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

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

confidence interval construction for proportion difference in small sample paired studies paired dichotomous data may arise in clinical trials such as pre post test comparison studies and equivalence trials reporting parameter estimates e g odds ratio rate difference and rate ratio along with their associated confidence interval estimates becomes a necessity in many medical journals various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions nevertheless the performance of these asymptotic methods may have poor coverage properties in small samples in this article we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small sample paired data specifically we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test the exact unconditional confidence interval guarantees the coverage probability and it is recommended if strict control of coverage probability is required however the exact method tends to be overly conservative and computationally demanding our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small sample designs and yet they are relatively easy to implement computationally we illustrate the methods using real examples from a pain management study and a cancer study

stochastic processes originating in deterministic microscopic dynamics we investigate the probability distribution of the scaled trajectory of a test particle moving in an equilibrium fluid according to the laws of classical mechanics i e ifq t is the displacement of the test particle we letqa t q at a and consider the distribution of the trajectory qa t in the limit a the randomness of the motion is due entirely to the randomness of the initial state of the fluid test particle or both and the process is generally non markovian nevertheless it can be proven in some cases and we expect it to be true in many more that qa t looks like brownian motion in the limit a some results for simple model systems are presented

online calibration via variable length computerized adaptive testing item calibration is an essential issue in modern item response theory based psychological or educational testing due to the popularity of computerized adaptive testing methods to efficiently calibrate new items have become more important than that in the time when paper and pencil test administration is the norm there are many calibration processes being proposed and discussed from both theoretical and practical perspectives among them the online calibration may be one of the most cost effective processes in this paper under a variable length computerized adaptive testing scenario we integrate the methods of adaptive design sequential estimation and measurement error models to solve online item calibration problems the proposed sequential estimate of item parameters is shown to be strongly consistent and asymptotically normally distributed with a prechosen accuracy numerical results show that the proposed method is very promising in terms of both estimation accuracy and efficiency the results of using calibrated items to estimate the latent trait levels are also reported

statistical properties of skew endomorphisms with bernoulli base abstract we analyse numerically the statistical properties of a class of mappings of the 2 torus t 2 onto itself whose investigation is suggested by some models of modulated diffusion these transformations can be written as a skew product of the endomorphism bp x px mod 1 p z 1 0 1 on the 1 torus t 1 0 1 and a translation on t 1 under suitable assumptions the skew product can be proven to be mixing w r t the lebesgue measure central limit cl and functional central limit fcl properties are numerically checked for analytic observables the result is remarkable because the mappings show no hyperbolic or quasi hyperbolic structure crucial for the proof of central limit theorem and donsker s invariance principle in all of the dynamical systems where these properties have been established up to now moreover cl and fcl behaviours seem to hold also in the case of purely ergodic endomorphisms and even for observables whose correlations do not decay at infinity

microscopic chaos and gaussian diffusion processes abstract in this paper we construct and analyze a prototypical model of microscopic chaos in particular we extend the results of beck and shimizu to the case where the microscopic time scale is no longer small the upshot is that a non ornstein uhlenbeck deterministic process can generate a gaussian diffusion process

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

large factorial designs for product engineering and marketing research applications we propose an algorithm that incorporates both combinatorial and heuristic optimization methods for generating d efficient factorial designs this includes an approach that can automatically construct more than 115 000 orthogonal arrays including at least one array for every known specification with fewer than 144 runs the algorithm tries various initialization and iteration methods chooses the most promising method and then applies more computational effort with the chosen method the algorithm can make orthogonal and nearly orthogonal arrays and it can accommodate restrictions interactions and large designs usage requires minimal expertise and input applications in the area of optimal product design choice modeling and marketing research are discussed

higher order correlations of tchebyscheff maps we determine the higher order correlation functions of iterates of tchebyscheff polynomials of arbitrary order n the non vanishing correlations can be described by suitable sets of graphs these graphs allow for a perturbative evaluation of invariant densities for langevin like systems that are driven by deterministic chaotic forces generated by tchebyscheff maps rather than gaussian white noise

