branch and bound search for experimental designs based on d optimality and other criteria this article presents a branch and bound algorithm that constructs a catalog of all d optimal n point designs for specified design region linear model and number of observations n while the primary design criterion is d optimality the algorithm may also be used to find designs performing well by other secondary criteria if a small sacrifice in ellkiency as measured by d optimahty is accepted finally some designs are supplied for a quadratic response surface model

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

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

efficient computational algorithm for optimal allocation in regression models in this article we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis monotonic convergence for a general class of multiplicative algorithms for d optimality has been discussed in the literature here we provide an alternate proof of the monotonic convergence for d criterion with a simple computational algorithm and furthermore show it converges to the d optimality we also discuss an algorithm as well as a conjecture of the monotonic convergence for a criterion monte carlo simulations are used to demonstrate the reliability efficiency and usefulness of the proposed algorithms

on optimal designs for nonlinear models a general and efficient algorithm finding optimal designs for nonlinear models is challenging in general although some recent results allow us to focus on a simple subclass of designs for most problems deriving a specific optimal design still mainly depends on numerical approaches there is need for a general and efficient algorithm that is more broadly applicable than the current state of the art methods we present a new algorithm that can be used to find optimal designs with respect to a broad class of optimality criteria when the model parameters or functions thereof are of interest and for both locally optimal and multistage design strategies we prove convergence to the optimal design and show in various examples that the new algorithm outperforms the current state of the art algorithms

optimal experimental design in the presence of nested factors abstracta common occurrence in practical design of experiments is that one factor called a nested factor can only be varied for some but not all the levels of a categorical factor called a branc

a note on the de la garza phenomenon for locally optimal designs the celebrated de la garza phenomenon states that for a polynomial regression model of degree p 1 any optimal design can be based on at most p design points in a remarkable paper yang ann statist 38 2010 2499 2524 showed that this phenomenon exists in many locally optimal design problems for nonlinear models in the present note we present a different view point on these findings using results about moment theory and chebyshev systems in particular we show that this phenomenon occurs in an even larger class of models than considered so far

designing for a response transformation parameter summary we investigate d optimum designs for experiments in which a linear model holds after an unknown power transformation of the univariate response variable this is a departure from standard d optimal design in which an appropriate scale for the response is assumed known before data collection the design problem that we formulate is intrinsically nonlinear requiring characterization of likely parameter values several applications are presented to illustrate the importance of recognizing the role of response transformations at the design stage

the construction of exact d optimum experimental designs with application to blocking response surface designs summary the properties of optimum designs are investigated when there are both qualitative and quantitative factors algorithms for the construction of exact designs are described which are of general applicability the case when the qualitative factors represent blocking variables is given special treatment a modified algorithm provides the opportunity to divide the experimental trials into blocks of specified sizes examples are given of second order models in the quantitative factors divided into two or three blocks of a variety of sizes use of the adjustment algorithm to improve such designs generated from a list of candidate points is demonstrated

a theorem of jacobi and its generalization summary a theorem of jacobi 1841 which shows how the ordinary least squares estimator from a linear regression can be represented as the weighted sum of elementary estimators of the parameters is extended to the generalized least squares estimator the generalization is applied to a problem in microwave engineering

i optimal design of mixture experiments abstractin mixture experiments the factors under study are proportions of the ingredients of a mixture the special nature of the factors necessitates specific types of regression models and specific types of experimental designs although mixture experiments usually are intended to predict the response s for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients little research has been done concerning their i optimal design this is surprising given that i optimal designs minimize the average variance of prediction and therefore seem more appropriate for mixture experiments than the commonly used d optimal designs which focus on a precise model estimation rather than precise predictions in this article we provide the first detailed overview of the literature on the i optimal design of mixture experiments and identify several contradictions for the second order and the special cubic model we present continuous i optimal designs and contrast the

