on the equivalence of constrained and compound optimal designs abstract constrained and compound optimal designs represent two well known methods for dealing with multiple objectives in optimal design as reflected by two functionals 1 and 2 on the space of information matrices a constrained optimal design is constructed by optimizing 2 subject to a constraint on 1 and a compound design is found by optimizing a weighted average of the functionals 1 1 2 0 1 we show that these two approaches to handling multiple objectives are equivalent

efficient sequential designs with binary data abstract a class of sequential designs for estimating the percentiles of a quantal response curve is proposed its updating rule is based on an efficient summary of all of the data available via a parametric model the logit mle version of the proposed designs can be viewed as a natural analog of the robbins monro procedure in the case of binary data it is shown to be asymptotically consistent optimal and nonparametric via its connection with the latter procedure for certain choices of initial designs the proposed method performs very well in a simulation study for sample sizes up to 35 a nonparametric sequential design via the spearman karber estimator for estimating the median is also proposed

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

designs for generalized linear models with random block effects via information matrix approximations summary the selection of optimal designs for generalized linear mixed models is complicated by the fact thatthefisherinformationmatrix onwhichmostoptimalitycriteriadepend iscomputationally expensive to evaluate we provide two novel approximations that reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes or monte carlo approximations thereof an asymptotic approximation that is accurate when there is strong dependence between observations in the same block and an approximation via kriging interpolators for logistic random intercept models we show how interpolation can be especially effective for finding pseudo bayesian designs that incorporate uncertainty in the values of the model parameters the new results are used to evaluate the efficiency for estimating conditional models of optimal designs from closed form approximations to the information matrix derived from marginal models correcting for the marginal attenuation of parameters in binary response models yields much improved designs typically with very high efficiencies however in some experiments exhibiting strong dependence designs for marginal models may still be inefficient forconditionalmodelling ourasymptoticresultsprovidesometheoreticalinsightsintowhysuch inefficiencies occur

bayesian design of experiments using approximate coordinate exchange abstractthe construction of decision theoretical bayesian designs for realistically complex nonlinear models is computationally challenging as it requires the optimization of analytically intractable expected utility functions over high dimensional design spaces we provide the most general solution to date for this problem through a novel approximate coordinate exchange algorithm this methodology uses a gaussian process emulator to approximate the expected utility as a function of a single design coordinate in a series of conditional optimization steps it has flexibility to address problems for any choice of utility function and for a wide range of statistical models with different numbers of variables numbers of runs and randomization restrictions in contrast to existing approaches to bayesian design the method can find multi variable designs in large numbers of runs without resorting to asymptotic approximations to the posterior distribution or expected utility the methodology is demonstrated on

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

bayesian experimental design for nonlinear mixed effects models with application to hiv dynamics bayesian experimental design is investigated for bayesian analysis of nonlinear mixed effects models existence of the posterior risk for parameter estimation is shown when the same prior distribution is used for both design and inference existence of the preposterior risk for design is also proven if the prior distribution used in design is different from that used for inference sufficient conditions are established for existence of the preposterior risk for design a case study of design for an experiment in population hiv dynamics is provided

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

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 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

the application of the annealing algorithm to the construction of exact optimal designs for linear regression models this article reports the application of the annealing algorithm to the construction of exact d i and g optimal designs for polynomial regression of degree 5 on the interval 1 l and for the second order model in two factors on the design space 1 l 1 1 details of the perturbation scheme and the annealing schedules used are given and the method of implementation is illustrated by means of a simple example the algorithm is assessed by comparing its performance in terms of computer time and effkiency with the modified fedorov procedure and it is shown to be particularly effective in finding g optimal designs the salient features of the exact designs constructed in this study are also summarized

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

bias reduction of maximum likelihood estimates summary it is shown how in regular parametric problems the first order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function in exponential families with canonical parameterization the effect is to penalize the likelihood by the jeffreys invariant prior in binomial logistic models poisson log linear models and certain other generalized linear models the jeffreys prior penalty function can be imposed in standard regression software using a scheme of iterative adjustments to the data