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

inference and sequential design summary if an experiment is designed sequentially repeated sampling inference may not necessarily be made using distributional results that are valid for fixed designs a few simple illustrative examples and alternative approaches are given sometimes the sequential nature of design can be ignored asymptotically links are forged with inference for stochastic processes and missing data problems

ergodic properties of a kicked damped particle we investigate a class of nonlinear dynamical systems describing the movement of a particle in a viscous medium under the influence of a kick force these systems can be regarded as a generalization of the langevin approach to brownian motion in the sense that the fluctuating force on the particle is not gaussian white noise but an arbitrary non gaussian process generated by a nonlinear dynamical system we investigate how certain properties of the force periodicity ergodicity mixing property transfer to the velocity of the particle moreover the relaxation properties of the system are analysed

generalized simulated annealing for function optimization a generalized simulated annealing method has been developed and applied to the optimization of functions possibly constrained having many local extrema the method is illustrated in some difftcult pedagogical examples and used to solve a problem analyzed by bates technometrics 25 pp 373 376 1983 for which we identify an improved optimum the sensitivity of the solution to changes in the constraints and in other specifications of the problem is analyzed and discussed

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

approach to gaussian stochastic behavior for systems driven by deterministic chaotic forces we consider skew product dynamical systems that describe the stroboscopic dynamics of a damped particle subjected to a chaotic kick force in a suitable scaling limit the dynamics converges to the ornstein uhlenbeck process we investigate the deterministic chaotic corrections in the vicinity of this gaussian limit case for various examples of chaotic forces we present numerical evidence that for certain classes of chaotic forces the deterministic chaotic corrections of the invariant density are universal we provide analytical results for forces generated by tchebyscheff maps and sketch a renormalization group theory in the space of probability densities

a robust criterion for experimental designs for serially correlated observations a new robust criterion for experimental designs is proposed for a given design the criterion is to minimize over all possible run orders the absolute value of the change of the variance function due to possible correlation between the observations the resulting design is robust against possible auto correlation among the observations in the sense that confidence interval coverage levels are maintained accurately applications are given for 2k factorial designs and one mixed level fractional experiment and robust runs are obtained computational strategies are also discussed and a simulated annealing algorithm is developed to search for robust designs

test based exact confidence intervals for the difference of two binomial proportions summary confidence intervals are often provided to estimate a treatment difference when the sample size is small as is typical in early phases of clinical trials confidence intervals based on large sample approximations may not be reliable in this report we propose test based methods of constructing exact confidence intervals for the difference in two binomial proportions these exact confidence intervals are obtained from the unconditional distribution of two binomial responses and they guarantee the level of coverage we compare the performance of these confidence intervals to ones based on the observed difference alone we show that a large improvement can be achieved by using the standardized z test with a constrained maximum likelihood estimate of the variance

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

minimax d optimal designs for item response theory models various different item response theory irt models can be used in educational and psychological measurement to analyze test data one of the major drawbacks of these models is that efficient parameter estimation can only be achieved with very large data sets therefore it is often worthwhile to search for designs of the test data that in some way will optimize the parameter estimates the results from the statistical theory on optimal design can be applied for efficient estimation of the parameters a major problem in finding an optimal design for irt models is that the designs are only optimal for a given set of parameters that is they are locally optimal locally optimal designs can be constructed with a sequential design procedure in this paper minimax designs are proposed for irt models to overcome the problem of local optimality minimax designs are compared to sequentially constructed designs for the two parameter logistic model and the results show that minimax design can be nearly as efficient as sequentially constructed designs

integer valued minimax robust designs for estimation and extrapolation in heteroscedastic approximately linear models abstract we present our findings on a new approach to robust regression design this approach differs from previous investigations into this area in three respects the use of a finite design space the use of simulated annealing to carry out the numerical minimization problems and in our search for integer valued rather than continuous designs we present designs for the situation in which the response is thought to be approximately polynomial we also discuss the cases of approximate first and second order multiple regression in each case we allow for possible heteroscedasticity and also obtain minimax regression weights the results are extended to cover extrapolation of the regression response to regions outside of the design space a case study involving dose response experimentation is undertaken the optimal robust designs which protect against bias as well as variance can be roughly described as being obtained from the classical variance minimizing designs by replacing replicates with clust

