a maximum likelihood algorithm for the estimation and renormalization of exponential densities we present an algorithm based on maximum likelihood for the estimation and renormalization marginalization of exponential densities the moment matching problem resulting from the maximization of the likelihood is solved as an optimization problem using the levenberg marquardt algorithm in the case of renormalization the moments needed to set up the moment matching problem are evaluated using swendsen s renormalization method we focus on the renormalization version of the algorithm where we demonstrate its use by computing the critical temperature of the two dimensional ising model possible applications of the algorithm are discussed

asymptotics of karhunen loeve eigenvalues and tight constants for probability distributions of passive scalar transport in this paper we study the asymptotics of the probability distribution function for a certain model of freely decaying passive scalar transport in particular we prove rigorous large n or semiclassical asymptotics for the eigenvalues of the covariance of a fractional brownian motion using these asymptotics along with some standard large deviations results we are able to derive tight asymptotics for the rate of decay of the tails of the probability density for a generalization of the majda model of scalar intermittency originally due to vanden eijnden we are also able to derive asymptotically tight estimates for the closely related problem of small l2 ball probabilities for a fractional brownian motion

approximate maximum likelihood hyperparameter estimation for gibbs priors the parameters of the prior the hyperparameters play an important role in bayesian image estimation of particular importance for the case of gibbs priors is the global hyperparameter spl beta which multiplies the hamiltonian here we consider maximum likelihood ml estimation of spl beta from incomplete data i e problems in which the image which is drawn from a gibbs prior is observed indirectly through some degradation or blurring process important applications include image restoration and image reconstruction from projections exact ml estimation of spl beta from incomplete data is intractable for most image processing here we present an approximate ml estimator that is computed simultaneously with a maximum a posteriori map image estimate the algorithm is based on a mean field approximation technique through which multidimensional gibbs distributions are approximated by a separable function equal to a product of one dimensional 1 d densities we show how this approach can be used to simplify the ml estimation problem we also show how the gibbs bogoliubov feynman gbf bound can be used to optimize the approximation for a restricted class of problems we present the results of a monte carlo study that examines the bias and variance of this estimator when applied to image restoration

a finite difference method for linearization in nonlinear estimation algorithms abstract linearizations of nonlinear functions that are based on jacobian matrices often cannot be applied in practical applications of nonlinear estimation techniques an alternative linearization method is presented in this paper the method assumes that covariance matrices are determined on a square root factored form a factorization of the output covariance from a nonlinear vector function is directly determined by perturbing the nonlinear function with the columns of the factored input covariance without explicitly calculating the linearization and with no differentiations involved the output covariance is more accurate than that obtained with the ordinary jacobian linearization method it also has an advantage that jacobian matrices do not have to be derived symbolically

efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice motivated by the autologistic model for the analysis of spatial binary data on the two dimensional lattice we develop efficient computational methods for calculating the normalizing constant for models for discrete data defined on the cylinder and lattice because the normalizing constant is generally unknown analytically statisticians have developed various ad hoc methods to overcome this difficulty our aim is to provide computationally and statistically efficient methods for calculating the normalizing constant so that efficient likelihood based statistical methods are then available for inference we extend the so called transition method to find a feasible computational method of obtaining the normalizing constant for the cylinder boundary condition to extend the result to the free boundary condition on the lattice we use an efficient path sampling markov chain monte carlo scheme the methods are generally applicable to association patterns other than spatial such as clustered binary data and to variables taking three or more values described by for example potts models

the statistics of burgers turbulence initialized with fractional brownian noise data the statistics of the solution to the inviscid burgers equation are investigated when the initial velocity potential is fractional brownian motion using the theory of large deviations for gaussian processes we characterize the tails of the probability distribution functions pdfs of the velocity the distance between shocks and the shock strength these pdfs are shown to decay like stretched exponentials of the form our method of proof can also be used to extend these results to a much larger class of gaussian potentials this work generalizes the results of avellaneda and e 2 3 on the inviscid burgers equation with white noise initial data

ml parameter estimation for markov random fields with applications to bayesian tomography markov random fields mrfs have been widely used to model images in bayesian frameworks for image reconstruction and restoration typically these mrf models have parameters that allow the prior model to be adjusted for best performance however optimal estimation of these parameters sometimes referred to as hyperparameters is difficult in practice for two reasons i direct parameter estimation for mrfs is known to be mathematically and numerically challenging ii parameters can not be directly estimated because the true image cross section is unavailable we propose a computationally efficient scheme to address both these difficulties for a general class of mrf models and we derive specific methods of parameter estimation for the mrf model known as generalized gaussian mrf ggmrf we derive methods of direct estimation of scale and shape parameters for a general continuously valued mrf for the ggmrf case we show that the ml estimate of the scale parameter spl sigma has a simple closed form solution and we present an efficient scheme for computing the ml estimate of the shape parameter p by an off line numerical computation of the dependence of the partition function on p we present a fast algorithm for computing ml parameter estimates when the true image is unavailable to do this we use the expectation maximization em algorithm we develop a fast simulation method to replace the e step and a method to improve the parameter estimates when the simulations are terminated prior to convergence experimental results indicate that our fast algorithms substantially reduce the computation and result in good scale estimates for real tomographic data sets

intrinsic autoregressions and related models on the two dimensional lattice summary stationary autoregressions on a two dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary prediction formulae and the asymptotic behaviour of the semivariogram are derived for parameter estimation we propose an approximate maximum likelihood estimator a generalization of whittle s estimator it is derived also for general intrinsic models

