multiple window parallel adaptive boundary finding in computer vision the problem considered in this paper is the estimation of highly variable object boundaries in noisy images boundaries may be those of a tank in an ir image a spinal canal in a cat scan a cloud in a visible light image etc or they may be internal to an object such as the boundary between a spherical surface and a cylindrical surface in a manufactured object the focus of the paper is on parallel multiple window boundary estimation algorithms here the image field is parti tioned into an array of rectangular windows and boundary finders are run simultaneously within the windows the boundary segments found within the windows are then seamed together to obtain meaningful global boundaries the entire procedure is treated within a maximum likelihood estimation framework that we have developed for boundary finding although our multiple window estimation approach can be used with a number of local boundary finding algorithms we concen trate on one which is based on dynamic programming and will produce the true maximum likelihood boundary some theoretical considera tions for boundary model design and boundary finding runtime are covered included is the use of a low computational cost f test for test ing whether a window contains a boundary and an analytical treatment which shows that use of coarse pixels with a chi square test or an f test improves the probability of correctly recognizing whether a boundary is present in a window

statistical inference based on latent ability estimates the quality of approximations to first and second order moments e g statistics like means variances regression coefficients based on latent ability estimates is being discussed the ability estimates are obtained using either the rasch or the two parameter logistic model straightforward use of such statistics to make inferences with respect to true latent ability is not recommended unless we account for the fact that the basic quantities are estimates in this paper true score theory is used to account for the latter the counterpart of observed true score being estimated true latent ability it is shown that statistics based on the true score theory are virtually unbiased if the number of items presented to each examinee is larger than fifteen three types of estimators are compared maximum likelihood weighted maximum likelihood and bayes modal furthermore the dis advantages of the true score method and direct modeling of latent ability is discussed

psychometrics behind computerized adaptive testing the paper provides a survey of 18 years progress that my colleagues students both former and current and i made in a prominent research area in psychometrics computerized adaptive testing cat we start with a historical review of the establishment of a large sample foundation for cat it is worth noting that the asymptotic results were derived under the framework of martingale theory a very theoretical perspective of probability theory which may seem unrelated to educational and psychological testing in addition we address a number of issues that emerged from large scale implementation and show that how theoretical works can be helpful to solve the problems finally we propose that cat technology can be very useful to support individualized instruction on a mass scale we show that even paper and pencil based tests can be made adaptive to support classroom teaching

on azema yor processes their optimal properties and the bachelier drawdown equation we study the class of azema yor processes defined from a gene ral semi martingale with a continuous running supremum process we show that they arise as unique strong solutions of the bachelier stochastic diff erential equation which we prove is equivalent to the drawdown equation solutions of the latter have the drawdown property they always stay above a given function of their past supre mum we then show that any process which satisfies the drawdow n property is in fact an azema yor process the proofs exploit group structure of the set of azema yor processes indexed by functions which we introduce secondly we study in detail azema yor martingales defined f rom a non negative local martingale converging to zero at infinity we establis h relations between

image compression using wavelet transform and multiresolution decomposition schemes for image compression of black and white images based on the wavelet transform are presented the multiresolution nature of the discrete wavelet transform is proven as a powerful tool to represent images decomposed along the vertical and horizontal directions using the pyramidal multiresolution scheme the wavelet transform decomposes the image into a set of subimages called shapes with different resolutions corresponding to different frequency bands hence different allocations are tested assuming that details at high resolution and diagonal directions are less visible to the human eye the resultant coefficients are vector quantized vq using the lgb algorithm by using an error correction method that approximates the reconstructed coefficients quantization error we minimize distortion for a given compression rate at low computational cost several compression techniques are tested in the first experiment several 512 spl times 512 images are trained together and common table codes created using these tables the training sequence black and white images achieve a compression ratio of 60 65 and a psnr of 30 33 to investigate the compression on images not part of the training set many 480 spl times 480 images of uncalibrated faces are trained together and yield global tables code images of faces outside the training set are compressed and reconstructed using the resulting tables the compression ratio is 40 psnrs are 30 36 images from the training set have similar compression values and quality finally another compression method based on the end vector bit allocation is examined

wavelet analysis on the circle the construction of a wavelet analysis over the circle is presented the spaces of infinitely times differentiable functions tempered distributions and square integrable functions over the circle are analyzed by means of the wavelet transform

