statistics of stable marriages in the stable marriage problem n men and n women have to be matched by pairs under the constraint that the resulting matching is stable we study the statistical properties of stable matchings in the large n limit using both numerical and analytical methods generalizations of the model including singles and unequal numbers of men and women are also investigated

a stochastic approximation algorithm with markov chain monte carlo method for incomplete data estimation problems we propose a general procedure for solving incomplete data estimation problems the procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model the nonlinear structural measurement error model and the random effects model the procedure is based on the general principle of stochastic approximation and the markov chain monte carlo method applying the theory on adaptive algorithms we derive conditions under which the proposed procedure converges simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model

functions with bounded spectrum let 0 o has the same behavior as the sequence sup q i 0 in other words if we know all far points of supp ff we can wholly describe this behavior without any concrete calculation of z a p a 0 a paley wiener schwartz theorem for a nonconvex case which is a consequence of the result is given

flat histogram method comparison on the two dimensional ising model we compare the convergence of several flat histogram methods applied to the two dimensional ising model including the recently introduced stochastic approximation with a dynamic update factor sad method we compare this method to the wang landau wl method the 1 t variant of the wl method and standard stochastic approximation monte carlo samc in addition we consider a procedure wl followed by a production run with fixed weights that refines the estimation of the entropy we find that wl followed by a production run does converge to the true density of states in contrast to pure wl three of the methods converge robustly sad 1 t wl and wl followed by a production run of these sad does not require a priori knowledge of the energy range this work also shows that wl followed by a production run performs superior to other forms of wl while ensuring both ergodicity and detailed balance

on real paley wiener theorems for certain integral transforms we prove real paley wiener theorems for the inverse jacobi transform characterising the space of l2 functions whose image under the jacobi transform are smooth functions with compact support

stable and efficient multiple smoothing parameter estimation for generalized additive models representation of generalized additive models gam s using penalized regression splines allows gam s to be employed in a straightforward manner using penalized regression methods not only is inference facilitated by this approach but it is also possible to integrate model selection in the form of smoothing parameter selection into model fitting in a computationally efficient manner using well founded criteria such as generalized cross validation the current fitting and smoothing parameter selection methods for such models are usually effective but do not provide the level of numerical stability to which users of linear regression packages for example are accustomed in particular the existing methods cannot deal adequately with numerical rank deficiency of the gam fitting problem and it is not straightforward to produce methods that can do so given that the degree of rank deficiency can be smoothing parameter dependent in addition models with the potential flexibility of gam s can also present

local polynomial kernel regression for generalized linear models and quasi likelihood functions abstract we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi likelihood contexts in the ordinary regression case local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity one noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators these properties are shown to carry over to generalized linear model and quasi likelihood settings we also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state of the art bandwidth selection methods

stability of stochastic approximation under verifiable conditions in this paper we address the problem of the stability and convergence of the stochastic approximation procedure theta n 1 theta n gamma n 1 h theta n xi n 1 the stability of such sequences theta n is known to heavily rely on the behavior of the mean field h at the boundary of the parameter set and the magnitude of the stepsizes used the conditions typically required to ensure convergence and in particular the boundedness or stability of theta n are either too difficult to check in practice or not satisfied at all this is the case even for very simple models the most popular technique for circumventing the stability problem consists of constraining theta n to a compact subset mathcal k in the parameter space this is obviously not a satisfactory solution as the choice of mathcal k is a delicate one in this paper we first prove a deterministic stability result which relies on simple conditions on the sequences xi n and gamma n we then propose and analyze an algorithm based on projections on adaptive truncation sets which ensures that the aforementioned conditions required for stability are satisfied we focus in particular on the case where xi n is a so called markov state dependent noise we establish both the stability and convergence with probability 1 w p 1 of the algorithm under a set of simple and verifiable assumptions we illustrate our results with an example related to adaptive markov chain monte carlo algorithms

on lagrange interpolations and kramer s sampling theorem associated with self adjoint boundary value problems abstract it is known that kramer s sampling theorem and lagrange type interpolation generalize the celebrated whittaker shannon kotel nikov sampling theorem in two different directions however no direct connection between these two directions seems to be known in this article we show that kramer s sampling theorem gives nothing more than the lagrange type interpolations provided that the kernel function associated with kramer s theorem arises from a self adjoint boundary value problem with sample eigenvalues

an irregular sampling theorem for functions bandlimited in a generalized sense it is shown that a well known irregular sampling formula for ordinary bandlimited functions is also valid for functions bandlimited in a generalized sense except for some necessary modifications