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

estimating the granularity coefficient of a potts markov random field within a markov chain monte carlo algorithm this paper addresses the problem of estimating the potts parameter jointly with the unknown parameters of a bayesian model within a markov chain monte carlo mcmc algorithm standard mcmc methods cannot be applied to this problem because performing inference on requires computing the intractable normalizing constant of the potts model in the proposed mcmc method the estimation of is conducted using a likelihood free metropolis hastings algorithm experimental results obtained for synthetic data show that estimating jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of on the other hand choosing an incorrect value of can degrade estimation performance significantly to illustrate the interest of this method the proposed algorithm is successfully applied to real bidimensional sar and tridimensional ultrasound images

conditional likelihood inference under complex ascertainment using data augmentation summary in many applications particularly in genetics samples are drawn under complex ascertainment rules for example families may only be selected for study if two or more siblings have trait values exceeding some threshold the correct likelihood for inference in such situations involves the probabilities of ascertainment and these are frequently intractable a consistent but not fully efficient method of analysis of such studies is proposed the main idea is to augment the data with additional pseudo observations simulated under the ascertainment scheme and to analyse using a conditional likelihood for discrimination between true observations and pseudoobservations ascertainment probabilities cancel in this likelihood the method is illustrated with a simple example involving left truncated failure times

rigorous estimates of the tails of the probability distribution function for the random linear shear model in previous work majda and mclaughlin and majda computed explicit expressions for the 2nth moments of a passive scalar advected by a linear shear flow in the form of an integral over r n in this paper we first compute the asymptotics of these moments for large moment number we are able to use this information about the large n behavior of the moments along with some basic facts about entire functions of finite order to compute the asymptotics of the tails of the probability distribution function we find that the probability distribution has gaussian tails when the energy is concentrated in the largest scales as the initial energy is moved to smaller and smaller scales we find that the tails of the distribution grow longer and the distribution moves smoothly from gaussian through exponential and stretched exponential we also show that the derivatives of the scalar are increasingly intermittent in agreement with experimental observations and relate the exponents of the scalar derivative to the exponents of the scalar

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

monte carlo state space likelihoods by weighted posterior kernel density estimation maximum likelihood estimation and likelihood ratio tests for nonlinear non gaussian state space models require numerical integration for likelihood calculations several methods including monte carlo mc expectation maximization mc likelihood ratios direct mc integration and particle filter likelihoods are inefficient for the motivating problem of stage structured population dynamics models in experimental settings an mc kernel likelihood mckl method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of bayesian posteriors mckl is derived by using bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals mc error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed zooming in on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant based approximation of mode bias a simulated example show

a non gaussian state space model and application to prediction of records on developpe une classe de modeles qui generalisent le travail de smith 1979 et bathes 1975 pour des donnees censurees

stein s method for concentration inequalities we introduce a version of stein s method for proving concentration and moment inequalities in problems with dependence simple illustrative examples from combinatorics physics and mathematical statistics are provided

instability sensitivity and degeneracy of discrete exponential families a number of discrete exponential family models for dependent data first and foremost relational data have turned out to be near degenerate and problematic in terms of markov chain monte carlo mcmc simulation and statistical inference i introduce the notion of instability with an eye to characterize detect and penalize discrete exponential family models that are near degenerate and problematic in terms of mcmc simulation and statistical inference i show that unstable discrete exponential family models are characterized by excessive sensitivity and near degeneracy in special cases the subset of the natural parameter space corresponding to nondegenerate distributions and mean value parameters far from the boundary of the mean value parameter space turns out to be a lower dimensional subspace of the natural parameter space these characteristics of unstable discrete exponential family models tend to obstruct mcmc simulation and statistical inference in applications to relational data i show that d

regeneration in markov chain samplers abstract markov chain sampling has recently received considerable attention in particular in the context of bayesian computation and maximum likelihood estimation this article discusses the use of markov chain splitting originally developed for the theoretical analysis of general state space markov chains to introduce regeneration into markov chain samplers this allows the use of regenerative methods for analyzing the output of these samplers and can provide a useful diagnostic of sampler performance the approach is applied to several samplers including certain metropolis samplers that can be used on their own or in hybrid samplers and is illustrated in several examples