the joint law of the maximum and terminal value of a martingale in this paper we characterise the possible joint laws of the maximum and terminal value of a uniformly integrable martingale we also characterise the joint laws of the maximum and terminal value of a convergent continuous local martingale vanishing at zero a number of earlier results on the possible laws of the maximum can be deduced quite easily

optimal transport and skorokhod embedding the skorokhod embedding problem is to represent a given probability as the distribution of brownian motion at a chosen stopping time over the last 50 years this has become one of the important classical problems in probability theory and a number of authors have constructed solutions with particular optimality properties these constructions employ a variety of techniques ranging from excursion theory to potential and pde theory and have been used in many different branches of pure and applied probability we develop a new approach to skorokhod embedding based on ideas and concepts from optimal mass transport in analogy to the celebrated article of gangbo and mccann on the geometry of optimal transport we establish a geometric characterization of skorokhod embeddings with desired optimality properties this leads to a systematic method to construct optimal embeddings it allows us for the first time to derive all known optimal skorokhod embeddings as special cases of one unified construction and leads to a variety of new embeddings while previous constructions typically used particular properties of brownian motion our approach applies to all sufficiently regular markov processes

on the monotonicity principle of optimal skorokhod embedding problem this is a continuation of our accompanying paper siam j control optim 54 2016 pp 2174 2201 we provide an alternative proof of the monotonicity principle for the optimal skorokhod embedding problem established in beiglbock cox and huesmann optimal transport and skorokhod embedding preprint 2013 our proof is based on the adaptation of the monge kantorovich duality in our context a delicate application of the optional cross section theorem and a clever conditioning argument introduced in beiglbock cox and huesmann optimal transport and skorokhod embedding preprint 2013

geometry of distribution constrained optimal stopping problems we adapt ideas and concepts developed in optimal transport and its martingale variant to give a geometric description of optimal stopping times tau of brownian motion subject to the constraint that the distribution of tau is a given probability mu the methods work for a large class of cost processes at a minimum we need the cost process to be measurable and mathcal f 0 t t ge 0 adapted continuity assumptions can be used to guarantee existence of solutions we find that for many of the cost processes one can come up with the solution is given by the first hitting time of a barrier in a suitable phase space as a by product we recover classical solutions of the inverse first passage time problem shiryaev s problem

martingale optimal transport duality we obtain a dual representation of the kantorovich functional defined for functions on the skorokhod space using quotient sets our representation takes the form of a choquet capacity generated by martingale measures satisfying additional constraints to ensure compatibility with the quotient sets these sets contain stochastic integrals defined pathwise and two such definitions starting with simple integrands are given another important ingredient of our analysis is a regularized version of jakubowski s s topology on the skorokhod space

the root solution to the multi marginal embedding problem an optimal stopping and time reversal approach we provide a complete characterisation of the root solution to the skorokhod embedding problem sep by means of an optimal stopping formulation our methods are purely probabilistic and the analysis relies on a tailored time reversal argument this approach allows us to address the long standing question of a multiple marginals extension of the root solution of the sep our main result establishes a complete solution to the n marginal sep using first hitting times of barrier sets by the time space process the barriers are characterised by means of a recursive sequence of optimal stopping problems moreover we prove that our solution enjoys a global optimality property extending the one marginal root case our results hold for general one dimensional martingale diffusions

complete duality for martingale optimal transport on the line we study the optimal transport between two probability measures on the real line where the transport plans are laws of one step martingales a quasi sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward cost functions absence of a duality gap and existence of dual optimizers both properties are shown to fail in the classical formulation as a consequence of the duality result we obtain a general principle of cyclical monotonicity describing the geometry of optimal transports

the asymptotic posterior normality of the latent trait in an irt model it has long been part of the item response theory irt folklore that under the usual empirical bayes unidimensional irt modeling approach the posterior distribution of examinee ability given test response is approximately normal for a long test under very general and nonrestrictive nonparametric assumptions we make this claim rigorous for a broad class of latent models

item selection in multidimensional computerized adaptive testing gaining information from different angles over the past thirty years obtaining diagnostic information from examinees item responses has become an increasingly important feature of educational and psychological testing the objective can be achieved by sequentially selecting multidimensional items to fit the class of latent traits being assessed and therefore multidimensional computerized adaptive testing mcat is one reasonable approach to such task this study conducts a rigorous investigation on the relationships among four promising item selection methods d optimality kl information index continuous entropy and mutual information some theoretical connections among the methods are demonstrated to show how information about the unknown vector can be gained from different perspectives two simulation studies were carried out to compare the performance of the four methods the simulation results showed that mutual information not only improved the overall estimation accuracy but also yielded the smallest conditional mean squared error in most region of in the end the overlap rates were calculated to empirically show the similarity and difference among the four methods

