probabilistic estimation of the number of prefixes of a trace abstract we present a generating function technique to evaluate the number of strings of a given length recognized by a particular kind of finite state automaton using the method we determine some asymptotic estimations of the number of prefixes in free partially commutative monoids more precisely we prove that for every concurrent alphabet c assuming equiprobable strings all of length n the average number of prefixes of a trace of length n is n k o n k 1 and its variance is o n 2 k 1 where k is the number of components of the dependency graph c c and is a rational constant depending only on c these combinatorial results allow to determine the probabilistic behaviour of some algorithms for problems on trace languages including the membership problems for regular and context free trace languages

estimating normal means with a dirichlet process prior abstract in this article the dirichlet process prior is used to provide a nonparametric bayesian estimate of a vector of normal means in the past there have been computational difficulties with this model this article solves the computational difficulties by developing a gibbs sampler algorithm the estimator developed in this article is then compared to parametric empirical bayes estimators peb and nonparametric empirical bayes estimators npeb in a monte carlo study the monte carlo study demonstrates that in some conditions the peb is better than the npeb and in other conditions the npeb is better than the peb the monte carlo study also shows that the estimator developed in this article produces estimates that are about as good as the peb when the peb is better and produces estimates that are as good as the npeb estimator when that method is better

spectral analysis for discrete longitudinal data abstract we develop a fourier type of analysis for data consisting of many short strings x 1 x 2 x n with x i x i 1 x ip the paper offers an approach testing and residual analysis based on a group theoretic decomposition of the sample space this is illustrated on a physical chance type data set where it is natural to allow each string to have its own parameter i i d coin tossing with parameter varying from string to string the usual model is rejected

recursive tracking of vascular networks in angiograms based on the detection deletion scheme a computer algorithm was developed for automated identification of 2 d vascular networks in x ray angiograms this was accomplished by using an adaptive tracking algorithm in a three stage recursive procedure first given a starting position and direction a segment in the vascular network was identified second by filling it with the surrounding background pixel values the detected segment was deleted from the angiogram the detection deletion scheme was employed to prevent the problem of tracking path reentry in those areas where vessels overlap third all branch points were detected by use of matched filtering along both edges of the vessel the detected branch points were used as the starting points in the next recursion the recursive procedure terminated when no new branch point was found the algorithm showed a good performance when it was applied to angiograms of coronary and radial arteries to provide a quantitative evaluation vascular networks identified by the algorithm were compared to those identified by a human the algorithm made some false negative errors but very few false positive errors

stopping time resampling for sequential monte carlo methods summary motivated by the statistical inference problem in population genetics we present a new sequential importance sampling with resampling strategy the idea of resampling is key to the recent surge of popularity of sequential monte carlo methods in the statistics and engineering communities but existing resampling techniques do not work well for coalescent based inference problems in population genetics we develop a new method called stopping time resampling which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on to illustrate the idea we first apply the new method to approximate the solution of a dirichlet problem and the likelihood function of a non markovian process then we focus on its application in population genetics all our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods

a countable representation of the fleming viot measure valued diffusion the fleming viot measure valued diffusion arises as the infinite population limit of various discrete genetic models with general type space the paper gives a countable construction of the process as the empirical measure carried by a certain interactive particle system this explicit representation facilitates the study of various properties of the fleming viot process the construction also carries versions of the familiar genealogical processes from population genetics in particular kingman s coalescent thus unifying the genealogical and measure valued approaches to the subject

particle representations for measure valued population models models of populations in which a type or location represented by a point in a metric space e is associated with each individual in the population are considered a population process is neutral if the chances of an individual replicating or dying do not depend on its type measurevalued processes are obtained as infinite population limits for a large class of neutral population models and it is shown that these measure valued processes can be represented in terms of the total mass of the population and the de finetti measures associated with an e valued particle model

survival of contact processes on the hierarchical group we consider contact processes on the hierarchical group where sites infect other sites at a rate depending on their hierarchical distance and sites become healthy with a constant recovery rate if the infection rates decay too fast as a function of the hierarchical distance then we show that the critical recovery rate is zero on the other hand we derive sufficient conditions on the speed of decay of the infection rates for the process to exhibit a nontrivial phase transition between extinction and survival for our sufficient conditions we use a coupling argument that compares contact processes on the hierarchical group with freedom two with contact processes on a renormalized lattice an interesting novelty in this renormalization argument is the use of a result due to rogers and pitman on markov functionals