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

optimal designs for comparing curves we consider the optimal design problem for a comparison of two regression curves which is used to establish the similarity between the dose response relationships of two groups an optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions optimal design theory equivalence theorems efficiency bounds is developed for this non standard design problem and for some commonly used dose response models optimal designs are found explicitly the results are illustrated in several examples modeling dose response relationships it is demonstrated that the optimal pair of designs for the comparison of the regression curves is not the pair of the optimal designs for the individual models in particular it is shown that the use of the optimal designs proposed in this paper instead of commonly used non optimal designs yields a reduction of the width of the confidence band by more than 50

computing exact d optimal designs by mixed integer second order cone programming i 1 wiaia t i where ai i 1 s are known matrices with m rows in this paper we show that the criterion of d optimality is secondorder cone representable as a result the method of second order cone programming can be used to compute an approximate d optimal design with any system of linear constraints on the vector of weights more importantly the proposed characterization allows us to compute an exact d optimal design which is possible thanks to highquality branch and cut solvers specialized to solve mixed integer second order cone programming problems our results extend to the case of the criterion of dk optimality which measures the quality of w for the estimation of a linear parameter subsystem defined by a full rank coefficient matrixk we prove that some other widely used criteria are also secondorder cone representable for instance the criteria of a ak gand i optimality we present several numerical examples demonstrating the efficiency and general applicability of the proposed method we show that in many cases the mixed integer second order cone programming approach allows us to find a provably optimal exact design while the standard heuristics systematically miss the optimum

optimum experimental designs for multinomial logistic models multinomial responses frequently occur in dose level experiments for example in a study of the influence of gamma radiation on the emergence of house flies musca domestica l 1758 three disjoint outcomes occurred death before the pupae opened death during emergence and life after emergence although the flies are easy to breed this sort of bioassay is in general very expensive since it requires the use of a gamma radiation source experiments therefore need to be designed to involve the minimum number of different doses here the theory of optimum experimental design is applied to provide efficient experiments to estimate the parameters of those multinomial logistic models that are a special case of the multivariate logistic models of glonek and mccullagh 1995 journal of the royal statistical society series b 57 533 546 the purpose is to reduce the overall experimental cost the general equivalence theorem fedorov 1972 theory of optimal experiments is adapted to this class of models providing an effective method of generating and checking the optimality of designs one example on flies demonstrates the method which can be easily implemented

on the de la garza phenomenon deriving optimal designs for nonlinear models is in general challenging one crucial step is to determine the number of support points needed current tools handle this on a case by case basis each combination of model optimality criterion and objective requires its own proof the celebrated de la garza phenomenon states that under a p 1 th degree polynomial regression model any optimal design can be based on at most p design points the minimum number of support points such that all parameters are estimable does this conclusion also hold for nonlinear models if the answer is yes it would be relatively easy to derive any optimal design analytically or numerically in this paper a novel approach is developed to address this question using this new approach it can be easily shown that the de la garza phenomenon exists for many commonly studied nonlinear models such as the emax model exponential model three and four parameter log linear models emax pk1 model as well as many classical polynomial regression models the proposed approach unifies and extends many well known results in the optimal design literature it has four advantages over current tools i it can be applied to many forms of nonlinear models to continuous or discrete data to data with homogeneous or nonhomogeneous errors ii it can be applied to any design region iii it can be applied to multiple stage optimal design and iv it can be easily implemented

optimal weights for experimental designs on linearly independent support points an explicit formula is derived to compute the a optimal design weights on linearly independent regression vectors for the mean parameters in a linear model with homoscedastic variances the formula emerges as a special case of a general result which holds for a wide class of optimality criteria there are close links to iterative algorithms for computing optimal weights

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

clans and regions in 2 structures abstract the concepts clan and region are central to the theory of 2 structures clans form the cornerstone of the decomposition theory and the notion of a region underlies the representation theory for 2 structures this paper examines in depth the basic properties of the two concepts and the relationship between them also a characterization of regions for angular 2 structures and a morphic characterization of regions in uniform 2 structures are obtained

use and abuse of variance models in regression in nonlinear regression with heteroscedastic errors introduction of a variance model can be useful to obtain good estimators of the regression parameter for example the variance model can be used to obtain the optimal weights in weighted least squares methodology of this kind is often used in the analysis of assay data in clinical chemistry pharmacokinetics and toxicology in a series of papers in the pharmacological literature sheiner and beal and others advocate the extended least squares els methodology that combines regression and variance model into a single objective function based on normal theory maximum likelihood the inadequacy of this method is folklore in the mathematical statistical literature in this article it is pointed out that this methodology may lead to inconsistent estimators in practically relevant situations a review is given of other methods that may be preferable to els