spatially adaptive wavelet based multiscale image restoration in this paper we present a new spatially adaptive approach to the restoration of noisy blurred images which is particularly effective at producing sharp deconvolution while suppressing the noise in the flat regions of an image this is accomplished through a multiscale kalman smoothing filter applied to a prefiltered observed image in the discrete separable 2 d wavelet domain the prefiltering step involves constrained least squares filtering based on optimal choices for the regularization parameter this leads to a reduction in the support of the required state vectors of the multiscale restoration filter in the wavelet domain and improvement in the computational efficiency of the multiscale filter the proposed method has the benefit that the majority of the regularization or noise suppression of the restoration is accomplished by the efficient multiscale filtering of wavelet detail coefficients ordered on quadtrees not only does this lead to potential parallel implementation schemes but it permits adaptivity to the local edge information in the image in particular this method changes filter parameters depending on scale local signal to noise ratio snr and orientation because the wavelet detail coefficients are a manifestation of the multiscale edge information in an image this algorithm may be viewed as an edge adaptive multiscale restoration approach

an iterated azema yor type embedding for finitely many marginals we solve the nn marginal skorokhod embedding problem for a continuous local martingale and a sequence of probability measures 1 n 1 n which are in convex order and satisfy an additional technical assumption our construction is explicit and is a multiple marginal generalization of the azema and yor in seminaire de probabilites xiii univ strasbourg strasbourg 1977 78 1979 90 115 springer solution in particular we recover the stopping boundaries obtained by brown hobson and rogers probab theory related fields 119 2001 558 578 and madan and yor bernoulli 8 2002 509 536 our technical assumption is necessary for the explicit embedding as demonstrated with a counterexample we discuss extensions to the general case giving details when n 3n 3 in our analysis we compute the law of the maximum at each of the nn stopping times this is used in henry labordere et al ann appl probab 26 2016 1 44 to show that the construction maximizes the distribution of the maximum among all solutions to the nn marginal skorokhod embedding problem the result has direct implications for robust pricing and hedging of lookback options

the recursive pyramid algorithm for the discrete wavelet transform the recursive pyramid algorithm rpa is a reformulation of the classical pyramid algorithm pa for computing the discrete wavelet transform dwt the rpa computes the n point dwt in real time running dwt using just l log n spl minus 1 words of storage as compared with o n words required by the pa l is the length of the wavelet filter the rpa is combined with the short length fir filter algorithms to reduce the number of multiplications and additions

investigating the impact of uncertainty about item parameters on ability estimation asymptotic expansions of the maximum likelihood estimator mle and weighted likelihood estimator wle of an examinee s ability are derived while item parameter estimators are treated as covariates measured with error the asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators a numerical example is presented to illustrate how to apply the formulae to evaluate the impact of uncertainty about item parameters on ability estimation and the appropriateness of estimating ability using the regular mle or wle method

psychometrics from practice to theory and back the paper surveys 15 years of progress in three psychometric research areas latent dimensionality structure test fairness and skills diagnosis of educational tests it is proposed that one effective model for selecting and carrying out research is to chose one s research questions from practical challenges facing educational testing then bring to bear sophisticated probability modeling and statistical analyses to solve these questions and finally to make effectiveness of the research answers in meeting the educational testing challenges be the ultimate criterion for judging the value of the research the problem solving power and the joy of working with a dedicated focused and collegial group of colleagues is emphasized finally it is suggested that the summative assessment testing paradigm that has driven test measurement research for over half a century is giving way to a new paradigm that in addition embraces skills level formative assessment opening up a plethora of challenging exciting and societally important research problems for psychometricians

a stochastic representation theorem with applications to optimization and obstacle problems we study a new type of representation problem for optional processes with connections to singular control optimal stopping and dynamic allocation problems as an application we show how to solve a variant of skorohod s obstacle problem in the context of backward stochastic differential equations

the minimum maximum of a continuous martingale with given initial and terminal laws let m t 0 t 1 be a continuous martingale with initial law m 0 0 and terminal law m 1 1 and let s sup 0 t 1 m t in this paper we prove that there exists a greatest lower bound with respect to stochastic ordering of probability measures on the law of s we give an explicit construction of this bound furthermore a martingale is constructed which attains this minimum by solving a skorokhod embedding problem the form of this martingale is motivated by a simple picture the result is applied to the robust hedging of a forward start digital option

