmental monitoring we want to select locations to measure in order to most effectively predict spatial phenomena often we want to select observations which are robust against a number of possible objective functions examples include minimizing the maximum posterior variance in gaussian process regression robust experimental design and sensor placement for outbreak detection in this paper we present the submodular saturation algorithm a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity an intuitive diminishing returns property moreover we prove that better approximation algorithms do not exist unless np complete problems admit efficient algorithms we show how our algorithm can be extended to handle complex cost functions incorporating non unit observation cost or communication and path costs we also show how the algorithm can be used to near optimally trade off expected case e g the mean square prediction error in gaussian process regression and worst case e g maximum predictive variance performance we show that many important machine learning problems fit our robust submodular observation selection formalism and provide extensive empirical evaluation on several real world problems for gaussian process regression our algorithm compares favorably with state of the art heuristics described in the geostatistics literature while being simpler faster and providing theoretical guarantees for robust experimental design our algorithm performs favorably compared to sdp based algorithms c 2008 andreas krause h brendan mcmahan carlos guestrin and anupam gupta krause mcmahan guestrin and gupta

when should one stop testing software abstract we derive an optimal rule for stopping the testing of a module of software prior to release based on the trade off between the cost of continued testing and the expected losses due to any bugs that remain in the released code our economic assumptions are that testing costs are perfectly predictable but of arbitrary form f t and that the costs of fixing a bug both during testing and subsequent to release are known constants our stochastic assumptions are as follows a the total number of bugs in the module n is unknown b n has a poisson distribution with a mean that is distributed randomly across modules according to a known gamma distribution c given a particular bug the time it takes to find it during testing is random with a known distribution g of arbitrary form and d the lifetimes of different bugs are independent with these assumptions we find conditions on f and g that ensure that the optimal stopping rule has a simple form which can be found by a dynamic progr

convex combination of gaussian processes for bayesian analysis of deterministic computer experiments the use of gaussian processes is a popular approach to analyzing data from computer experiments combining more than one gaussian process in a surrogate model for computer simulation could prove useful when there is uncertainty regarding the family of correlation functions or when one wishes to characterize both global trends and finer details all in the same model we suggest a fully bayesian treatment of the problem taking advantage of mcmc sampling methods and providing point estimates and bayesian credible intervals with a high degree of success according to simulation results we then provide guidelines for choosing a suitable batch sequential maximum entropy design for these models supplementary materials for this article are available online

ordinal association in contingency tables some interpretive aspects abstract two families of models for ordered contingency tables goodman s association models and canonical correlation models are investigated and compared with respect to the interpretation of their parameters we show that the two families of models actually refer to different kinds of ordinal association stochastic order extremity for correlation models and stochastic order entropy for association models this difference is related to the way the two models scale interaction the scale difference is proven to be of substantial consequence especially under strong association

reliability growth management metrics and statistical methods for discrete use systems in this article we present new methodology for analyzing reliability growth of discrete use systems i e systems whose test duration is measured in terms of discrete trials shots or demands the methodology is applicable to the case where corrective actions are applied to prototypes anytime after associated failure modes are first discovered thus the system configuration need not be constant the methodology consists of several model equations for estimating system reliability the expected number of failure modes observed during testing the probability of failure due to a new failure mode and the portion of system unreliability associated with repeat or known failure modes these model equations are used to 1 estimate the initial and projected reliability as well as the reliability growth potential 2 address model goodness of fit concerns 3 quantify programmatic risk and 4 assess reliability maturity of discrete use systems undergoing development statistical procedures for point