image transformations and blurring since cameras blur the incoming light during measurement different images of the same surface do not contain the same information about that surface thus in general corresponding points in multiple views of a scene have different image intensities while multiple view geometry constrains the locations of corresponding points it does not give relationships between the signals at corresponding locations this paper offers an elementary treatment of these relationships we first develop the notion of idealrdquo and realrdquo images corresponding to respectively the raw incoming light and the measured signal this framework separates the filtering and geometric aspects of imaging we then consider how to synthesize one view of a surface from another if the transformation between the two views is affine it emerges that this is possible if and only if the singular values of the affine matrix are positive next we consider how to combine the information in several views of a surface into a single output image by developing a new tool called frequency segmentation we show how this can be done despite not knowing the blurring kernel

d optimal split plot designs with given numbers and sizes of whole plots the design of split plot experiments has received considerable attention during the last few years the goal of this article is to provide an efficient algorithm to compute d optimal split plot designs with given numbers of whole plots and given whole plot sizes the algorithm is evaluated and applied to a protein extraction experiment in addition it is shown that two level factorial and fractional factorial designs are d optimal for estimating first order response surface models for specific numbers and sizes of whole plots

support points of locally optimal designs for nonlinear models with two parameters we propose a new approach for identifying the support points of a locally optimal design when the model is a nonlinear model in contrast to the commonly used geometric approach we use an approach based on algebraic tools considerations are restricted to models with two parameters and the general results are applied to often used special cases including logistic probit double exponential and double reciprocal models for binary data a loglinear poisson regression model for count data and the michaelis menten model the approach which is also of value for multi stage experiments works both with constrained and unconstrained design regions and is relatively easy to implement

model robust two level designs using coordinate exchange algorithms and a maximin criterion we propose a candidate list free exchange algorithm that facilitates construction of exact model robust two level experiment designs in particular we investigate two model spaces previously considered in the literature the first assumes that all main effects and an unknown subset of two factor interactions are active but that the experimenter knows the number of active interactions the second assumes that an unknown subset of the main effects and all associated two factor interactions are active previous literature uses two criteria for design construction first maximize the number of estimable models then differentiate between designs equivalent in estimability by choosing the design with the highest average efficiency we adopt a similar strategy but 1 do not impose orthogonality or factor level balance constraints resulting in generally equal or larger numbers of estimable models and 2 use a flexible secondary criterion that maximizes the minimum efficiency we provide results fo

bayesian t optimal discriminating designs the problem of constructing bayesian optimal discriminating designs for a class of regression models with respect to the t optimality criterion introduced by atkinson and fedorov 1975a is considered it is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally t optimal discriminating design problems with a large number of model comparisons current methodology for the numerical construction of discrimination designs can only deal with a few comparisons but the discretization of the bayesian prior easily yields to discrimination design problems for more than 100 competing models a new efficient method is developed to deal with problems of this type it combines some features of the classical exchange type algorithm with the gradient methods convergence is proved and it is demonstrated that the new method can find bayesian optimal discriminating designs in situations where all currently available procedures fail

design of experiments with both mixture and qualitative factors while the remaining l factors are qualitative i e they take only a distinct number of possible values the conditions for optimality of approximate designs for the general case of experiments with qualitative and quantitative factors have been established by kurotschka 1981 1987 and wierich 1986 exact designs for such experiments are described in atkinson and donev 1989 but neither set of researchers gives any special treatment to experiments with mixtures the mixture constraint 1 however introduces some special features which it is the purpose of this paper to investigate in section 2 some useful properties of the mixture experiments are listed in section 3 models and optimality conditions for experiments with mixture and qualitative factors are established discussion with examples is given in section 4 in section 5 more general mixture experiments are considered in which the response depends on the amount of the mixture as well as on the proportions of its components experiments of this kind are common in such areas as chemistry medicine and agriculture

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

d optimal design of split split plot experiments in industrial experimentation there is growing interest in studies that span more than one processing step convenience often dictates restrictions in randomization in passing from one processing step to another when the study encompasses three processing steps this leads to split split plot designs we provide an algorithm for computing d optimal split split plot designs and several illustrative examples

analysing data from hormone receptor assays assay results for hormone receptors in human breast cancer are generally plotted in the form of a scatchard plot usually a line is fitted to the data points by least squares regression and thence the concentration of binding sites present in the cancer is calculated the subsequent treatment of the patient with hormones depends on this value so a good estimate of it is necessary in this study three methods of representing the data namely the scatchard plot the reciprocal plot and the woolf plot were investigated and three ways of fitting lines to the data points of each graph namely least squares regression an unweighted robust procedure and a weighted robust procedure were examined when the data were well behaved all plots gave similar answers for the concentration of binding sites irrespective of the regression technique used however when there were up to three outlying points the scatchard plot particularly with least squares regression analysis performed poorly the robust regression analyses yielded more consistent results on all plots in particular the hitherto mistrusted reciprocal scale seemed to perform well under robust regression but other evidence indicated instability in the plot it is concluded that the most reliable way of representing binding data in these experiments is by a woolf plot and that the subsequent line fitting is made resistant by an unweighted robust regression analysis