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

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

statistical properties of lorentz gas with periodic configuration of scatterers in our previous paper markov partitions for some classes of dispersed billiards were constructed using these partitions we estimate the decay of velocity auto correlation function and prove the central limit theorem of probability theory and donsker s invariance principle for lorentz gas with periodic configuration of scatterers

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

dynamical systems of langevin type abstract dynamical systems of langevin type are deterministic mappings that arise if the gaussian white noise of a langevin equation is replaced by a deterministic chaotic dynamics we describe the various types of mappings that can be obtained in this way and investigate typical transition scenarios from complicated non gaussian to langevin like behavior that occur if a time scale parameter is changed we define a new characteristic quantify fir ergodic mappings called effective langevin radius which is related to the critical time scale where the marginal invariant density of the dynamical system of langevin type loses its differentiability the invariant density is shown to contain useful information on the entire characteristic functional of the chaotic driving force some general symmetry properties of the invariant densities are discussed

strange attractors and asymptotic measures of discrete time dissipative systems we investigate asymptotic properties of certain discrete time dynamical systems in two and three dimensions with solenoidal attractor it is proved that the asymptotic measures relevant for the generalized version of the ergodic theorem all derive from one haar measure

a model of modulated diffusion ii numerical results on statistical properties we investigate numerically the statistical properties of a model of modulated diffusion for which we have already computed analytically the diffusion coefficientd our model is constructed by adding a deterministic or random noise to the frequency of an integrable isochronous system we consider in particular the central limit theorem and the invariance principle and we show that they follow wheneverd is positive and for any magnitude of the noise we also investigate the asymptotic distribution in a case whend 0

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

unbiased confidence intervals for the odds ratio of two independent binomial samples with application to case control data the problem of confidence interval construction for the odds ratio of two independent binomial samples is considered two methods of eliminating the nuisance parameter from the exact likelihood conditioning and maximization are described a conditionally exact tail method exists by putting together upper and lower bounds a shorter interval can be obtained by simultaneous consideration of both tails we present here new methods that extend the tail and simultaneous approaches to the maximized likelihood the methods are unbiased and applicable to case control data for which the odds ratio is important the confidence interval procedures are compared unconditionally for small sample sizes in terms of their expected length and coverage probability a bayesian confidence interval method and a large sample chi2 procedure are included in the comparisons

fractal structure and gaussian distribution in chaotic brownian motion in brownian motion driven by a chaotic sequence of iterates of a map f y x t x t f t where f t yn 1 for n t n 1 n 1 2 and y n 1 f yn the fractal structure and the dependence of the recurrence relation xn 1 xn where xn x t n are studied the recurrence relation is shown to change from a shape similar to f y into a diagonal strip which does not depend on the details of f y if is decreased consequently it is shown that the stationary distribution of xn changes from a similar shape as the invariant density of f y into a gaussian shape

from the perron frobenius equation to the fokker planck equation we show that for certain classes of deterministic dynamical systems the perron frobenius equation reduces to the fokker planck equation in an appropriate scaling limit by perturbative expansion in a small time scale parameter we also derive the equations that are obeyed by the first and second order correction terms to the fokker planck limit case in general these equations describe non gaussian corrections to a langevin dynamics due to an underlying deterministic chaotic dynamics for double symmetric maps the first order correction term turns out to satisfy a kind of inhomogeneous fokker planck equation with a source term for a special example we are able solve the first and second order equations explicitly