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

a second order 3d electromagnetics algorithm for curved interfaces between anisotropic dielectrics on a yee mesh a new frequency domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a yee mesh with second order error in resonant frequencies the algorithm is systematically derived using the finite integration formulation of maxwell s equations on the yee mesh second order convergence of the error in resonant frequencies is achieved by guaranteeing first order error on dielectric boundaries and second order error in bulk possibly anisotropic regions convergence studies conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant both show second order convergence of frequency error the convergence is sufficiently smooth that richardson extrapolation yields roughly third order convergence the convergence of electric fields near the dielectric interface for the analytic problem is also presented

sequential experimental designs for generalized linear models we consider the problem of experimental design when the response is modeled by a generalized linear model glm and the experimental plan can be determined sequentially most previous research on this problem has been limited either to one factor binary response experiments or to augmenting the design when there are already sufficient data to compute parameter estimates we suggest a new procedure for the sequential choice of observations that offers five important advantages 1 it can be applied to multifactor experiments and is not limited to the one factor setting 2 it can be used with any glm not just binary responses 3 both fully sequential and group sequential settings are treated 4 it enables efficient design from the outset of the experiment and 5 the experimenter is not constrained to specify a single model and can use the prior to reflect uncertainty as to the link function and the form of the linear predictor our procedure is based on a d optimality criterion and on a bayesian

marginal modelling of multivariate categorical data this paper describes likelihood methods of analysis for multivariate categorical data the joint distribution is specified in terms of marginal mean functions and pairwise and higher order association measures for the association the emphasis is on global odds ratios the method allows flexible formulation of a broad class of designs such as repeated measurements longitudinal studies interrater agreement and cross over trials the proposed model can be used for parameter estimation and hypothesis testing simple fitting algorithms are proposed the method is illustrated using a data example

admissible estimation of the binomial parameter n suppose that x has a binomial distribution b n p with known p in 0 1 and unknown n in 1 2 cdots a natural estimator for n is given by t 0 1 t x x p x 1 2 cdots this estimator is shown to be inadmissible under quadratic loss it is shown that modifying t 0 to t 0 1 p p ln p results in an admissible estimator for p geq frac 1 2 it is further shown that this is the only admissible modification of t 0 a partial result is also obtained for p frac 1 2

unimodality of likelihood functions for the binomial distribution abstract a maximum likelihood estimate exists for both parameters of the binomial distribution if and only if the sample mean exceeds the sample variance the derivative of the log likelihood function has at most one finite root consequently the likelihood function is unimodular

estimating the binomial parameter n abstract estimating the parameter n of the binomial distribution on the basis of r independent observations has been considered sporadically over the years many questions regarding asymptotic and small sample properties of moment maximum likelihood and related estimators either have been ignored or have received inadequate treatment a unified and comprehensive study of these topics is given here we also consider the problem of zero truncated observations

optimal stopping with exact confidence on remaining defects we derive a new class of stopping rules which may be helpful to buyers of software testing for faults or to buyers of large lots screening for defectives or to database engineers converting a database from one schema to another suppose that a fixed but unknown number n of faults or defectives remain before testing in the testing phase these are observed at random times which are assumed to be iid exponentials with an unknown mean under this assumption we derive several stopping rules that guarantee for any chosen level and integer m that no matter what n is provided only that n m with probability exactly 1 when testing stops no more than m faults remain in the product we further show that one specific rule is most economical in the class of all scale equivariant rules that satisfy the exact confidence property we propose another class of rules based on gaps that can satisfy the exact confidence property

on the erratic behavior of estimators of n in the binomial n p distribution abstract the problem of estimating the number of trials in a binomial distribution is known to be particularly difficult in certain circumstances both the maximum likelihood and method of moments estimators can produce very erratic results being extremely sensitive to minor fluctuations in the data but existing asymptotic theory for these estimators does not provide any insight into this peculiar behavior as the theory typically produces asymptotic normal distributions with respectable means and variances likewise the limiting distributions of other estimators do not convey much information about why those estimators might perform better than their more classical counterparts in this article we develop an alternative asymptotic theory that clearly and vividly depicts not only the erratic performance of the maximum likelihood and method of moments estimators but also the more regular robust properties of alternative estimators proposed by carroll and lombard we note that the parameter configurati