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

digital image restoration using spatial interaction models this paper is concerned with developing fast nonrecursive algorithms for the minimum mean squared error restoration of degraded images the degradation is assumed to be due to a space invariant periodic nonseparable known point spread function and additive white noise our basic approach is to represent the images by a class of spatial interaction models namely the simultaneous autoregressve models and the conditional markov models defined on toroidal lattices and develop minimum mean squared error restoration algorithms using these models the restoration algorithms are optimal if the parameters characterizing the interaction models are exactly known however in practice the parameters are estimated from the images by using spatial interaction models we develop restoration algorithms that do not require the availability of the original image or its prototype the specific structure of the underlying lattice enables the implementation of the filters using fast fourier transform fft computations several restoration examples are given

martingale optimal transport and robust hedging in continuous time the duality between the robust or equivalently model independent hedging of path dependent european options and a martingale optimal transport problem is proved the financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time the hedging problem is to construct a minimal super hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given fixed maturity the dual is a monge kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that have a given marginal at maturity in addition to duality a family of simple piecewise constant super replication portfolios that asymptotically achieve the minimal super replication cost is constructed

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the geometry of multi marginal skorokhod embedding the skorokhod embedding problem is one of the classical problems in the theory of stochastic processes with applications in many different fields cf the surveys hobson in paris princeton lectures on mathematical finance 2010 volume 2003 of lecture notes in mathematics springer berlin 2011 obloj in probab surv 1 321 390 2004 many of these applications have natural multi marginal extensions leading to the optimal multi marginal skorokhod problem some of the first papers to consider this problem are brown et al probab theory relat fields 119 4 558 578 2001 hobson seminaire de probabilites xxxii volume 1686 of lecture notes in mathematics springer berlin 1998 madan and yor bernoulli 8 4 509 536 2002 however this turns out to be difficult using existing techniques only recently a complete solution was be obtained in cox et al probab theory relat fields 173 211 259 2018 establishing an extension of the root construction while other instances are only partially answered or remain wide open in this paper we extend the theory developed in beiglbock et al invent math 208 2 327 400 2017 to the multi marginal setup which is comparable to the extension of the optimal transport problem to the multi marginal optimal transport problem as for the one marginal case this viewpoint turns out to be very powerful in particular we are able to show that all classical optimal embeddings have natural multi marginal counterparts notably these different constructions are linked through a joint geometric structure and the classical solutions are recovered as particular cases moreover our results also have consequences for the study of the martingale transport problem as well as the peacock problem

fast algorithms for discrete and continuous wavelet transforms several algorithms are reviewed for computing various types of wavelet transforms the mallat algorithm 1989 the a trous algorithm and their generalizations by shensa the goal of this work is to develop guidelines for implementing discrete and continuous wavelet transforms efficiently and to compare the various algorithms obtained and give an idea of possible gains by providing operation counts most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform although this general method is already efficient it is shown that noticeable computational savings can be obtained by applying known fast convolution techniques such as the fft fast fourier transform in a suitable manner the modified algorithms are termed fast because of their ability to reduce the computational complexity per computed coefficient from l to log l within a small constant factor for large filter lengths l for short filters smaller gains are obtained fast running fir finite impulse response filtering techniques allow one to achieve typically 30 savings in computations

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

computerized adaptive testing under nonparametric irt models nonparametric item response models have been developed as alternatives to the relatively inflexible parametric item response models an open question is whether it is possible and practical to administer computerized adaptive testing with nonparametric models this paper explores the possibility of computerized adaptive testing when using nonparametric item response models a central issue is that the derivatives of item characteristic curves may not be estimated well which eliminates the availability of the standard maximum fisher information criterion as alternatives procedures based on shannon entropy and kullback leibler information are proposed for a long test these procedures which do not require the derivatives of the item characteristic eurves become equivalent to the maximum fisher information criterion a simulation study is conducted to study the behavior of these two procedures compared with random item selection the study shows that the procedures based on shannon entropy and kullback leibler information perform similarly in terms of root mean square error and perform much better than random item selection the study also shows that item exposure rates need to be addressed for these methods to be practical