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

another look at first order saturated designs the p efficient designs the problem of constructing first order saturated designs that are optimal in some sense has received a great deal of attention in the literature since these saturated designs are frequently used in screening situations the focus will be on the potential projective models rather than the full model this article discusses some practical concerns in choosing a design and presents some first order saturated designs having two desirable properties near equal occurrence and near orthogonality these saturated designs are shown to be reasonably efficient for estimating the parameters of projective submodels and thus are called p efficient designs comparisons with the efficiency of d optimal designs are given for designs for all n from 3 to 30

from dynamical systems to the langevin equation abstract it is shown that some dynamical systems which in microscopic time are fully deterministic exhibit a long time stochastic behavior governed by the langevin equation the limit in which this becomes a precise statement is obtained by an appropriate scaling of time and force the results are exemplified by a computer experiment

asymptotic inference from sequential design in a nonlinear situation summary it is shown that confidence regions for nonlinear parameters constructed by the repeated sampling principle are asymptotically valid for sequential designs in general linear models the related questions of consistency of parameter estimators and convergence of sequential design to an optimal design are answered positively an empirical finding of ford silvey 1980 is given a theoretical justification

on a comparative study between dependence scales determined by linear and non linear measures in this manuscript we present a comparative study about the determination of the relaxation i e independence time scales obtained from the correlation function the mutual information and a criterion based on the evaluation of a nonextensive generalisation of mutual entropy our results show that for systems with a small degree of complexity standard mutual information and the criterion based on its nonextensive generalisation provide the same scale whereas for systems with a higher complex dynamics the standard mutual information presents a time scale consistently smaller

driven chaotic motion in single and double well potentials abstract the stochastic motions in stable and bistable potentials are compared on the basis of a langevin like equation with a deterministic chaotic process replacing gaussian white noise ergodic and mixing properties are obtained under rather general circumstances in the case of the symmetric double well potential the system exhibits a behavior quite different from what one observes for stable potentials as the control parameters are varied the system undergoes a phase transition from an ergodic to a nonergodic phase lyapunov exponents and fractal dimensions are studied for more detailed insight

robustness of design in dose response studies summary we construct experimental designs for dose response studies the designs are robust against possibly misspecified link functions for this they minimize the maximum meansquared error of the estimated dose required to attain a response in 100p of the target population here p might be one particular value p d 0 5 corresponds to ed50 estimation or it might range over an interval of values of interest the maximum of the mean squared error is evaluated over a kolmogorov neighbourhood of the fitted link both the maximum and the minimum must be evaluated numerically the former is carried out by quadratic programming and the latter by simulated annealing

brownian motion as a problem of eliminating fast variables abstract the hamilton equations for a brownian particle involve its mass as a large parameter as a consequence its motion is relatively slow and the fast motion of the surrounding fluid molecules can be eliminated by the standard method of eliminating fast variables the result is equivalent to the known langevin equation plus additional higher orders all coefficients are expressed in terms of correlation functions of the microscopic force on the particle

multiobjective sampling design for parameter estimation and model discrimination in groundwater solute transport sampling design for site characterization studies of solute transport in porous media is formulated as a multiobjective problem optimal design of a sampling network is a sequential process in which the next phase of sampling is designed on the basis of all available physical knowledge of the system three objectives are considered model discrimination parameter estimation and cost minimization for the first two objectives physically based measures of the value of information obtained from a set of observations are specified in model discrimination value of information of an observation point is measured in terms of the difference in solute concentration predicted by hypothesized models of transport points of greatest difference in predictions can contribute the most information to the discriminatory power of a sampling design sensitivity of solute concentration to a change in a parameter contributes information on the relative variance of a parameter estimate inclusion of points in a sampling design with high sensitivities to parameters tends to reduce variance in parameter estimates cost minimization accounts for both the capital cost of well installation and the operating costs of collection and analysis of field samples sensitivities discrimination information and well installation and sampling costs are used to form coefficients in the multiobjective problem in which the decision variables are binary zero one each corresponding to the selection of an observation point in time and space the solution to the multiobjective problem is a noninferior set of designs to gain insight into effective design strategies a one dimensional solute transport problem is hypothesized then an approximation of the noninferior set is found by enumerating 120 designs and evaluating objective functions for each of the designs trade offs between pairs of objectives are demonstrated among the models the value of an objective function for a given design is shown to correspond to the ability of a design to actually meet an objective

specifying optimum examinees for item parameter estimation in item response theory information functions are used to find the optimum ability levels and maximum contributions to information for estimating item parameters in three commonly used logistic item response models for the three and two parameter logistic models examinees who contribute maximally to the estimation of item difficulty contribute little to the estimation of item discrimination this suggests that in applications that depend heavily upon the veracity of individual item parameter estimates e g adaptive testing or text construction better item calibration results may be obtained for fixed sample sizes from examinee calibration samples in which ability is widely dispersed