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

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

parameter neutral optimum design for non linear models some bayesian approaches to d optimum design of experiments are considered from the viewpoint of invariance under reparameterization of the underlying statistical model an invariant criterion is proposed which does not require the detailed specification of a prior and which is shown to be equivalent to g optimality under a jeffreys prior the methods are applied and discussed in the contexts of exponential decay and quantal response models

a general strategy for analyzing data from split plot and multistratum experimental designs increasingly industrial experiments use multistratum designs such as split plot and strip plot designs often these experiments span more than one processing stage the challenge is to identify an appropriate multistratum design along with an appropriate statistical model in this article we introduce hasse diagrams in the response surface context as a tool to visualize the unit structure of the experimental design the randomization and sampling approaches used the stratum in which each experimental factor is applied and the degrees of freedom available in each stratum to estimate main effects interactions and variance components we illustrate their use on several responses measured in a large study of the adhesion properties of coatings to polypropylene we discuss quantitative binary and ordered categorical responses for designs ranging from a simple split plot to a strip plot that involves repeated measurements of the response the datasets discussed in this article are available online a

model robust linear optimal designs motivated by a pioblem concerning the estimation of uranium content in calibration standards a new design criterion is developed that generalizes linear optimality to a situation in which a priori the exact form of the regression model need not be known an equivalence theorem is given some properties of the new designs are delineated and iterative methods for design construction are presented finally by using methods developed within optimal designs are computed in a number of situations including that of the motivating example

modified fuzzy c means algorithm for segmentation of t1 t2 weighted brain mri in the past decades fuzzy segmentation methods especially the fuzzy c means algorithms have been widely used in the segmentation of brain medical images because they can preserve more information from the original image than other segmentation methods this paper introduces a modified robust fuzzy c means algorithm with special weighted bias estimation for segmentation of brain magnetic resonance image in general the intensity inhomogeneities are endorsed to imperfections in the radio frequency coils or to the problems connected with the image acquisition the intensity inhomogeneities are seriously affecting the segmentation process when computer assisted segmentation algorithms used in differentiating borders between the tissues in medical images the proposed algorithm of this paper is considered the fact in the standard fuzzy c means with no spatial context information which makes it sensitive to noise hence the proposed method is capable to deal with the intensity inhomogeneities and noised image effectively further to reduce the number of iterations the proposed modified robust algorithm initializes the centroid using dist max initialization algorithm before the execution of algorithm iteratively experimental results carried out through the comparative studies of segmentation results of the proposed method and the segmentation results of other existed algorithms when these algorithms implemented on brain magnetic resonance image and benchmark lung cancer dataset the superiority of the proposed method has shown from the experimental results

large deviations for non zero initial conditions in linear systems transient response of linear systems with non zero initial conditions was at the center of attention for engineers and researchers at early stages of classical control theory however this field was not intensively investigated later for instance the breakthrough result on unavoidable peaking effect for systems with strong damping factor was obtained by izmailov in 1987 but it did not attract much attention we try to continue this line of research and provide explicit worst case lower bound then we exhibit large deviation effects for other pole locations and estimate lower bounds for them the upper bounds for deviations of trajectories are much better studied to obtain the smallest deviations by static linear feedback the techniques of linear matrix inequalities can be exploited we demonstrate that for such closed loop systems the upper and lower bounds have the same asymptotic behavior

some robust type d optimal designs in polynomial regression abstract consider a polynomial regression situation on an interval and also a robustness type formulation of stigler s a technique involving canonical moments is discussed and some explicit solutions are given

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

minimax d optimal designs for the logistic model summary we propose an algorithm for constructing minimax d optimal designs for the logistic model when only the ranges of the values for both parameters are assumed known properties of these designs are studied and compared with optimal bayesian designs and sitter s 1992 biometrics 48 1145 1155 minimax d optimal kk designs examples of minimax d optimal designs are presented for the logistic and power logistic models including a dose response design for rheumatoid arthritis patients

optimal experimental design for another s analysis abstract we consider the optimal design of experiments in which estimation and design are performed by different parties the parties are assumed to share similar goals as reflected by a common loss function but they may have different prior beliefs after presenting a few motivating examples we examine the problem of optimal sample size selection under a normal likelihood with constant cost per observation we also consider the problem of optimal allocation for given overall sample sizes we present results under both squared error loss and a logarithmic utility paying attention to the differences between one and two prior optimal designs an asymmetric discrepancy measure features repeatedly in our development and we question the extent of its role in optimal two prior design

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

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