on kramer s sampling theorem associated with general strum liouville problems and lagrange interpolation kramer s sampling theorem which is a generalization of shannon s sampling theorem and its relationship with lagrange interpolation is studied kramer s sampling theorem is extended to the case where the interval a b is infinite and it is shown that any function that has a sampling expansion in the scope of kramer s theorem also has a lagrange type interpolation expansion provided that the kernel associated with kramer s theorem arises from a second order sturm liouville boundary value problem whether it is regular or singular this new technique not only reproduces many of the known sampling expansions such as those for the cosine the finite hankel and the continuous legendre transforms but also generates new ones such as those for the continuous jacobi laguerre and hermite transforms

basic sturm liouville problems this paper is devoted to studying a q analogue of sturm liouville eigenvalue problems we formulate a self adjoint q difference operator in a hilbert space some of the properties of the eigenvalues and the eigenfunctions are discussed green s function is constructed and the problem in question is inverted into a q type fredholm integral operator with a symmetric kernel the set of eigenfunctions is shown to be a complete orthogonal set in the hilbert space examples involving basic trigonometric functions are involved

on sampling theory and basic sturm liouville systems we investigate the sampling theory associated with basic sturm liouville eigenvalue problems we derive two sampling theorems for integral transforms whose kernels are basic functions and the integral is of jackson s type the kernel in the first theorem is a solution of a basic difference equation and in the second one it is expressed in terms of basic green s function of the basic sturm liouville systems examples involving basic sine and cosine transforms are given

real paley wiener theorems and local spectral radius formulas we systematically develop real paley wiener theory for the fourier transform on d for schwartz functions l p functions and distributions in an elementary treatment based on the inversion theorem as an application we show how versions of classical paley wiener theorems can be derived from the real ones via an approach which does not involve domain shifting and which may be put to good use for other transforms of fourier type as well an explanation is also given as to why the easily applied classical paley wiener theorems are unlikely to be able to yield information about the support of a function or distribution which is more precise than giving its convex hull whereas real paley wiener theorems can be used to reconstruct the support precisely albeit at the cost of combinatorial complexity we indicate a possible application of real paley wiener theory to partial differential equations in this vein and furthermore we give evidence that a number of real paley wiener results can be expected to have an interpretation as local spectral radius formulas a comprehensive overview of the literature on real paley wiener theory is included

convergence of a stochastic approximation version of the em algorithm the expectation maximization em algorithm is a powerful computational technique for locating maxima of functions it is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models in certain situations however this method is not applicable because the expectation step cannot be performed in closed form to deal with these problems a novel method is introduced the stochastic approximation em saem which replaces the expectation step of the em algorithm by one iteration of a stochastic approximation procedure the convergence of the saem algorithm is established under conditions that are applicable to many practical situations moreover it is proved that under mild additional conditions the attractive stationary points of the saem algorithm correspond to the local maxima of the function presented to support our findings

monte carlo em for missing covariates in parametric regression models we propose a method for estimating parameters for general parametric regression models with an arbitrary number of missing covariates we allow any pattern of missing data and assume that the missing data mechanism is ignorable throughout when the missing covariates are categorical a useful technique for obtaining parameter estimates is the em algorithm by the method of weights proposed in ibrahim 1990 journal of the american statistical association85 765 769 we extend this method t o continuous or mixed categorical and continuous covariates and for arbitrary parametric regression models by adapting a monte carlo version of the em algorithm as discussed by wei and tanner 1990 journal of the american statistical association85 699 704 in addition we discuss the gibbs sampler for sampling from the conditional distribution of the missing covariates given the observed data and show that the appropriate complete conditionals are log concave the log concavity property of the conditional distributions will facilitate a straightforward implementation of the gibbs sampler via the adaptive rejection algorithm of gilks and wild 1992 applied statistics41 337 348 we assume the model for the response given the covariates is an arbitrary parametric regression model such as a generalized linear model a parametric survival model or a nonlinear model we model the marginal distribution of the covariates as a product of one dimensional conditional distributions this allows us a great deal of flexibility in modeling the distribution of the covariates and reduces the number of nuisance parameters that are introduced in the e step we present examples involving both simulated and real data

a problem of l l campbell on the equivalence of the kramer and shannon sampling theorems abstract a result concerning the equivalence of the sampling theorems of kramer and whittaker shannon kotelnikov is presented in case the associated kernels are bessel functions or jacobi functions the general problem is open a generalized mehler dirichlet formula for the jacobi functions is used to give the proof in this case for the bessel functions a generalization of poisson s integral is needed it turns out that in both cases kramer s theorem gives nothing more than shannon s theorem in the sense that each function that can be sampled by kramer s theorem can also be reconstructed by the classical shannon sampling result