association models and canonical correlation in the analysis of cross classifications having ordered categories abstract the association models considered in goodman 1979a for the analysis of cross classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories and these scores can be used to partition into relevant components the usual chi squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification however while the usual procedure for testing the statistical significance of chi squared components is invalid when these components are based on the canonical correlations a corresponding procedure is valid when these components are obtained with the association models the components of association obtained with the association mo

a single general method for the analysis of cross classified data reconciliation and synthesis of some methods of pearson yule and fisher and also some methods of correspondence analysis and association analysis 1 2 3 4 5 6 7 8 9 10 contents introduction and summary a general measure of nonindependence for the cells in the table a general method of nonindependence analysis some simple examples some special cases of generalized nonindependence analysis standardized generalized nonindependence analysis overall indices and graphical displays of generalized nonindependence saturated and unsaturated models symmetric nonindependence and generalized quasi symmetry closing comments on 2 x 2 table measures of nonindependence and some brief historical notes

optimal designs for dose response models with restricted design spaces in dose response studies the dose range is often restricted due to concerns over drug toxicity and or efficacy we present restricted and unrestricted interval locally optimal designs with respect to a very general class of optimality criteria for estimating the underlying dose response curve the underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form these include the fundamental binary response models the logit and the probit as well as the skewed versions of these models the results are illustrated through the re design of a dose ranging trial conducted at the merck research laboratories zeng and zhu 1997 this work is a generalization of the results of dai and zhu 2002 in terms of the design interval the underlying dose response curve and the optimality criterion

application of dey mittra conformal boundary algorithm to 3d electromagnetic modeling the dey mittra conformal boundary conditions have been implemented for the finite difference time domain fdtd electromagnetic solver of the vorpal plasma simulation framework and studied in the context of three dimensional large scale computations the maximum stable time step when using these boundary conditions can be arbitrarily small due to the presence of small fractional cells inside the vacuum region use of the gershgorin circle theorem allows the determination of a rigorous criterion for exclusion of small cells in order to have numerical stability for particular values of the ratio f d m dt dt c f l of the time step to the courant friedrichs lewy value for the infinite system application to a spherical cavity shows that these boundary conditions allow computation of frequencies with second order error for sufficiently small f d m however for sufficiently fine resolution dependent on f d m the error becomes first order just like the error for stair step boundary conditions nevertheless provided one does use a sufficiently small value of f d m one can obtain third order accuracy through richardson extrapolation computations for the tesla superconducting rf cavity design compare favorably with experimental measurements

bayesian methods for prevalence estimation from incomplete administrative lists many studies aimed at estimating prevalence use several administrative lists from different sources in an attempt to enumerate all persons affected with the health condition of interest each list is incomplete in the sense that none of them enumerates all persons affected with the health condition further because the lists are drawn from different administrative sources the probability of enumeration varies from list to list the goal is to use information from the lists to estimate the total number of affected persons in the population but with some accounting for the different but unknown probabilities of enumeration on each list this paper presents a bayesian method to estimate prevalence when the probability of enumeration varies from list to list data from a survey of children with spina bifida illustrate the methodology

on the existence of maximum likelihood estimators for the binomial response models summary necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response this includes logit and probit models the question of existence of maximum likelihood estimators mle for logit models arose in an analysis of the relationship of psychiatric caseness to scores on a psychiatric screening questionnaire tennant 1977 administered the ghq general health questionnaire goldberg 1972 to 120 patients attending a general practitioner s surgery and also gave each one a standardized psychiatric interview from the interview patients were classified as psychiatric case non case in a secondary analysis of tennant s data duncan jones and henderson 1978 fitted a logit regression of caseness on ghq score and obtained a good fit with the model

staircase free finite difference time domain formulation for general materials in complex geometries a stable cartesian grid staircase free finite difference time domain formulation for arbitrary material distributions in general geometries is introduced it is shown that the method exhibits higher accuracy than the classical yee 1966 scheme for complex geometries since the computational representation of physical structures is not of a staircased nature furthermore electromagnetic boundary conditions are correctly enforced the method significantly reduces simulation times as fewer points per wavelength are needed to accurately resolve the wave and the geometry both perfect electric conductors and dielectric structures have been investigated numerical results are presented and discussed