logit models and logistic regressions for social networks iii valued relations this paper generalizes thep model for dichotomous social network data wasserman pattison 1996 to the polytomous case the generalization is achieved by transforming valued social networks into three way binary arrays this data transformation requires a modification of the hammersley clifford theorem that underpins thep class of models we demonstrate that provided that certain non observed data patterns are excluded from consideration a suitable version of the theorem can be developed we also show that the approach amounts to a model for multiple logits derived from a pseudo likelihood function estimation within this model is analogous to the separate fitting of multinomial baseline logits except that the hammersley clifford theorem requires the equating of certain parameters across logits the paper describes how to convert a valued network into a data array suitable for fitting the model and provides some illustrative empirical examples

statistics of shocks in solutions of inviscid burgers equation the purpose of this paper is to analyze statistical properties of discontinuities of solutions of the inviscid burgers equation having a typical realizationb y of the brownian motion as an initial datum this case was proposed and studied numerically in the companion paper by she aurell and frisch the description of the statistics is given in terms of the behavior of the convex hull of the random process w y int limits 0 y b eta eta d eta the hausdorff dimension of the closed set of thosey where the convex hull coincides withw is also studied

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

a hybrid estimator in nonlinear and generalised linear mixed effects models summary a hybrid method that combines laplace s approximation and monte carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family an asymptotic theory of this hybrid method for parametric estimation without requiring the true mixing distribution to belong to the assumed parametric family is developed to explain these results this hybrid method and its asymptotic theory are also extended to generalised linear mixed effects models

self similar decay in the kraichnan model of a passive scalar we study the two point correlation function of a freely decaying scalar in kraichnan s model of advection by a gaussian random velocity field that is stationary and white noise in time but fractional brownian in space with roughness exponent 0 2 appropriate to the inertial convective range of the scalar we find all self similar solutions by transforming the scaling equation to kummer s equation it is shown that only those scaling solutions with scalar energy decay exponent a d 1 are statistically realizable where d is space dimension and 2 an infinite sequence of invariants jp p 0 1 2 is pointed out where j0 is corrsin s integral invariant but the higher invariants appear to be new we show that at least one of the invariants j0 or j1 must be nonzero possibly infinite for realizable initial data initial datum with a finite nonzero invariant the first being jp converges at long times to a scaling solution p with a d p p 0 1 the latter belongs to an exceptional series of self similar solutions with stretched exponential decay in space however the domain of attraction includes many initial data with power law decay when the initial datum has all invariants zero or infinite and also it exhibits power law decay then the solution converges at long times to a nonexceptional scaling solution with the same power law decay these results support a picture of a two scale decay with breakdown of self similarity for a range of exponents d a d 2 analogous to what has recently been found in the decay of burgers turbulence

iterative simulation methods abstract the standard methods of generating sample from univariate distributions often become hopelessly inefficient when applied to realizations of stochastic processes iterative methods are not widely known amongst statisticians but some are standard practice in statistical physics and chemistry the methods are surveyed and compared with particular reference to their convergence properties

a monte carlo metropolis hastings algorithm for sampling from distributions with intractable normalizing constants simulating from distributions with intractable normalizing constants has been a long standing problem in machine learning in this letter we propose a new algorithm the monte carlo metropolis hastings mcmh algorithm for tackling this problem the mcmh algorithm is a monte carlo version of the metropolis hastings algorithm it replaces the unknown normalizing constant ratio by a monte carlo estimate in simulations while still converges as shown in the letter to the desired target distribution under mild conditions the mcmh algorithm is illustrated with spatial autologistic models and exponential random graph models unlike other auxiliary variable markov chain monte carlo mcmc algorithms such as the moller and exchange algorithms the mcmh algorithm avoids the requirement for perfect sampling and thus can be applied to many statistical models for which perfect sampling is not available or very expensive the mcmh algorithm can also be applied to bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals

forecasting records by maximum likelihood abstract a maximum likelihood method of fitting a model to a series of records is proposed using ideas from the analysis of censored data to construct a likelihood function based on observed records this method is tried out by fitting several models to series of athletics records for mile and marathon races a form of residual analysis is proposed for testing the models forecasting consequences are also considered in the case of mile records a steady linear improvement since 1931 is found the marathon data are harder to interpret with a steady improvement until 1965 with only slight improvement in world records since then in both cases the normal distribution appears at least as good as extreme value distributions for the distribution of annual best performances short term forecasts appear satisfactory but serious reservations are expressed about using regression type methods to predict long term performance limits