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

stochastic approximation em for large scale exploratory irt factor analysis a stochastic approximation em algorithm saem is described for exploratory factor analysis of dichotomous or ordinal variables the factor structure is obtained from sufficient statistics that are updated during iterations with the robbins monro procedure two large scale simulations are reported that compare accuracy and cpu time of the proposed saem algorithm to the metropolis hasting robbins monro procedure and to a generalized least squares analysis of the polychoric correlation matrix a smaller scale application to real data is also reported including a method for obtaining standard errors of rotated factor loadings a simulation study based on the real data analysis is conducted to study bias and error estimates the saem factor algorithm requires minimal lines of code no derivatives and no large matrix inversion it is programmed entirely in r

the marriage problem from the bar of appointments to the agency abstract we study the stable marriage problem from different points of view we proposed a microscopic dynamic that led the system to a stationary state that we are able to characterize analytically then we derive a thermodynamical description of the nash equilibrium states of the system that agree very well with the results of monte carlo simulations finally through large scale numerical simulations we compare the global optimum of the society with the stable marriage of lower energy we showed that both states are strongly correlated and that the selfish attitude results in a benefit for most of the practitioners belonging to blocking pairs in the global optimum of the society

an adaptive exchange algorithm for sampling from distributions with intractable normalizing constants sampling from the posterior distribution for a model whose normalizing constant is intractable is a long standing problem in statistical research we propose a new algorithm adaptive auxiliary variable exchange algorithm or in short adaptive exchange aex algorithm to tackle this problem the new algorithm can be viewed as a mcmc extension of the exchange algorithm which generates auxiliary variables via an importance sampling procedure from a markov chain running in parallel the convergence of the algorithm is established under mild conditions compared to the exchange algorithm the new algorithm removes the requirement that the auxiliary variables must be drawn using a perfect sampler and thus can be applied to many models for which the perfect sampler is not available or very expensive compared to the approximate exchange algorithms such as the double metropolis hastings sampler the new algorithm overcomes their theoretical difficulty in convergence the new algorithm is tested on the spat

paley wiener subspace of vectors in a hilbert space with applications to integral transforms article history the goal of this article is to introduce an analogue of the paley wiener space of bandlimited functions pw in hilbert spaces and then apply the general result to more specific examples guided by the role that the differentiation operator plays in some of the characterizations of the paley wiener space we construct a space of vectors using a self adjoint operator d in a hilbert space h and denote this space by pw d t he article can be virtually divided into two parts in the first part we show that the space pw d has similar properties to those of the space pw including an analogue of the bernstein inequality and the riesz interpolation formula we also develop a new characterization of the abstract paley wiener space in terms of solutions of cauchy problems associated with abstract schrodinger equations finally we prove two sampling theorems for vectors in pw d one of which uses the notion of hilbert frames and the other is based on the notion of variational splines in h in the second part of the paper we apply our abstract results to integral transforms associated with singular sturm liouville problems in particular we obtain two new sampling formulas related to one dimensional schrodinger

statistical mechanics of a simplified bipartite matching problem an analytical treatment we perform an analytical study of a simplified bipartite matching problem in which there exists a constant matching energy and both heterosexual and homosexual pairings are allowed we obtain the partition function in a closed analytical form and we calculate the corresponding thermodynamic functions of this model we conclude that the model is favored at high temperatures for which the probabilities of heterosexual and homosexual pairs tend to become equal in the limits of low and high temperatures the system is extensive however this property is lost in the general case there exists a relation between the matching energies for which the system becomes more stable under external thermal perturbations as the difference of energies between the two possible matches increases the system becomes more ordered while the maximum of entropy is achieved when these energies are equal in this limit there is a first order phase transition between two phases with constant entropy

on the inversion of integral transforms associated with sturm liouville problems consider the sturm liouville boundary value problem 1 1 y q x y t2y a x b 2 2 y a cos y a sin 0 3 3 y b cos y b sin 0 where q x is continuous on a b let x t be a solution of either the initial value problem 1 and 2 or 1 and 3 in this paper we develop two techniques to invert the integral f t abf x x t dx where f x l2 a b one technique is based on the construction of some biorthogonal sequence of functions and the other is based on poisson s summation formula

adaptive bayesian time frequency analysis of multivariate time series abstractthis article introduces a nonparametric approach to multivariate time varying power spectrum analysis the procedure adaptively partitions a time series into an unknown number of approximately stationary segments where some spectral components may remain unchanged across segments allowing components to evolve differently over time local spectra within segments are fit through whittle likelihood based penalized spline models of modified cholesky components which provide flexible nonparametric estimates that preserve positive definite structures of spectral matrices the approach is formulated in a bayesian framework in which the number and location of partitions are random and relies on reversible jump markov chain and hamiltonian monte carlo methods that can adapt to the unknown number of segments and parameters by averaging over the distribution of partitions the approach can approximate both abrupt and slowly varying changes in spectral matrices empirical performance is evaluated in sim