the asymptotic posterior normality of the latent trait for polytomous irt models chang and stout 1993 presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous irt models this paper presents an extention of their results to polytomous irt models in a fairly straightforward manner in addition a global information function is defined and the relationship between the global information function and the currently used information functions is discussed an information index that combines both the global and local information is proposed for adaptive testing applications

on holland s dutch identity conjecture the manifest probabilities of observed examinee response patterns resulting from marginalization with respect to the latent ability distribution produce the marginal likelihood function in item response theory under the conditions that the posterior distribution of examinee ability given some test response pattern is normal and the item logit functions are linear holland 1990a gives a quadratic form for the log manifest probabilities by using the dutch identity further holland conjectures that this special quadratic form is a limiting one for all smooth unidimensional item response models as test length tends to infinity the purpose of this paper is to give three counterexamples to demonstrate that holland s dutch identity conjecture does not hold in general the counterexamples suggest that only under strong assumptions can it be true that the limits of log manifest probabilities are quadratic three propositions giving sets of such strong conditions are given

wasserstein barycenters over riemannian manifolds we study barycenters in the space of probability measures on a riemannian manifold equipped with the wasserstein metric under reasonable assumptions we establish absolute continuity of the barycenter of general measures p p m p p m on wasserstein space extending on one hand results in the euclidean case for barycenters between finitely many measures of agueh and carlier 1 to the riemannian setting and on the other hand results in the riemannian case of cordero erausquin mccann schmuckenschlager 12 for barycenters between two measures to the multi marginal setting our work also extends these results to the case where is not finitely supported as applications we prove versions of jensen s inequality on wasserstein space and a generalized brunn minkowski inequality for a random measurable set on a riemannian manifold

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

kullback leibler information and its applications in multi dimensional adaptive testing this paper first discusses the relationship between kullback leibler information kl and fisher information in the context of multi dimensional item response theory and is further interpreted for the two dimensional case from a geometric perspective this explication should allow for a better understanding of the various item selection methods in multi dimensional adaptive tests mat which are based on these two information measures the kl information index ki method is then discussed and two theorems are derived to quantify the relationship between ki and item parameters due to the fact that most of the existing item selection algorithms for mat bear severe computational complexity which substantially lowers the applicability of mat two versions of simplified kl index ski built from the analytical results are proposed to mimic the behavior of ki while reducing the overall computational intensity

optimal transportation under controlled stochastic dynamics we consider an extension of the monge kantorovitch optimal transportation problem the mass is transported along a continuous semimartingale and the cost of transportation depends on the drift and the diffusion coefficients of the continuous semimartingale the optimal transportation problem minimizes the cost among all continuous semimartingales with given initial and terminal distributions our first main result is an extension of the kantorovitch duality to this context we also suggest a finite difference scheme combined with the gradient projection algorithm to approximate the dual value we prove the convergence of the scheme and we derive a rate of convergence we finally provide an application in the context of financial mathematics which originally motivated our extension of the monge kantorovitch problem namely we implement our scheme to approximate no arbitrage bounds on the prices of exotic options given the implied volatility curve of some maturity

log multiplicative association models as item response models log multiplicative association lma models which are special cases of log linear models have interpretations in terms of latent continuous variables two theoretical derivations of lma models based on item response theory irt arguments are presented first we show that anderson and colleagues anderson vermunt 2000 anderson bockenholt 2000 anderson 2002 who derived lma models from statistical graphical models made the equivalent assumptions as holland 1990 when deriving models for the manifest probabilities of response patterns based on an irt approach we also present a second derivation of lma models where item response functions are specified as functions of rest scores these various connections provide insights into the behavior of lma models as item response models and point out philosophical issues with the use of lma models as item response models we show that even for short tests lma and standard irt models yield very similar to nearly identical results when data arise from standard irt models log multiplicative association models can be used as item response models and do not require numerical integration for estimation