non parametric maximum likelihood estimators for disease mapping a non parametric maximum likelihood approach to the estimation of relative risks in the context of disease mapping is discussed and a npml approximation to conditional autoregressive models is proposed npml estimates have been compared to other proposed solutions maximum likelihood via monte carlo scoring hierarchical bayesian models using real examples overall the npml autoregressive estimates with weighted term were closer to the bayesian estimates the exchangeable npml model ranked immediately after even if it implied a greater shrinkage while the truncated auto poisson showed inadequate for disease mapping the coefficients of the autoregressive term for the different mixtures have clear interpretations in the breast cancer example the larger cities in the region showed high rates and very low correlation with the neighbouring areas while the less populated rural areas with low rates were strongly positively correlated each other this pattern is expected since breast cancer is strongly correlated with parity and age at first birth and the female population of the rural areas experienced a decline in fertility much later than those living in the larger cities the leukemia example highlighted the failure of the poisson gamma model and other general overdispersion tests to detect high risk areas under specific conditions the npml approach in aitkin is very general simple and flexible however the user should be warned against the possibility of local maxima and the difficulty in detecting the optimal number of components special software such as caman or dismapwin had been developed and should be recommended mainly to not experienced users

on monte carlo methods for estimating ratios of normalizing constants recently estimating ratios of normalizing constants has played an important role in bayesian computations applications of estimating ratios of normalizing constants arise in many aspects of bayesian statistical inference in this article we present an overview and discuss the current monte carlo methods for estimating ratios of normalizing constants then we propose a new ratio importance sampling method and establish its theoretical framework we find that the ratio importance sampling method can be better than the current methods for example the bridge sampling method meng and wong and the path sampling method gelman and meng in the sense of minimizing asymptotic relative mean square errors of estimators an example is given for illustrative purposes finally we present two special applications and the general implementation issues for estimating ratios of normalizing constants

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

bayesian morphology fast unsupervised bayesian image analysis abstract we consider the problems of image segmentation and classification and image restoration when the true image is made up of a small number of unordered colors our emphasis is on both performance and speed speed has become increasingly important for analyzing large images and multispectral images with many bands processing large image databases real time or near realtime image analysis and the online analysis of video bayesian image analysis provides an elegant solution to these problems but it is computationally expensive and the solutions it provides may be sensitive to unrealistic global properties of the models on which it is based the icm algorithm is faster and based on the local properties of the models underlying bayesian image analysis parameter estimation is performed iteratively via pseudolikelihood mathematical morphology is faster again and is widely considered to perform well but lacks a statistical basis method selection analogous to parameter estimation is done in a

pca based hurst exponent estimator for fbm signals under disturbances in this paper the validity of pca eigenspectrum based hurst exponent estimator proposed in j b gao y cao and j m lee ldquoprincipal component analysis of 1 f alpha noise rdquo phys lett a vol 314 no 5 6 pp 392 400 2003 for single fbm signal is proved moreover how to apply this estimator for fbm signals corrupted with some other signals are discussed theoretical analysis and experiments show that it can also be used for 1 mixed fbm signals with different hurst exponents 2 fbm signals corrupted with additive gaussian white noise when the signal to noise ratio snr is not too small and 3 fbm signals corrupted with additive deterministic sine cosine signals however the estimation accuracy depends on the snr value for the first two situations

burgers equation with self similar gaussian initial data tail probabilities the statistical properties of solutions of the one dimensional burgers equation in the limit of vanishing viscosity are considered when the initial velocity potential is fractional brownian motion fbm we establish the asymptotic power law order for log probability of large values both velocity and shock amplitude of velocity discontinuity this confirms the conjecture of u frisch and his collaborators rigorous results for this problem were previously derived for the case of brownian motion using markov techniques our approach is based on the intrinsic properties of fbm and the theory of extreme values for gaussian processes

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

the em algorithm an old folk song sung to a fast new tune celebrating the 20th anniversary of the presentation of the paper by dempster laird and rubin which popularized the em algorithm we investigate after a brief historical account strategies that aim to make the em algorithm converge faster while maintaining its simplicity and stability e g automatic monotone convergence in likelihood first we introduce the idea of a working parameter to facilitate the search for efficient data augmentation schemes and thus fast em implementations second summarizing various recent extensions of the em algorithm we formulate a general alternating expectation conditional maximization algorithm aecm that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations we illustrate these methods using multivariate t models with known or unknown degrees of freedom and poisson models for image reconstruction we show through both empirical and theoretical evidence the potential for a dramatic reduction in computational time with little increase in human effort we also discuss the intrinsic connection between em type algorithms and the gibbs sampler and the possibility of using the techniques presented here to speed up the latter the main conclusion of the paper is that with the help of statistical considerations it is possible to construct algorithms that are simple stable and fast

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

a crossed random effects modeling approach for estimating diagnostic accuracy from ordinal ratings without a gold standard in diagnostic studies without a gold standard the assumption on the dependence structure of the multiple tests or raters plays an important role in model performance in case of binary disease status both conditional independence and crossed random effects structure have been proposed and their performance investigated less attention has been paid to the situation where the true disease status is ordinal in this paper we propose crossed subject specific and rater specific random effects to account for the dependence structure and assess the robustness of the proposed model to misspecification in the random effects distributions we applied the models to data from the physician reliability study which focuses on assessing the diagnostic accuracy in a population of raters for the staging of endometriosis a gynecological disorder in women using this new methodology we estimate the probability of a correct classification and show that regional experts can more easily classify the intermediate stage than resident physicians