what is variable bandwidth we propose a new notion of variable bandwidth that is based on the spectral subspaces of an elliptic operator apf ddx p x ddx f where p 0 is a strictly positive function denote by c ap the orthogonal projection of ap corresponding to the spectrum of ap in the range of this projection is the space of functions of variable bandwidth with spectral set in we will develop the basic theory of these function spaces first we derive nonuniform sampling theorems second we prove necessary density conditions in the style of landau roughly for a spectrum 0 the main results say that in a neighborhood of x a function of variable bandwidth behaves like a band limited function with local bandwidth p x 1 2 although the formulation of the results is deceptively similar to the corresponding results for classical band limited functions the methods of proof are much more involved on the one hand we use the oscillation method from sampling theory and frame theoretic methods on the other hand we need the precise spectral theory of sturm liouville operators and the scattering theory of one dimensional schrodinger operators 2017 wiley periodicals inc

a finite continuous gegenbauer transform and its inverse ii the continuous gegenbauer transform is extended to noninteger values of the parameter 2 lambda the transformed function is no longer an entire function but is always holomorphic in a half plane the inverse transform is found for these parameter values its kernel is given both by a series and in closed form by an integral

sampling of vector valued transforms associated with green s matrix of dirac systems recently a sampling theorem associated with regular one dimensional dirac systems has been developed integral transforms whose kernels are solutions of the systems have been reconstructed from their values at the eigenvalues in the present article the situation is considered where the kernels are replaced by green s matrix of the problem thus a vector valued sampling theorem is established for vector valued transforms a family of examples where the systems have variable coefficients and a vector valued kramer type sampling lemma are given at the end of the paper

dynamically weighted importance sampling in monte carlo computation this article describes a new monte carlo algorithm dynamically weighted importance sampling dwis for simulation and optimization in dwis the state of the markov chain is augmented to a population at each iteration the population is subject to two move steps dynamic weighting and population control these steps ensure that dwis can move across energy barriers like dynamic weighting but with the weights well controlled and with a finite expectation the estimates can converge much faster than they can with dynamic weighting a generalized theory for importance sampling is introduced to justify the new algorithm numerical examples are given to show that dynamically weighted importance sampling can perform significantly better than the metropolis hastings algorithm and dynamic weighting in some situations

a generalized weber transform and its inverse formula a generalized weber transform is introduced and its inverse formula is proved a well with constant output production in an infinite fractal reservoir of fluid mechanics in porous medium has been considered as an application of this generalized weber transform

geometric convergence and central limit theorems for multidimensional hastings and metropolis algorithms we develop results on geometric ergodicity of markov chains and apply these and other recent results in markov chain theory to multidimensional hastings and metropolis algorithms for those based on random walk candidate distributions we find sufficient conditions for moments and moment generating functions to converge at a geometric rate to a prescribed distribution by phrasing the conditions in terms of the curvature of the densities we show that the results apply to all distributions with positive densities in a large class which encompasses many commonly used statistical forms from these results we develop central limit theorems for the metropolis algorithm converse results showing non geometric convergence rates for chains where the rejection rate is not bounded away from unity are also given these show that the negative definiteness property is not redundant

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

paley wiener type theorems for a class of integral transforms abstract a characterization of weighted l 2 i spaces in terms of their images under various integral transformations is derived where i is an interval finite or infinite this characterization is then used to derive paley wiener type theorems for these spaces unlike the classical paley wiener theorem our theorems use real variable techniques and do not require analytic continuation to the complex plane the class of integral transformations considered is related to singular sturm liouville boundary value problems on a half line and on the whole line

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

minorization conditions and convergence rates for markov chain monte carlo abstract general methods are provided for analyzing the convergence of discrete time general state space markov chains such as those used in stochastic simulation algorithms including the gibbs sampler the methods provide rigorous a priori bounds on how long these simulations should be run to give satisfactory results results are applied to two models of the gibbs sampler a bivariate normal model and a hierarchical poisson model with gamma conditionals the methods use the notion of minorization conditions for markov chains

matching games with partial information abstract we analyze different ways of pairing agents in a bipartite matching problem with regard to its scaling properties and to the distribution of individual satisfactions then we explore the role of partial information and bounded rationality in a generalized marriage problem comparing the benefits obtained by self searching and by a matchmaker finally we propose a modified matching game intended to mimic the way consumers information makes firms to enhance the quality of their products in a competitive market

stochastic approximation boosting for incomplete data problems boosting is a powerful approach to fitting regression models this article describes a boosting algorithm for likelihood based estimation with incomplete data the algorithm combines boosting with a variant of stochastic approximation that uses markov chain monte carlo to deal with the missing data applications to fitting generalized linear and additive models with missing covariates are given the method is applied to the pima indians diabetes data where over half of the cases contain missing values

a generalized wang landau algorithm for monte carlo computation inference for a complex system with a rough energy landscape is a central topic in monte carlo computation motivated by the successes of the wang landau algorithm in discrete systems we generalize the algorithm to continuous systems the generalized algorithm has some features that conventional monte carlo algorithms do not have first it provides a new method for monte carlo integration based on stochastic approximation second it is an excellent tool for monte carlo optimization in an appropriate setting the algorithm can lead to a random walk in the energy space and thus it can sample relevant parts of the sample space even in the presence of many local energy minima the generalized algorithm can be conveniently used in many problems of monte carlo integration and optimization for example normalizing constant estimation model selection highest posterior density interval construction and function optimization our numerical results show that the algorithm outperforms simulated annealing an