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

a new online calibration method for multidimensional computerized adaptive testing multidimensional method a m method a has been proposed as an efficient and effective online calibration method for multidimensional computerized adaptive testing mcat chen xin paper presented at the 78th meeting of the psychometric society arnhem the netherlands 2013 however a key assumption of m method a is that it treats person parameter estimates as their true values thus this method might yield erroneous item calibration when person parameter estimates contain non ignorable measurement errors to improve the performance of m method a this paper proposes a new mcat online calibration method namely the full functional mle m method a ffmle m method a this new method combines the full functional mle jones jin in psychometrika 59 59 75 1994 stefanski carroll in annals of statistics 13 1335 1351 1985 with the original m method a in an effort to correct for the estimation error of ability vector that might otherwise adversely affect the precision of item calibration two correction schemes are also proposed when implementing the new method a simulation study was conducted to show that the new method generated more accurate item parameter estimation than the original m method a in almost all conditions

white noise limits for discrete dynamical systems driven by fast deterministic dynamics abstract we study a class of singularly perturbed dynamical systems that have fast and slow components e 1 being the fast to slow timescale ratio the fast components are governed by a strongly mixing discrete map which is iterated at time intervals e the slow components are governed by a first order finite difference equation that uses a time step e as e tends to zero the fast components may be eliminated giving rise to sdes for the slow components the emerging stochastic calculus is in the general case of neither ito nor stratonovich type but depends on the correlation time of the mixing process

convergence of an annealing algorithm the annealing algorithm is a stochastic optimization method which has attracted attention because of its success with certain difficult problems including np hard combinatorial problems such as the travelling salesman steiner trees and others there is an appealing physical analogy for its operation but a more formal model seems desirable in this paper we present such a model and prove that the algorithm converges with probability arbitrarily close to 1 we also show that there are cases where convergence takes exponentially long that is it is no better than a deterministic method we study how the convergence rate is affected by the form of the problem finally we describe a version of the algorithm that terminates in polynomial time and allows a good deal of practical confidence in the solution

a mechanical model of brownian motion we consider a dynamical system consisting of one large massive particle and an infinite number of light point particles we prove that the motion of the massive particle is in a suitable limit described by the ornstein uhlenbeck process this extends to three dimensions previous results by holley in one dimension

from ruelle s transfer operator to the schro dinger operator abstract we show that ruelle s transfer operator defined for an appropriate class of strongly chaotic mappings reduces to the schrodinger operator with imaginary time in an appropriate scaling limit we also derive the equations for the next order corrections to the schrodinger behavior if the scaling limit is not completely performed in the simplest case the first order corrections turns out to obey a schrodinger equation with a source term this means a possible chaotic dynamics underlying the feynman kac formula on a very small time scale e g the planc scale leads generalized quantum mechanics with an additional source term

continuous online item calibration parameter recovery and item utilization parameter recovery and item utilization were investigated for different designs for online test item calibration the design was adaptive in a double sense it assumed both adaptive testing of examinees from an operational pool of previously calibrated items and adaptive assignment of field test items to the examinees four criteria of optimality for the assignment of the field test items were used each of them based on the information in the posterior distributions of the examinee s ability parameter during adaptive testing as well as the sequentially updated posterior distributions of the field test item parameters in addition different stopping rules based on target values for the posterior standard deviations of the field test parameters and the size of the calibration sample were used the impact of each of the criteria and stopping rules on the statistical efficiency of the estimates of the field test parameters and on the time spent by the items in the calibration procedure was investigated recommendations as to the practical use of the designs are given

brownian motion from deterministic dynamics abstract certain deterministic dynamical systems exhibit a transition from non gaussian chaotic to brownian motion behavior when a suitable scaling limit is applied for a simple hyperbolic model system we analyze the structure of the corresponding strange attractor determine the invariant measure and elucidate the transition scenario leading to a gaussian stochastic process