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

characterizing the manifest probability distributions of three latent trait models for accuracy and response time in this paper we study the statistical relations between three latent trait models for accuracies and response times the hierarchical model hm of van der linden psychometrika 72 3 287 308 2007 the signed residual time model sm proposed by maris and van der maas psychometrika 77 4 615 633 2012 and the drift diffusion model dm as proposed by tuerlinckx and de boeck psychometrika 70 4 629 650 2005 one important distinction between these models is that the hm and the dm either assume or imply that accuracies and response times are independent given the latent trait variables while the sm does not in this paper we investigate the impact of this conditional independence property or a lack thereof on the manifest probability distribution for accuracies and response times we will find that the manifest distributions of the latent trait models share several important features such as the dependency between accuracy and response time but we also find important differences such as in what function of response time is being modeled our method for characterizing the manifest probability distributions is related to the dutch identity holland in psychometrika 55 6 5 18 1990

weighted likelihood estimation of ability in item response theory applications of item response theory which depend upon its parameter invariance property require that parameter estimates be unbiased a new method weighted likelihood estimation wle is derived and proved to be less biased than maximum likelihood estimation mle with the same asymptotic variance and normal distribution wle removes the first order bias term from mle two monte carlo studies compare wle with mle and bayesian modal estimation bme of ability in conventional tests and tailored tests assuming the item parameters are known constants the monte carlo studies favor wle over mle and bme on several criteria over a wide range of the ability scale

a characterization of monotone unidimensional latent variable models recently the problem of characterizing monotone unidimensional latent variable models for binary repeated measures was studied by ellis and van den wollenberg and by junker we generalize their work with a de finetti like characterization of the distribution of repeated measures x x 1 x 2 that can be represented with mixtures of likelihoods of independent but not identically distributed random variables where the data satisfy a stochastic ordering property with respect to the mixing variable the random variables x j may be arbitrary real valued random variables we show that the distribution of x can be given a monotone unidimensional latent variable representation that is useful in the sense of junker if and only if this distribution satisfies conditional association ca and a vanishing conditional dependence vcd condition which asserts that finite subsets of the variables in x become independent as we condition on a larger and larger segment of the remaining variables in x it is also interesting that the mixture representation is in a certain ordinal sense unique when ca and vcd hold the characterization theorem extends and simplifies the main result of junker and generalizes methods of ellis and van den wollenberg to a much broader class of models exchangeable sequences of binary random variables also satisfy both ca and vcd as do exchangeable sequences arising as location mixtures in the same way that de finetti s theorem provides a path toward justifying standard i i d mixture components in hierarchical models on the basis of our intuitions about the exchangeability of observations this theorem justifies one dimensional latent variable components in hierarchical models in terms of our intuitions about positive association and redundancy between observations because these conditions are on the joint distribution of the observable data x they may also be used to construct asymptotically power 1 tests for unidimensional latent variable models

max plus decomposition of supermartingales and convex order application to american options and portfolio insurance we are concerned with a new type of supermartingale decomposition in the max plus algebra which essentially consists in expressing any supermartingale of class d as a conditional expectation of some running supremum process as an application we show how the max plus supermartingale decomposition allows in particular to solve the american optimal stopping problem without having to compute the option price some illustrative examples based on one dimensional diffusion processes are then provided another interesting application concerns the portfolio insurance hence based on the max plus martingale we solve in the paper an optimization problem whose aim is to find the best martingale dominating a given floor process on every intermediate date w r t the convex order on terminal values

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

structure of optimal martingale transport plans in general dimensions given two probability measures mu and nu in convex order on r d we study the profile of one step martingale plans pi on r d x r d that optimize the expected value of the modulus of their increment among all martingales having mu and nu as marginals while there is a great deal of results for the real line i e when d 1 much less is known in the richer and more delicate higher dimensional case that we tackle in this paper we show that many structural results can be obtained provided the initial measure mu is absolutely continuous with respect to the lebesgue measure one such a property is that mu almost every x in r d is transported by the optimal martingale plan into a probability measure pi x concentrated on the extreme points of the closed convex hull of its support this will be established for the distance cost c x y vertical bar x y vertical bar in the two dimensional case and also for any d 3 as long as the marginals are in subharmonic order in some cases pi x is supported on the vertices of a k x dimensional polytope such as when the target measure is discrete duality plays a crucial role in our approach even though in contrast to standard optimal transports the dual extremal problem may not be attained in general we show however that martingale supporting borel subsets of r d x r d can be decomposed into a collection of mutually disjoint components by means of a convex paving of the source space in such a way that when the martingale is optimal for a general cost function each of the components then supports a restricted optimal martingale transport whose dual problem is attained this decomposition is used to obtain structural results in cases where global duality is not attained on the other hand it shows that certain optimal martingale supporting borel sets can be viewed as higher dimensional versions of nikodym type sets the paper focuses on the distance cost but much of the results hold for general lipschitz cost functions