a bayesian analysis for change point problems a sequence of observations undergoes sudden changes at unknown times we model the process by supposing that there is an underlying sequence of parameters partitioned into contiguous blocks of equal parameter values the beginning of each block is said to be a change point observations are then assumed to be independent in different blocks given the sequence of parameters in a bayesian analysis it is necessary to give probability distributions to both the change points and the parameters we use product partition models barry and hartigan 1992 which assume that the probability of any partition is proportional to a product of prior cohesions one for each block in the partition and that given the blocks the parameters in different blocks have independent prior distributions given the observations a new product partition model holds with posterior cohesions for the blocks and new independent block posterior distributions for parameters the product model thus provides a convenient machinery for allo

adaptive markov chain monte carlo through regeneration abstract markov chain monte carlo mcmc is used for evaluating expectations of functions of interest under a target distribution this is done by calculating averages over the sample path of a markov chain having as its stationary distribution for computational efficiency the markov chain should be rapidly mixing this sometimes can be achieved only by careful design of the transition kernel of the chain on the basis of a detailed preliminary exploratory analysis of an alternative approach might be to allow the transition kernel to adapt whenever new features of are encountered during the mcmc run however if such adaptation occurs infinitely often then the stationary distribution of the chain may be disturbed we describe a framework based on the concept of markov chain regeneration which allows adaptation to occur infinitely often but does not disturb the stationary distribution of the chain or the consistency of sample path averages

on lagrange interpolation and kramer type sampling theorems associated with sturm liouville problems this article is devoted to a connection between kramer s sampling theorem and sampling expansions generated by lagrange interpolation it is shown that any function that has a sampling expansion in the scope of kramer s theorem also has a lagrange type interpolation expansion provided that the kernel associated with kramer s theorem arises from a second order sturm liouville boundary value problem this new approach which for a variety of regular and singular sturm liouville problems leads to associated sampling theorems recovers not only many known sampling expansions but also gives new ways to calculate the corresponding sampling functions new sampling series are included

bounded rank one perturbations in sampling theory sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points in this paper we derive an orthogonal sampling theory and associated lagrange interpolation formulae from a family of bounded rank one perturbations of a self adjoint operator that has only discrete spectrum of multiplicity one

what are textons textons refer to fundamental micro structures in natural images and videos and are considered as the atoms of pre attentive human visual perception julesz 1981 unfortunately the word texton remains a vague concept in the literature for lack of a good mathematical model in this article we first present a three level generative image model for learning textons from texture images in this model an image is a superposition of a number of image bases selected from an over complete dictionary including various gabor and laplacian of gaussian functions at various locations scales and orientations these image bases are in turn generated by a smaller number of texton elements selected from a dictionary of textons by analogy to the waveform phoneme word hierarchy in speech the pixel base texton hierarchy presents an increasingly abstract visual description and leads to dimension reduction and variable decoupling by fitting the generative model to observed images we can learn the texton dictionary as parameters of the generative model then the paper proceeds to study the geometric dynamic and photometric structures of the texton representation by further extending the generative model to account for motion and illumination variations 1 for the geometric structures a texton consists of a number of image bases with deformable spatial configurations the geometric structures are learned from static texture images 2 for the dynamic structures the motion of a texton is characterized by a markov chain model in time which sometimes can switch geometric configurations during the movement we call the moving textons as motons the dynamic models are learned using the trajectories of the textons inferred from video sequence 3 for photometric structures a texton represents the set of images of a 3d surface element under varying illuminations and is called a lighton in this paper we adopt an illumination cone representation where a lighton is a texton triplet for a given light source a lighton image is generated as a linear sum of the three texton bases we present a sequence of experiments for learning the geometric dynamic and photometric structures from images and videos and we also present some comparison studies with k mean clustering sparse coding independent component analysis and transformed component analysis we shall discuss how general textons can be learned from generic natural images

statistical properties and network structure of the marriage problem abstract we study the statistical properties of the distribution of total energies or costs over the set of n configurations for the marriage problem with n men and n women analytical results and exhaustive numerical calculations for the whole configuration space are presented taking into account several definitions of the individual energies the distribution of the minimal energy is evaluated approximately moreover we point out a natural association between the configuration space of the marriage problem and a network we study the topological and metric properties of this network as well as the distribution of local energy minima on it