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

optimal design in nonlinear multiresponse estimation poisson model for filter feeding summary d optimality criteria have been applied to construct locally optimal designs for a multiresponse nonlinear model simulated annealing was used to perform the needed numerical optimization calculations as this method can locate the global optimum of a function and can efficiently handle constraints in the independent variables the calculated optimal designs greatly reduce variances of model parameter estimates compared to variances from previously used empirical designs the effect of several design variables including the number of design points and the number of responses on the efficiency of the design was investigated and designs for various subsets of parameters were also calculated new directions for the design of future experiments were suggested by this analysis

limit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustness abstract in this paper we numerically investigate the distribution of the sums of the iterates of the logistic map and the relationships among the important properties of the nonlinear dynamics in the vicinity of the chaos threshold by adding two kinds of contributions with different densities the first one is the well known white noise whereas the second is a newly defined one named as quartic term which makes contributions from the own structure of the map as the chaos threshold is approached the iterates of the standard logistic map i e noise free have strong correlations and the standard central limit theorem is not valid anymore in a recent work tirnakli 2009 it has been shown that the limit distribution seems to converge to q gaussian distribution which maximizes the nonadditive entropy s q 1 i p i q q 1 under appropriate conditions in this work we investigate the effect of these contributions i e white noise and quartic term on the limit distribution and on the range of the obtained q gaussian distribution as a result of these findings under the existence of white noise and also the quartic term we analyse the validity of the scaling relations among correlation fractality the lyapunov divergence and q gaussian distributions which have recently been observed in afsar 2014 the results obtained here strengthen the argument that the central limit behaviour is given by a q gaussian as the chaos threshold is approached and indicate that the scaling relations obtained for the standard logistic map among the range of the q gaussian the correlation dimension the correlation length the lyapunov exponent fractality and the distance from the chaos threshold are robust under the existence of white noise and the quartic term

the n city travelling salesman problem statistical mechanics and the metropolis algorithm in any n city travelling salesman problem there are n 1 mathord left vphantom 2 right kern nulldelimiterspace 2 possible tours we use the metropolis algorithm to generate a sequence of such tours this sequence may be viewed as the random evolution of a physical system in contact with a heat bath as the temperature is lowered the tours generated approach the optimal tour it appears that for large n one arrives within a few percent of the optimal solution in better than quadratic time

efficient computational algorithm for optimal continuous experimental designs abstract a simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed an alternative proof of the monotonic convergence for d optimal criterion on continuous design spaces is provided we further show that the proposed algorithm converges to the d optimal design we also provide an algorithm for the a optimality and conjecture that the algorithm converges monotonically on continuous design spaces different numerical examples are used to demonstrate the usefulness and performance of the proposed algorithms

the transition from deterministic chaos to a stochastic process abstract deterministic dynamical systems of langevin type recently introduced by beck and roepsdorf physica a 145 1987 1 generate langevin dynamics in a suitable limit we discuss the transition from chaos to randomness in these systems under the point of view of the attractor dimension and dynamical entropy and show that the limit of a stochastic process is reached via a shift of the deterministic properties towards the infinitesimal length scales

the equivalence of constrained and weighted designs in multiple objective design problems abstract several competing objectives may be relevant in the design of an experiment the competing objectives may not be easy to characterize in a single optimality criterion one approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria an alternative approach has been to optimize one criterion subject to constraints on the other criteria an equivalence theorem is presented for the bayesian constrained design problem equivalence theorems are essential in verifying optimality of proposed designs especially when as in most nonlinear design problems numerical optimization is required this theorem is used to show that the results of cook and wong on the equivalence of the weighted and constrained problems apply much more generally the results are applied to bayesian nonlinear design problems with several objectives