duality of i projections and maximum likelihood estimation for log linear models under cone constraints abstract important order restrictions and general log linear models for multinomial experiments can often be expressed by requiring that the vector composed of the logs of the probabilities fall within a closed convex cone here we exhibit a duality relationship by way of a fenchel duality theorem between these types of problems and projections in i divergence geometry we show that many cone constrained maximum likelihood estimation problems are exactly equivalent to an i projection onto a translation of the negative polar cone this duality relationship permits the concise characterization of cone restricted maximum likelihood estimates and the use of iterative algorithms proposed by csiszar 1975 and dykstra 1985b which are analogous to the iterative proportional fitting procedure computational aspects of maximum likelihood estimates are discussed and a relationship with least squares projections onto isotonic cones is presented we discuss examples in detail to exhibit the usefulness and power

generalized bilinear models generalized bilinear models are presented for the statistical analysis of two way arrays these models combine bilinear models and generalized linear modeling and yield a family of models that includes many existing models as well as suggest other potentially useful ones this approach both unifies and extends models for two way arrays including the ability to treat response and explanatory variables differently in the models and the incorporation of external information about the variables directly into the analysis a unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature a three step procedure is proposed to analyze data sets by generalized bilinear models two data sets of different nature are analyzed

a d optimal design for estimation of parameters of an exponential linear growth curve of nanostructures we consider the problem of determining an optimal experimental design for estimation of parameters of a class of complex curves characterizing nanowire growth that is partially exponential and partially linear locally d optimal designs for some of the models belonging to this class are obtained by using a geometric approach further a bayesian sequential algorithm is proposed for obtaining d optimal designs for models with a closed form solution and for obtaining efficient designs in situations where theoretical results cannot be obtained the advantages of the proposed algorithm over traditional approaches adopted in recently reported nanoexperiments are demonstrated using monte carlo simulations the computer code implementing the sequential algorithm is available as supplementary materials

convergent cartesian grid methods for maxwell s equations in complex geometries a convergent second order cartesian grid finite difference scheme for the solution of maxwell s equations is presented the scheme employs a staggered grid in space and represents the physical location of the material and metallic boundaries correctly hence eliminating problems caused by staircasing and contrary to the popular yee scheme enforces the correct jump conditions on the field components across material interfaces a detailed analysis of the accuracy of the new embedding scheme is presented confirming its second order global accuracy furthermore the scheme is proven to be a bounded error scheme and thus convergent conditions for fully discrete stability is furthermore established this enables the derivation of bounds for fully discrete stability with cfl restrictions being almost identical to those of the much simpler yee scheme the analysis exposes that the effects of staircasing as well as a lack of properly enforced jump conditions on the field components have significant consequences for the global accuracy it is among other things shown that for cases in which a field component is discontinuous along a grid line as happens at general two and three dimensional material interfaces the yee scheme may exhibit local divergence and loss of global convergence to validate the analysis several one and two dimensional test cases are presented showing an improvement of typically 1 to 2 orders of accuracy at little or no additional computational cost over the yee scheme which in most cases exhibits first order accuracy c 2001 academic press

stabilizing binomial n estimators abstract the maximum likelihood estimator of the binomial parameter n can be highly unstable resulting in huge fluctuations in the estimate when the data are only slightly perturbed a method of assessing this sensitivity based on perturbing the log likelihood function is proposed and examined

a comparison of n estimators for the binomial distribution abstract estimating the number n of trials given a sequence of independent success counts obtained by replicating the n trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution both the method of moments and the maximum likelihood estimators of n are considered when p is unknown and small while n is large both estimators become highly unstable stabilized versions of these estimators are proposed and their performance is described in terms of results obtained by simulation