theory of 2 structures part i clans basic subclasses and morphisms abstract the notion of a 2 structure is more general than the notion of a graph and less general than the notion of a relational structure this paper develops the theory of 2 structures and in particular it demonstrates that each 2 structure can be constructed from decomposed into three sorts of basic 2 structures this result is obtained through a hierarchical representation of 2 structures by trees

theory of 2 structures part ii representation through labeled tree families abstract this paper which is the second part of a whole consisting of two parts continues the investigation of the theory of 2 structures initiated in part i in particular we investigate hierarchical representations of 2 structures through trees where the local relationship between direct descendants of an inner node of a tree is given through a 2 structure the main result of the paper is that for such hierarchical definition it suffices to consider trees where these local relationships are given by either a primitive 2 structure or a complete 2 structure or a linear 2 structure hence each 2 structure can be constructed from decomposed into primitive complete and linear 2 structures

multistratum response surface designs response surface designs are usually described as if the treatments have been completely randomized to the experimental units however in practice there is often a structure to the units implying the need for blocking if in addition some factors are more difficult to vary between units than others a multistratum structure arises naturally we present a general strategy for constructing response surface designs in multistratum unit structures designs are constructed stratum by stratum starting in the highest stratum in each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata allowing for all the effects that have to be estimated three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set finally some practical considerations in randomization are discussed

some guidelines for constructing exact d optimal designs on convex design spaces some problems unique to the construction of n point d optimal designs on convex design spaces are considered multiple point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single point procedures moreover some recommendations for improving single point methods are given finally empirical evidence is found that supports the galil and kiefer option for constructing initial designs and powell s optimization method for design augmentation

optimal design of blocked and split plot experiments for fixed effects and variance component estimation in general modeling data from blocked and split plot response surface experiments requires the use of generalized least squares and the estimation of two variance components the literature on the optimal design of blocked and split plot response surface experiments however focuses entirely on the precise estimation of the fixed factor effects and completely ignores the necessity to estimate the variance components as well to overcome this problem we propose a new bayesian optimal design criterion which focuses on both the variance components and the fixed effects a novel feature of the criterion is that it incorporates prior information about the variance components through log normal or beta prior distributions the resulting designs allow for a more powerful statistical inference than traditional optimal designs in our algorithm for generating optimal blocked and split plot designs we implement efficient quadrature approaches for the numerical approximation of the new optimal design criterion

response surface designs for quantitative and qualitative variables when some variables are quantitative and some qualitative in a response surface context standard designs may not be suitable the reasons for this are illuminated some alternative designs are discussed every n point design provides n linearly independent estimation contrasts some of these p say are needed to estimate the p parameters of the postulated model the remaining n p linearly independent estimation contrasts are available to estimate pure error if used and to test for lack of fit either overall or in particular ways the key to choosing a good design is to use the available degrees of freedom well given certain assumptions about the model to be fitted when there is also uncertainty about the model assumptions dogmatic design advice is not possible sound guidelines are available however and these are presented and illustrated

adaptive scale filtering a general method for obtaining shape from texture introduces adaptive scale filtering a general method for deriving shape from texture under perspective projection without recourse to prior segmentation of the image into geometric texture elements texels and without thresholding of filtered images if texels on a given surface can be identified in an image then the orientation of that surface can be obtained however there is no general characterization of texels for arbitrary textures furthermore even if the size and shape of texels on the surface is invariant with regard to position perspective projection ensures that the size and shape of the corresponding image texels vary by orders of magnitude commencing with an initial set f sub o of identical image filters adaptive scale filtering iteratively derives a set f sub n which contains a unique filter for each image position each element of f sub n is tuned to the three dimensional structure of the surface that is all image filters in f sub n back project to an identical shape and size on the surface thus image texels of various sizes but associated with a single spatial scale on the surface can be identified in different parts of the image when combined with conventional shape from texture methods edges derived using f sub n provide accurate estimates of surface orientation results for planar surfaces are presented