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

efficient recursions for general factorisable models let n s valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant for an unnormalised joint likelihood expressible as a product of factors we give an algebraic recursion which can be used for computing the normalising constant and other summations a saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution with maximum computational efficiency as the subsets attain their minimum size if each subset contains at most r 1 of the n components in the joint distribution we term this a lag r model whose normalising constant can be computed using a forward recursion in o sr 1 computations as opposed to o sn for the direct computation we show how a lag r model represents a markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood we illustrate the method by showing how the normalising constant of the ising or autologistic model can be computed

non gaussian invariant measures for the majda model of decaying turbulent transport the problem of turbulent transport of a scalar field by a random velocity field is considered the scalar field amplitude exhibits rare but very large fluctuations whose typical signature is fatter than gaussian tails for the probability distribution of the scalar the existence of such large fluctuations is related to clustering phenomena of the lagrangian paths within the flow this suggests an approach to turn the large deviation problem for the scalar field into a small deviation or small ball problem for some appropriately defined process measuring the spreading with time of the lagrangian paths here such a methodology is applied to a model proposed by majda consisting of a white in time linear shear flow and some generalizations of it where the velocity field has finite or even infinite correlation time the non gaussian invariant measure for the reduced scalar field is derived and in particular it is shown that the one point distribution of the scalar has stretched exponential tails with a stretching exponent depending on the parameters in the model different universality classes for the scalar behavior are identified which all other parameters being kept fixed display a one to one correspondence with an exponent measuring time persistence effects in the velocity field c 2001 john wiley sons inc

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

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

a monte carlo method for high dimensional integration a new method for the numerical integration of very high dimensional functions is introduced and implemented based on the metropolis monte carlo algorithm the logarithm of the high dimensional integral is reduced to a 1 dimensional integration of a certain statistical function with respect to a scale parameter over the range of the unit interval the improvement in accuracy is found to be substantial comparing to the conventional crude monte carlo integration several numerical demonstrations are made and variability of the estimates are shown

an efficient markov chain monte carlo method for distributions with intractable normalising constants maximum likelihood parameter estimation and sampling from bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter in this paper an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value the proposal distribution is constructed so that the normalising constant cancels from the metropolis hastings ratio the method is illustrated by producing posterior samples for parameters of the ising model given a particular lattice realisation

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

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

bayesian analysis of agricultural field experiments the paper describes bayesian analysis for agricultural field experiments a topic that has received very little previous attention despite a vast frequentist literature adoption of the bayesian paradigm simplifies the interpretation of the results especially in ranking and selection also complex formulations can be analysed with comparative ease by using markov chain monte carlo methods a key ingredient in the approach is the need for spatial representations of the unobserved fertility patterns this is discussed in detail problems caused by outliers and by jumps in fertility are tackled via hierarchical f formulations that may find use in other contexts the paper includes three analyses of variety trials for yield and one example involving binary data none is entirely straightforward some numerical comparisons with frequentist analyses are made

markov chain monte carlo for autologistic regression models with application to the distribution of plant species summary in this paper we explore using autologistic regression models for spatial binary data with covariates autologistic regression models can handle binary responses exhibiting both spatial correlation and dependence on covariates we use markov chain monte carlo mcmc to estimate the parameters in these models the distributional behavior of the mcmc maximum likelihood estimates mcmc mles is studied via simulation we find that the mcmc mles are approximately normally distributed and that the mcmc estimates of fisher information may be used to estimate the variance of the mcmc mles and to construct confidence intervals finally we illustrate by example how our studies may be applied to model the distribution of plant species

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

goodness of fit of social network models we present a systematic examination of a real network data set using maximum likelihood estimation for exponential random graph models as well as new procedures to evaluate how well the models fit the observed networks these procedures compare structural statistics of the observed network with the corresponding statistics on networks simulated from the fitted model we apply this approach to the study of friendship relations among high school students from the national longitudinal study of adolescent health addhealth we focus primarily on one particular network of 205 nodes although we also demonstrate that this method may be applied to the largest network in the addhealth study with 2 209 nodes we argue that several well studied models in the networks literature do not fit these data well and demonstrate that the fit improves dramatically when the models include the recently developed geometrically weighted edgewise shared partner geometrically weighted dyadic shared partner and geometrically w

multivariate methods in ophthalmology with application to other paired data situations methods are presented for performing multiple regression analyses and multiple logistic regression analyses on ophthalmologic data with normally and binomially distributed outcome variables while accounting for the intraclass correlation between eyes these methods are extended to more general nested data structures where a variable number of subunits are available for each primary unit of analysis as in familial data these methods can also be applied to other types of paired data as in matched studies with a variable matching ratio where one has a continuous outcome variable and wishes to control for other confounding variables while maintaining the matching examples are given of these methods with a group of over 400 patients with retinitis pigmentosa in which spherical refractive error and visual acuity are related to genetic type after the effects of age sex and the presence of cataract have been controlled