the analysis of dependence in cross classifications having ordered categories using log linear models for frequencies and log linear models for odds summary to analyse the dependence of a qualitative dichotomous or polytomous response variable upon one or more qualitative explanatory variables log linear models for frequencies are compared with loglinear models for odds when the categories of the response variable are ordered and the categories of each explanatory variable may be either ordered or unordered the log linear models for odds express the odds or log odds pertaining to adjacent response categories in terms of appropriate multiplicative or additive factors these models include the null log odds model the uniform log odds model the parallel log odds model and other log linear models for the odds with these models the dependence of the response variable with ordered categories can be analysed in a manner analogous to the usual multiple regression analysis and related analysis of variance and analysis of covariance application of log linear models for the odds sheds light on earlier applications of log linear models for the frequencies in contingency tables with ordered categories when the categories of a qualitative dichotomous or polytomous response variable are ordered the odds for adjacent response categories and how these odds depend upon one or more qualitative explanatory variables can be of considerable interest we shall consider models that express these odds in terms of appropriate multiplicative factors pertaining to the joint categories of the qualitative explanatory variables or equivalently models that express the corresponding log odds in terms of appropriate additive factors these log linear models for the odds can be applied in situations in which the response categories are ordered and the categories of each explanatory variable may be either ordered or unordered the log linear models for the odds are related to certain log linear models for the frequencies in contingency tables with ordered categories using the models considered here for the odds we shall reanalyse two sets of data that have been analysed previously with loglinear models used for the frequencies our findings shed additional light on the earlier analyses and on the data the models considered here for the odds can be described in rather simple terms being somewhat analogous to the usual models used in multiple regression analysis the analysis of variance and the analysis of covariance they also give further insight into the meaning of the related log linear models for the frequencies there are a great many log linear models for the frequencies in contingency tables see for example goodman 1970 haberman 1974a with the introduction of odds log linear models we exclude from consideration all those frequency log linear models that are not relevant when one of the variables in the contingency table is a response variable and the other variables are possible explanatory or regressor variables and we also focus attention

objective priors for discrete parameter spaces this article considers the development of objective prior distributions for discrete parameter spaces formal approaches to such development such as the reference prior approach often result in a constant prior for a discrete parameter which is questionable for problems that exhibit certain types of structure to take advantage of structure this article proposes embedding the original problem in a continuous problem that preserves the structure and then using standard reference prior theory to determine the appropriate objective prior four different possibilities for this embedding are explored and applied to a population size model the hypergeometric distribution the multivariate hypergeometric distribution the binomial beta distribution and the binomial distribution the recommended objective priors for the first third and fourth problems are new

a new model for ordinal pain data from a pharmaceutical study for the pain data analysed previously by cox and chuang this paper proposes a new model that assumes monotone scores for ordered response categories this proposed model possesses several attractive features and allows a stochastic ordering of the drugs under comparison such a model also provides insight regarding the ordinal scale used to classify response estimation of the parameters in the model is obtained by use of bmdp3r

application of the symplectic finite difference time domain scheme to electromagnetic simulation an explicit fourth order finite difference time domain fdtd scheme using the symplectic integrator is applied to electromagnetic simulation a feasible numerical implementation of the symplectic fdtd sfdtd scheme is specified in particular new strategies for the air dielectric interface treatment and the near to far field nff transformation are presented by using the sfdtd scheme both the radiation and the scattering of three dimensional objects are computed furthermore the energy conserving characteristic hold for the sfdtd scheme is verified under long term simulation numerical results suggest that the sfdtd scheme is more efficient than the traditional fdtd method and other high order methods and can save computational resources

two stage design of quantal response studies in a quantal response study there may be insufficient knowledge of the response relationship for the stimulus or dose levels to be chosen properly information from such a study can be scanty or even unreliable a two stage design is proposed for such studies which can determine whether and how a follow up i e second stage study should be conducted to select additional stimulus levels to compensate for the scarcity of information in the initial study these levels are determined by using optimal design theory and are based on the fitted model from the data in the initial study its advantages are demonstrated using a fishery study