optimal bayesian adaptive design for test item calibration an optimal adaptive design for test item calibration based on bayesian optimality criteria is presented the design adapts the choice of field test items to the examinees taking an operational adaptive test using both the information in the posterior distributions of their ability parameters and the current posterior distributions of the field test parameters different criteria of optimality based on the two types of posterior distributions are possible the design can be implemented using an mcmc scheme with alternating stages of sampling from the posterior distributions of the test takers ability parameters and the parameters of the field test items while reusing samples from earlier posterior distributions of the other parameters results from a simulation study demonstrated the feasibility of the proposed mcmc implementation for operational item calibration a comparison of performances for different optimality criteria showed faster calibration of substantial numbers of items for the criterion of d optimality relative to a optimality a special case of c optimality and random assignment of items to the test takers

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

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

optimal designs for the rasch model in this paper optimal designs will be derived for estimating the ability parameters of the rasch model when difficulty parameters are known it is well established that a design is locally d optimal if the ability and difficulty coincide but locally optimal designs require that the ability parameters to be estimated are known to attenuate this very restrictive assumption prior knowledge on the ability parameter may be incorporated within a bayesian approach several symmetric weight distributions e g uniform normal and logistic distributions will be considered furthermore maximin efficient designs are developed where the minimal efficiency is maximized over a specified range of ability parameters

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

fast chaos versus white noise entropy analysis and a fokker planck model for the slow dynamics abstract we show in detail how methods of time series analysis such as dimension and entropy estimates support the idea that fast low dimensional chaos can be modelled properly by noise motivated by this observation we derive a formalism by which fast chaotic degrees of freedom in systems with time scale separation can be replaced by a suitable stochastic process a fokker planck equation for the phase space density of the slow degrees of freedom is derived from the full deterministic system by a projection operator technique together with a perturbation expansion we compare two different projection strategies and illustrate the resulting equations by specifying them for a simple model system

coarse grained dynamical entropies investigation of high entropic dynamical systems abstract coarse grained dynamical entropies characterize in a quantitative way the precision dependent predictability of a system this gives a much more complete description than solely the kolmogorov sinai entropy the concept is applied to two classes of high entropic systems to one class which simulates stochastic processes in some suitable limit and another class of extensively chaotic spatially extended systems in both cases the coarse grained entropies yield new insight into the length scale dependent complexity of the systems

optimal sequential designs for on line item estimation replenishing item pools for on line ability testing requires innovative and efficient data collection designs by generating locald optimal designs for selecting individual examinees and consistently estimating item parameters in the presence of error in the design points sequential procedures are efficient for on line item calibration the estimating error in the on line ability values is accounted for with an item parameter estimate studied by stefanski and carroll locallyd optimaln point designs are derived using the branch and bound algorithm of welch in simulations the overall sequential designs appear to be considerably more efficient than random seeding of items

applications of the annealing algorithm to combinatorial problems in statistics summary there are several problems in statistics which can be formulated so that the desired solution is the global minimum of some explicitly defined objective function in many cases the number of candidate solutions increases exponentially with the size of the problem making exhaustive search impossible but descent procedures devised to reduce the number of solutions examined can terminate with local minima in this paper we describe the annealing algorithm a widely applicable stochastic search procedure which can escape local optima and we use the evolutionary tree problem to illustrate the method of application

on intrinsic randomness of dynamical systems we discuss the problem of nonunitary equivalence via positivity preserving similarity transformations between the unitary groups associated with deterministic dynamical evolution and semigroups associated with stochastic processes dynamical systems admitting such nonunitary equivalence with stochastic markov processes are said to beintrinsically random in a previous work it was found that the so called bernoulli systems discrete time are intrinsically random in this sense this result is extended here by showing that a more general class of dynamical systems the so calledk systems andk flows are intrinsically random the connection of intrinsic randomness with local instability of motion is briefly discussed we also show that markov processes associated through nonunitary equivalence tononisomorphic k flows are necessarily non isomorphic