transformed unscented kalman filter this technical note concerns the deterministic sampling points construction strategy for unscented kalman filter ukf and cubature kalman filter ckf from the numerical integration viewpoint a new deterministic sampling points set is derived by orthogonal transformation on the cubature points by embedding these points into the ukf framework a modified nonlinear filter named transformed unscented kalman filter tukf is derived the tukf can address the nonlocal sampling problem inherent in ckf while maintaining the virtue of numerical stability for high dimensional problems moreover the methodology proposed in this technical note can be used to construct nonlinear filters with improved accuracy for certain problems the performance of the proposed algorithm is demonstrated through a nonlinear high dimensional problem

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

evolution of the probability measure for the majda model new invariant measures and breathing pdfs in 1993 majda proposed a simple random shear model from which scalar inter mittency was rigorously predicted for the invariant probability measure of passive tracers in this work we present an integral formulation for the tracer measure which leads to a new comprehensive study on its temporal evolution based on monte carlo simulation and direct numerical integration an interesting non monotonic breathing phenomenon is discov ered from these results and carefully defined with a solid example for special initial data to predict such phenomenon the signature of this phenomenon may persist at long time char acterized by the approach of the pdf core to its infinite time invariant value we find that this approach may be strongly dependent on the non dimensional peclet number of which the invariant measure itself is independent further the breathing pdf is recovered as a new invariant measure in a distinguished time scale in the diffusionless limit rigorous as ymptotic analysis is also performed to identify the gaussian core of the invariant measures and the critical rate at which the heavy stretched exponential regime propagates towards the tail as a function of time is calculated

sequential monte carlo p values summary the assessment of statistical significance by monte carlo simulation may be costly in computer time this paper looks at a number of ways of calculating exact monte carlo p values by sequential sampling such p values are shown to have properties similar to those obtained by sampling with a fixed sample size both standard and generalized monte carlo procedures are discussed and in particular a sequential method is proposed for dealing with situations in which values can only be conveniently generated using a markov chain conditioned to pass through the observed data

statistical am fm models extended kalman filter demodulation cramer rao bounds and speech analysis a stochastic dynamical system model for describing time signals that are jointly amplitude am and frequency fm modulated is presented the signal is assumed to be bandpass perhaps originating from a filter bank applied to a broadband signal and includes the constraint that the magnitude of the complex baseband signal is positive motivated by speech processing and the desire for narrowband modulating signals time is divided into frames and the modulating signals are smoothly interpolated across each frame the model allows a detailed characterization of the bandwidth of the modulating signals and the statistical character of the measurement noise an adaptive estimation algorithm based on extended kalman filtering ideas for extracting the modulating signals from the measured signal is described and demonstrated on both voiced and unvoiced speech signals the cramer rao bound on the performance of any estimator is computed

likelihood analysis of spatial point patterns summary the likelihood procedure for estimating the pairwise interaction potential function is developed for statistical analysis of homogeneous spatial point patterns approximation methods of the normalizing factor of gibbs canonical distribution are discussed both to estimate a scale parameter and to measure the softness or hardness of repulsive interactions the approximations are useful up to a considerably high density the validity of our procedure is demonstrated by some computer experi ments some real data are analysed

a note on the existence of the posterior distribution for a class of mixed models for binomial responses summary necessary and sufficient conditions are given for the existence of the posterior distribution of the variance components in a class of mixed models for binomial responses the implications of our results are illustrated through an example

generalized monte carlo significance tests summary simple monte carlo significance testing has many applications particularly in the preliminary analysis of spatial data the method requires the value of the test statistic to be ranked among a random sample of values generated according to the null hypothesis however there are situations in which a sample of values can only be conveniently generated using a markov chain initiated by the observed data so that independence is violated this paper describes two methods that overcome the problem of dependence and allow exact tests to be carried out the methods are applied to the rasch model to the finite lattice ising model and to the testing of association between spatial processes power is discussed in a simple case

mixed fractional brownian motion a spectral take abstract this paper provides yet another look at the mixed fractional brownian motion fbm this time from the spectral perspective the main result is an asymptotic approximation for the eigenvalues of its covariance operator using this approximation we derive the exact asymptotics of the l 2 small ball probabilities which was previously known only with logarithmic accuracy the obtained expression exhibits an interesting stratification of scales which occurs at certain values of the hurst parameter of the fractional component some of them have been previously encountered in other problems involving such mixtures

exact logistic regression theory and examples we provide an alternative to the maximum likelihood method for making inferences about the parameters of the logistic regression model the method is based appropriate permutational distributions of sufficient statistics it is useful for analysing small or unbalanced binary data with covariates it also applies to small sample clustered binary data we illustrate the method by analysing several biomedical data sets