generalized semiparametrically structured ordinal models motivated by recent work studying massive imaging data in the neuroimaging literature we propose multivariate varying coefficient models mvcm for modeling the relation between multiple functional responses and a set of covariates we develop several statistical inference procedures for mvcm and systematically study their theoretical properties we first establish the weak convergence of the local linear estimate of coefficient functions as well as its asymptotic bias and variance and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate we establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions we propose a global test for linear hypotheses of varying coefficient functions and derive its asymptotic distribution under the null hypothesis we also propose a simultaneous confidence band for each individual effect curve we conduct monte carlo simulation to examine the finite sample performance of the proposed procedures we apply mvcm to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment

a 3 d tensor fdtd formulation for treatment of sloped interfaces in electrically inhomogeneous media a general integral finite difference time domain fdtd formulation on cubical grids for the modeling of electrically inhomogeneous media of arbitrary shape is derived the simple cubical structure is maintained and no modifications of the integral paths are necessary instead a three dimensional tensor relationship between the average electric flux density and electric field is determined beforehand and used during the simulation to account for discontinuities in the neighborhood of sloped interfaces the accuracy of the method is confirmed by comparisons with analytical solutions

robust designs for poisson regression models we consider the problem of how to construct robust designs for poisson regression models an analytical expression is derived for robust designs for first order poisson regression models where uncertainty exists in the prior parameter estimates given certain constraints in the methodology it may be necessary to extend the robust designs for implementation in practical experiments with these extensions our methodology constructs designs that perform similarly in terms of estimation to current techniques and offers the solution in a more timely manner we further apply this analytic result to cases where uncertainty exists in the linear predictor the application of this methodology to practical design problems such as screening experiments is explored given the minimal prior knowledge that is usually available when conducting such experiments it is recommended to derive designs robust across a variety of systems however incorporating such uncertainty into the design process can be a computational

bayesian methods for estimation of the size of a closed population summary a bayesian methodology for estimating the size of a closed population from multiple incomplete administrative lists is proposed the approach allows for a variety of dependence structures between the lists can make use of covariates and explicitly accounts for model uncertainty interval estimates from this approach are compared to frequentist and previously published bayesian approaches several examples are considered

modeling and identifying optimum designs for fitting dose response curves based on raw optical density data abstract for raw optical density rod data such as those generated in biological assays using a 96 well plate reader d optimal designs are identified for a family of homogeneous nonlinear models with two parameters developed for fitting and studying dose response curves further within the class of k point equally spaced and uniform designs d optimal designs are specified also the d efficiency of the d optimal equally spaced and uniform k point designs are compared to d optimal design for 3 k 7 the efficiency robustness of these optimal designs with respect to initial nominal values of the parameters are investigated in addition d optimal designs are derived for a family of heterogeneous nonlinear models

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

on bayesian estimation of group size summary in estimating the size of a group of animals it is commonly the case that the sighting probability for individuals is less than one if each individual in the group is independently sighted with equal probability the problem is one of estimating the number of trials from the number of successes in one or more binomial experiments in many cases some individuals in the group have unit sighting probability whereas others do not this note describes the bayesian estimation of group size for this case

an explicit fourth order staggered finite difference time domain method for maxwell s equations a new explicit fourth order accurate staggered finite difference time domain fdtd scheme is proposed and applied to electromagnetic wave problems it is fourth order accurate in both space and time conditionally stable and highly efficient with respect to yee s scheme and still retains much of the original simplicity of yee s scheme both extension to perfectly matched layers and modification to deal with dielectric interfaces and perfectly conducting boundaries of the scheme have also been presented numerical examples are shown to illustrate the efficiency of the method

robust experimental design for multivariate generalized linear models a simple heuristic is proposed for constructing robust experimental designs for multivariate generalized linear models the method is based on clustering a set of local optimal designs a method for finding local d optimal designs using available resources is also introduced clustering with its simplicity and minimal computation needs is demonstrated to outperform more complex and sophisticated methods