equi energy sampler with applications in statistical inference and statistical mechanics we introduce a new sampling algorithm the equi energy sampler for efficient statistical sampling and estimation complementary to the widely used temperature domain methods the equi energy sampler utilizing the temperature energy duality targets the energy directly the focus on the energy function not only facilitates efficient sampling but also provides a powerful means for statistical estimation for example the calculation of the density of states and microcanonical averages in statistical mechanics the equi energy sampler is applied to a variety of problems including exponential regression in statistics motif sampling in computational biology and protein folding in biophysics we congratulate samuel kou qing zhou and wing wong referred to subsequently as kzw for this beautifully written paper which opens a new direction in monte carlo computation this discussion has two parts first we describe a very closely related method multicanonical sampling mcs and report a simulation example that compares the equi energy ee sampler with mcs overall we found the two algorithms to be of comparable efficiency for the simulation problem considered in the second part we develop some additional convergence results for the ee sampler novel sampling algorithms can significantly impact open questions in computational biology most notably the in silico protein folding problem by using computational methods protein folding aims to find the three dimensional structure of a protein chain given the sequence of its amino acid building blocks the complexity of the problem strongly depends on the protein representation and its energy function the more detailed the model the more complex its corresponding energy function and the more challenge it sets for sampling algorithms kou zhou and wong have introduced a novel sampling method which could contribute significantly to the field of structural prediction

sampling expansions associated with kamke problems the present paper is devoted to the derivation of sampling expansions for entire functions which are represented as integral transforms where a differential operator is acting on the kernels the situation generalizes the results obtained in sampling theory associated with boundary value problems to the case when the differential equation has the form n y lambda p y where n and p are two differential expressions of orders n and p respectively n p and lambda is the eigenvalue parameter both self adjoint and non self adjoint cases will be considered with examples in which the boundary conditions are strongly regular

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

generalized additive modeling with implicit variable selection by likelihood based boosting the use of generalized additive models in statistical data analysis suffers from the restriction to few explanatory variables and the problems of selection of smoothing parameters generalized additive model boosting circumvents these problems by means of stagewise fitting of weak learners a fitting procedure is derived which works for all simple exponential family distributions including binomial poisson and normal response variables the procedure combines the selection of variables and the determination of the appropriate amount of smoothing penalized regression splines and the newly introduced penalized stumps are considered as weak learners estimates of standard deviations and stopping criteria which are notorious problems in iterative procedures are based on an approximate hat matrix the method is shown to be a strong competitor to common procedures for the fitting of generalized additive models in particular in high dimensional settings with many nuisance predictor variables it performs very well

the normalized acoustic power of a thin clamped annular plate vibrating in a flat screen around a perpendicular semi infinite circular cylinder abstract the neumann boundary value problem is presented for the time harmonic excited steady state vibrations of a thin clamped annular plate embedded in a flat rigid baffle around a perpendicular circular cylindrical rigid semi infinite baffle the system of two coupled differential equations is solved for this purpose one of them being the wave equation of the fluid filling the space between the two baffles and the other being the equation of motion of the plate for its excited vibrations first the acoustic pressure is presented in its spectral form using the weber inverse transform then the time averaged acoustic power is presented using the plate s modal impedance coefficients and the coupling factors the modal coefficients are presented as the integrals together with the corresponding asymptotic formulations the influence of the cylindrical baffle on the acoustic power is analyzed numerically the fluid loading and the internal attenuation of the plate s vibrations are both included whereas the attenuation of the acoustic waves in fluid is neglected

sampling theory associated with q difference equations of the sturm liouville type we will show that if the kernel k x t in the representation f t a0k x t u t dqt with u l2q 0 a is a solution of a second order q sturm liouville boundary problem then f admits a representation as a sampling formula of the form f t n 0f n w t w n t n where n is the nth eigenvalue of the associated q sturm liouville boundary problem and w t is the q wronskian of two solutions selected in a specified way

on integral transforms whose kernels are solutions of singular sturm liouville problems on etudie des transformees integrales du type f x 0 f s x s d ou x s est la solution du probleme de sturm liouville y s 2 q x y 0 0 x avec y 0 cos y 0 sin 0 y x est bornee a l infini et d est la mesure spectrale

fitting full information item factor models and an empirical investigation of bridge sampling abstract based on item response theory bock and aitken introduced a method of item factor analysis termed full information item factor fiif analysis by bartholomew because it uses all distinct item response vectors as data but a limitation of their fitting algorithm is its reliance on fixed point gauss hermite quadrature which can produce appreciable numerical errors especially in high dimension problems the first purpose of this article is to offer more reliable methods by using recent advances in statistical computation specifically we illustrate two ways of implementing monte carlo expectation maximization em algorithm to fit a fiif model using the gibbs sampler to carry out the computation for the e steps we also show how to use bridge sampling to simulate the likelihood ratios for monitoring the convergence of a monte carlo em a strategy that is useful in general simulations demonstrate substantial improvement over bock and aitken s algorithm in recovering known factor loadings in hig