asymptotic null distribution of person fit statistics with estimated person parameter person fit statistics are considered for dichotomous item response models the asymptotic null distribution is derived for statistics which are linear in the item responses and in which the ability parameter is replaced by an estimate this allows the asymptotically correct standardization of linear person fit statistics with estimated ability parameter the fact that the ability parameter is estimated usually decreases the asymptotic variance

efficient matrix sampling instruments for correlated latent traits examples from the national assessment of educational progress abstract we study the efficiency of administering different subsets of a large collection of items in a sample survey to different people to estimate the distribution of several correlated traits the designs are motivated by examples from the national assessment of educational progress an ongoing survey of u s students in the fourth eighth and twelfth grades in this survey the traits represent proficiency in different subjects for example the mathematics assessment estimates proficiency with numbers and operations measurement and several other traits time constraints and concerns about student motivation limit the number of items that can be administered to a small subset of the items defining each trait we find that effective matrix designs assign some items to measure each trait even if the resulting number of items assigned to each trait must be small efficient allocations of items are ones that produce measurement error variances for a given trait that are similar for each sampled studen

bootstrap calibrated interval estimates for latent variable scores in item response theory in most item response theory applications model parameters need to be first calibrated from sample data latent variable lv scores calculated using estimated parameters are thus subject to sampling error inherited from the calibration stage in this article we propose a resampling based method namely bootstrap calibration bc to reduce the impact of the carryover sampling error on the interval estimates of lv scores bc modifies the quantile of the plug in posterior i e the posterior distribution of the lv evaluated at the estimated model parameters to better match the corresponding quantile of the true posterior i e the posterior distribution evaluated at the true model parameters over repeated sampling of calibration data furthermore to achieve better coverage of the fixed true lv score we explore the use of bc in conjunction with jeffreys prior we investigate the finite sample performance of bc via monte carlo simulations and apply it to two empirical data examples

superreplication of financial derivatives via convex programming we give a method based on convex programming to calculate the optimal superreplicating and subreplicating prices and corresponding hedging portfolios of a financial derivative in terms of other financial derivatives in a discrete time setting our method produces a model that matches the superreplicating or subreplicating price within an arbitrary precision and is consistent with the other financial derivatives prices applications include robust replication in terms of call prices with various strikes and maturities of forward start options volatility and variance swaps and derivatives cliquet calls barrier options and lookback and asian options numerical examples show that in some cases the best superreplicating and or subreplicating prices are within 10 of the price obtained by a standard model but considerably differ from it in other cases our method can incorporate bid ask spreads interest rates and dividends and various limitations to the diffusion model the supplementary material is a

on a problem of optimal transport under marginal martingale constraints the basic problem of optimal transportation consists in minimizing the expected costs e c x 1 x 2 by varying the joint distribution x 1 x 2 where the marginal distributions of the random variables x 1 and x 2 are fixed inspired by recent applications in mathematical finance and connections with the peacock problem we study this problem under the additional condition that x i i 1 2 is a martingale that is e x 2 x 1 x 1 we establish a variational principle for this problem which enables us to determine optimal martingale transport plans for specific cost functions in particular we identify a martingale coupling that resembles the classic monotone quantile coupling in several respects in analogy with the celebrated theorem of brenier the following behavior can be observed if the initial distribution is continuous then this monotone martingale is supported by the graphs of two functions t 1 t 2 r r

constrained optimal transport the classical duality theory of kantorovich c r doklady acad sci urss ns 37 199 201 1942 and kellerer z wahrsch verw gebiete 67 4 399 432 1984 for classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided this abstract generalization is set in a banach lattice mathcal x with an order unit the problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of mathcal x and the dual problem is defined on the bi dual of mathcal x these results are then applied to several extensions of the classical optimal transport

the importance of strictly local martingales applications to radial ornstein uhlenbeck processes for a wide class of local martingales m t there is a default function which is not identically zero only when m t is strictly local i e not a true martingale this default in the martingale property allows us to characterize the integrability of functions of sup s t m s in terms of the integrability of the function itself we describe some paradoxical mean decreasing local sub martingales and the default functions for bessel processes and radial ornstein uhlenbeck processes in relation to their first hitting and last exit times