two level designs to estimate all main effects and two factor interactions we study the design of two level experiments with n runs and n factors large enough to estimate the interaction model which contains all the main effects and all the two factor interactions yet an effect hierarchy assumption suggests that main effect estimation should be given more prominence than the estimation of two factor interactions orthogonal arrays oas favor main effect estimation however complete enumeration becomes infeasible for cases relevant for practitioners we develop a partial enumeration procedure for these cases and we establish upper bounds on the d efficiency for the interaction model based on arrays that have not been generated by the partial enumeration we also propose an optimal design procedure that favors main effect estimation designs created with this procedure have smaller d efficiencies for the interaction model than d optimal designs but standard errors for the main effects in this model are improved generated oas for 7 10 factors and 32 72 runs are smaller or have a higher d efficiency than the smallest oas from the literature designs obtained with the new optimal design procedure or strength 3 oas which have main effects that are not correlated with two factor interactions are recommended if main effects unbiased by possible two factor interactions are of primary interest d optimal designs are recommended if interactions are of primary interest supplementary materials for this article are available online 2017 american statistical association and the american society for quality

location of several outliers in multiple regression data using elemental sets the outlying tendency of any case in a multiple regression of p predictors may be estimated by drawing all subsets of size p from the remaining cases and fitting the model each such subset yields an elemental residual for the case in question and a suitable summary statistic of them can be used as an estimate of the case s outlying tendency we propose two such summary statistics an unweighted median which is of bounded influence and a weighted median which is more efficient but less robust the computational load of the procedure is reduced by using random samples in place of the full set of subsets of size p as a byproduct the method yields useful information on the influence or leverage of cases and the mutual masking of high leverage points

monotonic convergence of a general algorithm for computing optimal designs 1 a general class of algorithms optimal experimental design approximate theory is a well developed area and we refer to kiefer 1974 silvey 1980 p zm n 1986 and pukelsheim 1993 for a general introduction and basic results we consider computational aspects of optimal designs focusing on a finite design space x x xn suppose the probability density or mass function of the response is specified as p y x where 0i 9m t is the parameter of interest let a denote the m m expected fisher information matrix from a unit assigned to x with the j k entry the expectation is with respect to p y x

the coordinate exchange algorithm for constructing exact optimal experimental designs we describe the cyclic coordinate exchange algorithm for constructing d optimal and linear optimal experimental designs the algorithm uses a variant of the gauss southwell cyclic coordinate descent algorithm within the k exchange algorithm to achieve substantive reductions in required computing among its advantages are the following candidate sets which grow exponentially in the number of factors need not be explicitly constructed or enumerated convex design spaces or mixed convex by discrete design spaces are handled directly without the need for sophisticated nonlinear programming routines or candidate set adjustment for design problems having 10 or more factors the reductions in execution time are typically two or more orders of magnitude when compared to standard candidateset based procedures such as k exchange yet the designs produced exhibit no loss of efficiency

locally optimal designs for errors in variables models we consider the construction of optimal designs for nonlinear regression models when there are measurement errors in the covariates corresponding approximate design theory is developed for maximum likelihood and least squares estimation with the latter leading to nonconcave optimization problems analytical characterizations of the locally d optimal saturated designs are provided for the michaelis menten e rm max and exponential regression models through concrete applications we illustrate how measurement errors in the covariates affect the optimal choice of design and show that the locally d optimal saturated designs are highly efficient for relatively small misspecifications of the parameter values

robust and efficient designs for the michaelis menten model for the michaelis menten model we determine designs that maximize the minimum of the d efficiencies over a certain interval for the nonlinear parameter the best two point designs can be found explicitly and a characterization is given when these designs are optimal within the class of all designs in most cases of practical interest the determined designs are highly efficient and robust with respect to misspecification of the nonlinear parameter the results are illustrated and applied in an example of a hormone receptor assay

mixed response surface models with heterogeneous within block error variances the experimental error variance in a response surface model with a block effect has traditionally been assumed to be constant in some experimental situations however this variance may be different for the different blocks that compose the associated design this article discusses the analysis of a response surface model with a random block effect and heterogeneous error variances among the blocks the model includes interactions between the fixed polynomial effects and the block effect procedures for estimating and testing the fixed effects and the random effects in the model are described in particular anova based procedures for testing equality of the error variances and testing the random effects are introduced