some relations between extended and unscented kalman filters the unscented kalman filter ukf has become a popular alternative to the extended kalman filter ekf during the last decade ukf propagates the so called sigma points by function evaluations using the unscented transformation ut and this is at first glance very different from the standard ekf algorithm which is based on a linearized model the claimed advantages with ukf are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model we point out several less known links between ekf and ukf in terms of two conceptually different implementations of the kalman filter the standard one based on the discrete riccati equation and one based on a formula on conditional expectations that does not involve an explicit riccati equation first it is shown that the sigma point function evaluations can be used in the classical ekf rather than an explicitly linearized model second a less cited version of the ekf based on a second order taylor expansion is shown to be quite closely related to ukf the different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications

parametric likelihood inference for record breaking problems summary in this paper we consider the analysis of record breaking data sets where only observations that exceed or only those that fall below the current extreme value are recorded example application areas include industrial stress testing meteorological analysis sporting and athletic events and oil and mining surveys a closely related area is that of threshold modelling where the observations are those that cross a certain threshold value the inherent missing data structure present in these problems leads to likelihood functions that contain possibly high dimensional integrals rendering traditional maximum likelihood methods difficult or not feasible fortunately we may obtain arbitrarily accurate approximations to the likelihood function by iteratively applying monte carlo integration methods geyer thompson 1992 subiteration using the gibbs sampler may help to evaluate any multivariate integrals encountered during this process this approach can handle far more sophisticated parametric models than have been used previously in record breaking and threshold data contexts in particular the methodology allows for observations that are dependent and subject to mean shifts over time we present a numerical example involving records in olympic high jump competition where besides estimation we also address related issues in model selection and prediction

on the convergence of monte carlo maximum likelihood calculations summary monte carlo maximum likelihood for normalized families of distributions can be used for an extremely broad class of models given any family he 0 e 0 of non negative integrable functions maximum likelihood estimates in the family obtained by normalizing the functions to integrate to 1 can be approximated by monte carlo simulation the only regularity conditions being a compactification of the parameter space such that the evaluation maps 0 h0 x remain continuous then with probability 1 the monte carlo approximant to the log likelihood hypoconverges to the exact log likelihood its maximizer converges to the exact maximum likelihood estimate approximations to profile likelihoods hypoconverge to the exact profile and level sets of the approximate likelihood support regions converge to the exact sets in painleve kuratowski set convergence the same results hold when there are missing data if a wald type integrability condition is satisfied asymptotic normality of the monte carlo error and convergence of the monte carlo approximation to the observed fisher information are also shown

estimation with selected binomial information or do you really believe that dave winfield is batting 471 abstract often sports announcers particularly in baseball provide the listener with exaggerated information concerning a player s performance for example we may be told that dave winfield a popular baseball player has hit safely in 8 of his last 17 chances a batting average of 471 this is biased or selected information as the 17 was chosen to maximize the reported percentage we model this as observing a maximum success rate of a bernoulli process and show how to construct the likelihood function for a player s true batting ability the likelihood function is a high degree polynomial but it can be computed exactly alternatively the problem yields to solutions based on either the em algorithm or gibbs sampling using these techniques we compute maximum likelihood estimators bayes estimators and associated measures of error we also show how to approximate the likelihood using a brownian motion calculation we find that although constructing good estimators from selected information is d

markov chain monte carlo in stastical mechanics the appearance of the article by n metropolis a w rosenbluth m n rosenbluth a h teller and e teller marked the birth of the monte carlo method for the study of statistical mechanical systems and of a specific form of importance sampling namely markov chain monte carlo after nearly 40 years of statistical usage this technique has had a profound impact on statistical theory on both bayesian and classical statistics markov chain monte carlo is used essentially to estimate integrals in high dimensions this article addresses the accuracy of such estimation through computer experiments performed on the two dimensional ising model we compare the most common method for error estimates in statistical mechanics it appears that the moving block bootstrap outperforms other methods based on subseries values when the number of observations is relatively small and the time correlation between successive configurations decays slowly moreover the moving block bootstrap enables estimates of the sta

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

on a general class of models for interaction this paper develops a class of probability models for configurations of interacting points in a domain the distributions depend on a function which may be viewed as giving the potential energy of the configurations examples include models for interaction in a spatial region and on lattices and graphs new models in the general class arise naturally an example being a spatial model for points of different categories some general methods including series expansions and a simulation method known from statistical mechanics can be useful for many of these models several applications of this kind are considered and some connections between the models and with the statistical mechanics are explored

inference for discrete markov fields the simplest nontrivial case abstract markov fields provide a general context for describing the strength and structure of spatial interactions the gibbs markov equivalence theorem preston 1974 parameterizes markov fields via their neighborhood structures yielding exponential families in canonical form likelihood inference is therefore apparently straightforward the requisite normalizing constants however are obstreperous even when asymptotic characterizations can be obtained substantial location errors arise during implementation moreover markov fields can exhibit phase transitions and long range interactions thereby creating identifiability problems these issues are illustrated in the simplest nontrivial case the classical ising model of ferromagnetism