on the range of the hankel and extended hankel transforms abstract the range of the hankel and extended hankel transforms on some spaces of functions is described the paley wiener theorem for the hankel transform is also obtained

maximum likelihood estimation for spatial models by markov chain monte carlo stochastic approximation we propose a two stage algorithm for computing maximum likelihood estimates for a class of spatial models the algorithm combines markov chain monte carlo methods such as the metropolis hastings green algorithm and the gibbs sampler and stochastic approximation methods such as the off line average and adaptive search direction a new criterion is built into the algorithm so stopping is automatic once the desired precision has been set simulation studies and applications to some real data sets have been conducted with three spatial models we compared the algorithm proposed with a direct application of the classical robbins monro algorithm using wiebe s wheat data and found that our procedure is at least 15 times faster

applications of krein s theory of regular symmetric operators to sampling theory the classical kramer sampling theorem establishes general conditions that allow the reconstruction of functions by mean of orthogonal sampling formulae one major task in sampling theory is to find concrete non trivial realizations of this theorem in this paper we provide a new approach to this subject on the basis of krein s theory of representation of simple regular symmetric operators having deficiency indices 1 1 we show that the resulting sampling formulae have the form of lagrange interpolation series we also characterize the space of function reconstructible by our sampling formulae our construction allows a rigorous treatment of certain ideas proposed recently in quantum gravity

sampling theorem associated with a dirac operator and the hartley transform abstract kramer s sampling theorem indicates that under certain conditions sampling theorems associated with boundary value problems involving n th order self adjoint differential operators can be obtained in this paper we extend this result and derive a sampling theorem associated with boundary value problems involving a one dimensional system of dirac operators as a special case we obtain a sampling theorem for the hartley transform of a bandlimited function

sampling theorems for jackson norlund transforms associated with hahn difference operators abstract for 0 q 1 and 0 the q hahn difference operator approximates the classical derivative as q 1 and 0 a q hahn sturm liouville theory is established in the regular setting the present paper introduces a couple of sampling theorems of lagrange type interpolation for q integral transforms whose kernels are either solutions or green s function of the q hahn sturm liouville problem the new theorems are illustrated in numerical examples indicating that they approximate the classical results as q 1 and 0

sampling for the fourth order sturm liouville differential operator we extend the sampling method to compute the eigenvalues of a fourth order differential operator we show that the shannon sampling theorem is not applicable due to the growth of the solutions on the real line the inverse spectral theory as developed by mclaughlin and kramer s theorem allow us to express the characteristic function explicitly by a new sampling formula

improving samc using smoothing methods theory and applications to bayesian model selection problems stochastic approximation monte carlo samc has recently been proposed by liang liu and carroll j amer statist assoc 102 2007 305 320 as a general simulation and optimization algorithm in this paper we propose to improve its convergence using smoothing methods and discuss the application of the new algorithm to bayesian model selection problems the new algorithm is tested through a change point identification example the numerical results indicate that the new algorithm can outperform samc and reversible jump mcmc significantly for the model selection problems the new algorithm represents a general form of the stochastic approximation markov chain monte carlo algorithm it allows multiple samples to be generated at each iteration and a bias term to be included in the parameter updating step a rigorous proof for the convergence of the general algorithm is established under verifiable conditions this paper also provides a framework on how to improve efficiency of monte carlo simulations by incorporating some nonparametric techniques

improving estimates of genetic maps a maximum likelihood approach as a result of previous large multipoint linkage studies there is a substantial amount of existing marker data due to the increased sample size genetic maps estimated from these data could be more accurate than publicly available maps however current methods for map estimation are restricted to data sets containing pedigrees with a small number of individuals or cannot make full use of marker data that are observed at several loci on members of large extended pedigrees in this article a maximum likelihood ml method for map estimation that can make full use of the marker data in a large multipoint linkage study is described the method is applied to replicate sets of simulated marker data involving seven linked loci and pedigree structures based on the real multipoint linkage study of abkevich et al 2003 american journal of human genetics 73 1271 1281 the variance of the ml estimate is accurately estimated and tests of both simple and composite null hypotheses are performed an efficient procedure for combining map estimates over data sets is also suggested

stochastic approximation in monte carlo computation the wang landau wl algorithm is an adaptive markov chain monte carlo algorithm used to calculate the spectral density for a physical system a remarkable feature of the wl algorithm is that it is not trapped by local energy minima which is very important for systems with rugged energy landscapes this feature has led to many successful applications of the algorithm in statistical physics and biophysics however there does not exist rigorous theory to support its convergence and the estimates produced by the algorithm can reach only a limited statistical accuracy in this article we propose the stochastic approximation monte carlo samc algorithm which overcomes the shortcomings of the wl algorithm we establish a theorem concerning its convergence the estimates produced by samc can be improved continuously as the simulation proceeds samc also extends applications of the wl algorithm to continuum systems the potential uses of samc in statistics are discussed through two classes of applications i