least squares polynomial chaos expansion a review of sampling strategies abstract as non intrusive polynomial chaos expansion pce techniques have gained growing popularity among researchers we here provide a comprehensive review of major sampling strategies for the least squares based pce traditional sampling methods such as monte carlo latin hypercube quasi monte carlo optimal design of experiments ode gaussian quadratures as well as more recent techniques such as coherence optimal and randomized quadratures are discussed we also propose a hybrid sampling method dubbed alphabetic coherence optimal that employs the so called alphabetic optimality criteria used in the context of ode in conjunction with coherence optimal samples a comparison between the empirical performance of the selected sampling methods applied to three numerical examples including high order pce s high dimensional problems and low oversampling ratios is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand we observed that the alphabetic coherence optimal technique outperforms other sampling methods specially when high order ode are employed and or the oversampling ratio is low

experimental design for engineering dimensional analysis dimensional analysis da is a fundamental method in the engineering and physical sciences for analytically reducing the number of experimental variables affecting a given phenomenon prior to experimentation two powerful advantages associated with the method relative to standard design of experiment doe approaches are a a priori dimension reduction and b scalability of results the latter advantage permits the experimenter to effectively extrapolate results to similar experimental systems of differing scale unfortunately da experiments are underused because very few statisticians are familiar with them in this article we first provide an overview of da and give basic recommendations for designing da experiments next we consider various risks associated with the da approach the foremost among them is the possibility that the analyst might omit a key explanatory variable leading to an incorrect da model when this happens the da model will fail and experimentation will be largely wasted to

an adjustment algorithm for the construction of exact d optimum experimental designs existing algorithms for the construction of exact d optimum designs customarily search a list of candidate points this article describes a computationally simple method of improving such designs tables are given of designs for second order models with as many as five factors found by search over candidate points these are compared with designs already in the literature and used as the starting point for the adjustment algorithm

identifying locally optimal designs for nonlinear models a simple extension with profound consequences we extend the approach in ann statist 38 2010 2499 2524 for identifying locally optimal designs for nonlinear models conceptually the extension is relatively simple but the consequences in terms of applications are profound as we will demonstrate we can obtain results for locally optimal designs under many optimality criteria and for a larger class of models than has been done hitherto in many cases the results lead to optimal designs with the minimal number of support points

statistical analysis of the michaelis menten equation summary an application of the method of maximum likelihood ml is described for analysing the results of enzyme kinetic experiments in which the michaelis menten equation is obeyed accurate approximate solutions to the ml equations for the parameter estimates are presented for the case in which the experimental errors are of constant relative magnitude formulae are derived that approximate the standard errors of these estimates the estimators are shown to be asymptotically unbiased and the standard errors observed in simulated data rapidly approach the theoretical lower bound as the sample size increases the results of a large scale monte carlo simulation study indicate that for data with a constant coefficient of variation the present method is superior to other published methods including the conventional transformations to linearity and the nonparametric technique proposed by eisenthal and cornish bowden 1974 biochemical journal 139 715 720 finally the present results are extended to the analysis of simple receptor binding experiments using the general approach described by munson and rodbard 1980 analytical biochemistry 107 220 239

angular 2 structures abstract the theory of 2 structures forms a convenient framework for investigating graphs in this paper we investigate the class of angular 2 structures which results by requiring that the primitivity is forbidden on the lowest possible level i e it is required that no substructure on three elements is primitive the paper presents the basic theory of angular 2 structures and in particular the theory of primitive angular 2 structures we demonstrate that the notion of an angular 2 structure is a well chosen generalization of the notions of a symmetric graph and a partial order

computer aided blocking of factorial and response surface designs we consider the problem of blocking response surface and factorial designs when block sizes are prespecified often rendering standard approaches inapplicable a generalization of harville s 1974

combined algorithm to compute d optimal designs algorithmic techniques for computing optimal designs continue being a need in the optimal experimental design field the increasing interest in finding the optimal experimental conditions makes that new methods are demanded for more complex frameworks showing more realistic situations numerical techniques are often the unique viable option for computing these designs since to tackle analytically the problem results impracticable in most of cases wynn fedorov algorithm multiplicative algorithm and their modifications are the more frequently used methods in the literature for computing d optimal designs however they are not always suitable and efficient to compute optimal designs since their procedures are very limited by the computational requirements a new algorithm to obtain d optimal designs is proposed in this paper it is based on combining suitable strategies followed by the traditional algorithms a proof of the convergence is provided and several numerical examples are presented to illustrate its improved results