multitype spatial point patterns with hierarchical interactions multitype spatial point patterns with hierarchical interactions are considered here hierarchical interaction means directionality points on a higher level of hierarchy affect the locations of points on the lower levels but not vice versa such relations are common for example in ecological communities interacting point patterns are often modeled by gibbs processes with pairwise interactions however these models are inherently symmetric and the hierarchy can be acknowledged only when interpreting the results we suggest the following in allowing the inclusion of the hierarchical structure in the model instead of regarding the pattern as a realization of a stationary multivariate point process we build the pattern one type at a time according to the order of the hierarchy by using nonstationary univariate processes as interactions connected to points x on a certain level are considered the effect of the higher levels is interpreted as heterogeneity of the pattern x and the points on the lower levels are neglected because of the hierarchical structure

new developments in state estimation for nonlinear systems based on an interpolation formula accurate state estimators for nonlinear systems can be derived the estimators do not require derivative information which makes them simple to implement

a derivative free implementation of the extended kalman filter a nonlinear estimation paradigm is developed to estimate the mean and covariance of a time evolving state distribution the approach represents uncertainty by an ensemble set of state vectors rather than by the traditional mean and covariance measures avoiding the need for the calculation of matrix partial derivatives jacobian matrices the paradigm is shown to be equivalent to the extended kalman filter in a limiting case implementation of the new filtering approach is illustrated with a simple example and a step by step description the paradigm is not significantly more computationally intensive than traditional filters and proves ideal for the rapid implementation of complex nonlinear system and observation models

conditional logistic regression models for correlated binary data summary a class of conditional logistic regression models for clustered binary data is considered this includes the polychotomous logistic model of rosner 1984 as a special case properties such as the joint distribution and pairwise odds ratio are investigated a class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach an example on chronic obstructive pulmonary disease among sibs is presented for illustration

maximum of a fractional brownian motion probabilities of small values let b t b 0 0 be a fractional brownian motion i e a gaussian process with the structure function e b t b s 2 t s 0 2 we study the logarithmic asymptotics of pt p b t 1 t t as t where is either the interval 0 1 or a bounded region that contains a vicinity of 0 for the case of multidimensional time it is shown that ln pt d ln t 1 o 1 where d is the dimension of zeroes of b t in the former case and the dimension of time in the latter

constrained monte carlo maximum likelihood for dependent data maximum likelihood estimates mles in autologistic models and other exponential family models for dependent data can be calculated with markov chain monte carlo methods the metropolis algorithm or the gibbs sampler which simulate ergodic markov chains having equilibrium distributions in the model from one realization of such a markov chain a monte carlo approximant to the whole likelihood function can be constructed the parameter value if any maximizing this function approximates the mle

brief paper adaptive divided difference filtering for simultaneous state and parameter estimation a novel adaptive version of the divided difference filter ddf applicable to non linear systems with a linear output equation is presented in this work in order to make the filter robust to modeling errors upper bounds on the state covariance matrix are derived the parameters of this upper bound are then estimated using a combination of offline tuning and online optimization with a linear matrix inequality lmi constraint which ensures that the predicted output error covariance is larger than the observed output error covariance the resulting sub optimal high gain filter is applied to the problem of joint state and parameter estimation simulation results demonstrate the superior performance of the proposed filter as compared to the standard ddf

on the symmetry properties of a random passive scalar with and without boundaries and their connection between hot and cold states abstract we consider the evolution of a decaying passive scalar in the presence of a gaussian white noise fluctuating linear shear flow known as the majda model we focus on deterministic initial data and establish the short intermediate and long time symmetry properties of the evolving point wise probability measure pdf for the random passive scalar we identify for the cases of both point source and line source initial data regions in the x yplane outside of which the pdf skewness is sign definite for all time while inside these regions we observe multiple sign changes corresponding to exchanges in symmetry between hot and cold leaning states using exact representation formula for the pdf at the origin and away from the origin using numerical evaluation of the exact available mehler kernel formulae for the scalar s statistical moments a new rapidly convergent monte carlo method is developed dubbed direct monte carlo dmc using the available random green s functions which allows for the fast construction of the pdf for single point statistics as well as multi point statistics including spatially integrated quantities natural for full monte carlo simulations of the underlying stochastic differential equations fmc this new method demonstrates the full evolution of the pdf from short times to its long time limiting and collapsing universal distribution at arbitrary points in the plane further this method provides a strong benchmark for fmc and we document numbers of field realization criteria for the fmc to faithfully compute this complete dynamics armed with this benchmark we apply the fmc to a channel with a no flux boundary condition enforced on parallel planes and observe a dramatically different long time state resulting from the existence of the wall in particular the channel case collapsing invariant measure has negative skewness with random states leaning heavily towards the hot state in stark contrast to free space where the limiting skewness is positive with its states leaning heavily towards the cold state

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12