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

nonlinear sequential designs for logistic item response theory models with applications to computerized adaptive tests computerized adaptive testing is becoming increasingly popular due to advancement of modern computer technology it differs from the conventional standardized testing in that the selection of test items is tailored to individual examinee s ability level arising from this selection strategy is a nonlinear sequential design problem we study in this paper the sequential design problem in the context of the logistic item response theory models we show that the adaptive design obtained by maximizing the item information leads to a consistent and asymptotically normal ability estimator in the case of the rasch model modifications to the maximum information approach are proposed for the two and three parameter logistic models similar asymptotic properties are established for the modified designs and the resulting estimator examples are also given in the case of the two parameter logistic model to show that without such modifications the maximum likelihood estimator of the ability parameter may not be consistent

a shift invariant discrete wavelet transform this article presents a unifying approach to the derivation and implementation of a shift invariant wavelet transform of one and two dimensional 1 d and 2 d discrete signals starting with mallat s 1989 multiresolution wavelet representation mrwar it presents an analytical process through which a shift invariant orthogonal discrete wavelet transform called the multiscale wavelet representation mswar is obtained the coefficients in the mswar are shown to be inclusive of those in the mrwar with the implication that the derived representation is invertible the computational complexity of the mswar is quantified in terms of the required convolutions and its implementation is shown to be equivalent to the filter upsampling technique

on the sampling theory roundations of item response theory models item response theory it models are now in common use for the analysis of dichotomous item responses this paper examines the sampling theory foundations for statistical inference in these models the discussion includes some history on the stochastic subject versus the random sampling interpretations of the probability in irt models the relationship between three versions of maximum likelihood estimation for irt models estimating versus estimating predictors irt models and loglinear models the identifiability of irt models and the role of robustness and bayesian statistics from the sampling theory perspective

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

the maximum maximum of a martingale constrained by an intermediate law let m t be any martingale with m0 0 an intermediate law m1 1 and terminal law m2 2 and let m 2 sup0 t 2m t in this paper we prove that there exists an upper bound with respect to stochastic ordering of probability measures on the law of m 2 we construct using excursion theory a martingale which attains this maximum finally we apply this result to the robust hedging of a lookback option

what can we learn from plausible values in this paper we show that the marginal distribution of plausible values is a consistent estimator of the true latent variable distribution and furthermore that convergence is monotone in an embedding in which the number of items tends to infinity we use this result to clarify some of the misconceptions that exist about plausible values and also show how they can be used in the analyses of educational surveys

the advanced oca for 2 d discrete periodized wavelet transformation we develop a novel computation method for the 2 d discrete periodized wavelet transformation dpwt the new algorithm is based on the operator correlation algorithm oca compared with the classical 2 d pyramid algorithm the new advanced operator correlation algorithm aoca has two major advantages it requires half the number of multiplications and can yield the same output snr with half the precision of the dpwt filter coefficients furthermore the modular structure of the adca makes it particularly suitable for a vlsi implementation

the two sided stefan problem with a spatially dependent latent heat we prove existence and uniqueness of solutions to a problem which generalizes the two sided stefan problem the initial temperature distribution and variable latent heat may be given by positive measures rather than point functions and the free boundaries which result are essentially arbitrary increasing functions which need not exhibit any degree of smoothness in general nevertheless the solutions are classical in the sense that all derivatives and boundary values have the classical interpretation we also study connections with the skorohod embedding problem of probability theory and with a general class of optimal stoppmg problems

standard error of ability estimates and the classification accuracy and consistency of binary decisions while estimation bias is a primary concern in psychological and educational measurement the standard error is of equal importance in linking key aspects of the assessment structure especially when the assessment goal concerns the classification of individuals into categories e g master non mastery in this paper we show analytically how standard error of ability estimates affects expected classification accuracy and consistency when the decision is binary when standard error decreases the conditional classification accuracy and consistency increase given an examinee population and a cut score smaller standard error over the entire latent trait continuum guarantees higher overall expected classification accuracy and consistency we were also able to show the interrelationship between standard error the expected classification consistency and reliability utilizing the relationship between standard error and expected classification accuracy and consistency we derive the upper bounds of the overall expected classification accuracy and consistency of a fixed length computerized adaptive test the lower bound of the expected classification accuracy and consistency is also derived given a number of stopping rules of variable length computerized adaptive testing implications of these analytical results on operational tests are discussed

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159