real paley wiener theorems for the koornwinder swarttouw q hankel transform abstract we derive two real paley wiener theorems in the setting of quantum calculus the first uses techniques due to tuan and zayed v k tuan a i zayed paley wiener type theorems for a class of integral transforms j math anal appl 266 1 2002 200 226 in order to describe the image of the space l q 2 0 r under koornwinder and swarttouw q hankel transform t h koornwinder r f swarttouw on q analogues of the fourier and hankel transforms trans amer math soc 333 1 1992 445 461 and contains as a special case a description of the domain of the q sampling theorem associated with the q hankel transform l d abreu a q sampling theorem related to the q hankel transform proc amer math soc 133 4 2005 1197 1203 the second characterizes the image of compactly supported q smooth functions under a rescaled version of the q hankel transform and is a q analogue of a recent result due to andersen n b andersen real paley wiener theorems for the hankel transform j fourier anal appl 12 1 2006 17 25

on the relationship between item response theory and factor analysis of discretized variables equivalence of marginal likelihood of the two parameter normal ogive model in item response theory irt and factor analysis of dichotomized variables fa was formally proved the basic result on the dichotomous variables was extended to multicategory cases both ordered and unordered categorical data pair comparison data arising from multiple judgment sampling were discussed as a special case of the unordered categorical data a taxonomy of data for the irt and fa models was also attempted

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

oversampling and aliasing in de branges spaces arising from bessel operators abstract we show that a class of de branges spaces generated by means of generalized fourier transforms associated with perturbed bessel differential equations has the properties of oversampling and aliasing

sampling in paley wiener spaces associated with fractional integro differential operators this paper employs the theory of kramer analytic kernels established by everitt et al results in math 34 1998 310 to derive sampling expansions the kernels of the recovered transforms are mittag leffler functions of two parameters these kernels are solutions of certain classes of fractional integro differential equations the technique used here is different from the analytic approach by djrbashian harmonic analysis and boundary value problems in the complex domain birkhauser basel 1993

high dimensional exploratory item factor analysis by a metropolis hastings robbins monro algorithm a metropolis hastings robbins monro mh rm algorithm for high dimensional maximum marginal likelihood exploratory item factor analysis is proposed the sequence of estimates from the mh rm algorithm converges with probability one to the maximum likelihood solution details on the computer implementation of this algorithm are provided the accuracy of the proposed algorithm is demonstrated with simulations as an illustration the proposed algorithm is applied to explore the factor structure underlying a new quality of life scale for children it is shown that when the dimensionality is high mh rm has advantages over existing methods such as numerical quadrature based em algorithm extensions of the algorithm to other modeling frameworks are discussed

sampling theorems associated with fourth and higher order self adjoint eigenvalue problems abstract consider a regular self adjoint eigenvalue problem of n th order and the associated whittaker shannon kramer sampling series the samples being taken at the eigenvalues and the sinc function being replaced by the generalized fourier coefficients of the kernel arising from the eigenvalue problem with respect to the complete set of orthogonal eigenfunctions the major aim of this paper is to show that each such sampling expansion can be written as a lagrange interpolation series provided the kernel satisfies suitable conditions two concrete fourth order eigenvalue problems are examined a regular one as an application of the general result and a singular one the problem whether the two resulting sampling series are really new or can be reduced to already known results is in part open

smoothing spline anova frailty model for recurrent event data summary gap time hazard estimation is of particular interest in recurrent event data this article proposes a fully nonparametric approach for estimating the gap time hazard smoothing spline analysis of variance anova decompositions are used to model the log gap time hazard as a joint function of gap time and covariates and general frailty is introduced to account for between subject heterogeneity and within subject correlation we estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the newton raphson procedure the stochastic approximation algorithm saa and the markov chain monte carlo mcmc method the convergence of the algorithm is guaranteed by decreasing the step size of parameter update and or increasing the mcmc sample size along iterations model selection procedure is also developed to identify negligible components in a functional anova decomposition of the log gap time hazard we evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data

annealing markov chain monte carlo with applications to ancestral inference abstract markov chain monte carlo mcmc the metropolis hastings algorithm has been used for many statistical problems including bayesian inference likelihood inference and tests of significance though the method generally works well doubts about convergence often remain here we propose mcmc methods distantly related to simulated annealing our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time they simulate realizations from a sequence of distributions allowing the distribution being simulated to vary randomly over time if the sequence of distributions is well chosen then the sampler will mix well and produce accurate answers for all the distributions even when there is only one distribution of interest these annealing like samplers may be the only known way to get a rapidly mixing sampler these methods are essential for attacking very hard problems which arise in areas such as statistical genetics we illustrate the methods wi

the continuous α β jacobi transform and its inverse when α β 1 is a positive integer definition de la transformation de jacobi continue determination de la transformation inverse application a une variante du theoreme d echantillonnage