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

model based morphological segmentation and labeling of coronary angiograms a method for extraction and labeling of the coronary arterial tree cat using minimal user supervision in single view angiograms is proposed the cat structural description skeleton and borders is produced along with quantitative information for the artery dimensions and assignment of coded labels based on a given coronary artery model represented by a graph the stages of the method are 1 cat tracking and detection 2 artery skeleton and border estimation 3 feature graph creation and iv artery labeling by graph matching the approximate cat centerline and borders are extracted by recursive tracking based on circular template analysis the accurate skeleton and borders of each cat segment are computed based on morphological homotopy modification and watershed transform the approximate centerline and borders are used for constructing the artery segment enclosing area asea where the defined skeleton and border curves are considered as markers using the marked asea an artery gradient image is constructed where all the asea pixels except the skeleton ones are assigned the gradient magnitude of the original image the artery gradient image markers are imposed as its unique regional minima by the homotopy modification method the watershed transform is used for extracting the artery segment borders and the feature graph is updated finally given the created feature graph and the known model graph a graph matching algorithm assigns the appropriate labels to the extracted cat using weighted maximal cliques on the association graph corresponding to the two given graphs experimental results using clinical digitized coronary angiograms are presented

a change of variable formula with ito correction term we consider the solution u x t to a stochastic heat equation for fixed x the process f t u x t has a nontrivial quartic variation it follows that f is not a semimartingale so a stochastic integral with respect to f cannot be defined in the classical ito sense we show that for sufficiently differentiable functions g x t a stochastic integral g f t t d f t exists as a limit of discrete midpoint style riemann sums where the limit is taken in distribution in the skorokhod space of cadlag functions moreover we show that this integral satisfies a change of variable formula with a correction term that is an ordinary ito integral with respect to a brownian motion that is independent of f

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

pruned enriched rosenbluth method simulations of θ polymers of chain length up to 1 000 000 we present an algorithm for simulating flexible chain polymers it combines the rosenbluth rosenbluth method with recursive enrichment although it can be applied also in more general situations it is most efficient for three dimensional theta polymers on the simple cubic lattice there it allows high statistics simulations of chains of length up to n 10 sup 6 for storage reasons this is feasable only for polymers in a finite volume for free theta polymers in infinite volume we present very high statistics runs with n 10000 these simulations fully agree with previous simulations made by hegger and grassberger j chem phys bold 102 6681 1995 with a similar but less efficient algorithm showing that logarithmic corrections to mean field behavior are much stronger than predicted by field theory but the finite volume simulations show that the density inside a collapsed globule scales with the distance from the theta point as predicted by mean field theory in contrast to claims in the work mentioned above in addition to the simple cubic lattice we also studied two versions of the bond fluctuation model but with much shorter chains finally we show that our method can be applied also to off lattice models and illustrate this with simulations of amore model studied in detail by freire ital et al macromolecules bold 19 452 1986 and later work copyright ital 1997 ital the american physical society less

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

macroscopic limits for stochastic partial differential equations of mckean vlasov type a class of quasilinear stochastic partial differential equations spdes driven by spatially correlated brownian noise is shown to become macroscopic i e deterministic as the length of the correlations tends to 0 the limit is the solution of a quasilinear partial differential equation the quasilinear spdes are obtained as a continuum limit from the empirical distribution of a large number of stochastic ordinary differential equations sodes coupled though a mean field interaction and driven by correlated brownian noise the limit theorems are obtained by application of a general result on the convergence of exchangeable systems of processes we also compare our approach to sodes with the one introduced by kunita

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

the tree length of an evolving coalescent a well established model for the genealogy of a large population in equilibrium is kingman s coalescent for the population together with its genealogy evolving in time this gives rise to a time stationary tree valued process we study the sum of the branch lengths briefly denoted as tree length and prove that the suitably compensated sequence of tree length processes converges as the population size tends to infinity to a limit process with cadlag paths infinite infinitesimal variance and a gumbel distribution as its equilibrium

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 reliable data based bandwidth selection method for kernel density estimation we present a new method for data based selection of the bandwidth in kernel density estimation which has excellent properties it improves on a recent procedure of park and marron which itself is a good method in various ways first the new method has superior theoretical performance second it also has a computational advantage third the new method has reliably good performance for smooth densities in simulations performance that is second to none in the existing literature these methods are based on choosing the bandwidth to approximately minimize good quality estimates of the mean integrated squared error the key to the success of the current procedure is the reintroduction of a non stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

smaller population size at the mrca time for stationary branching processes we consider an elementary model of random size varying population governed by a stationary continuous state branching process we compute the distributions of various variables related to the most recent common ancestor mrca the time to the mrca the size of the current population and the size of the population just before the mrca in particular we observe a natural mild bottleneck effect as the size of the population just before the mrca is stochastically smaller than the size of the current population we also compute the number of individuals involved in the last coalescent event of the genealogical tree that is the number of individuals at the time of the mrca who have descendants in the current population by studying more precisely the genealogical structure of the population we get asymptotics for the number of ancestors just before the current time we give explicit computations in the case of the quadratic branching mechanism in this case the size of the population at the mrca is in mean 2 3 of the size of the current population we also provide in this case the fluctuations for the renormalized number of ancestors

importance weighted marginal bayesian posterior density estimation abstract markov chain sampling schemes generate dependent observations i 0 i n from a full joint posterior distribution data frequently only certain marginals of this full posterior density are of interest thus an interesting problem is how to estimate the marginal posterior densities based on the dependent observations i 0 i n from data we propose a new importance weighted marginal density estimation iwmde method an iwmde is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w the asymptotic properties for the iwmde and the guidelines for choosing a weighting conditional density w are also considered a bivariate normal model and a constrained linear multiple regression model are used to illustrate how to derive the iwmde s for the marginal posterior densities

resolvent estimates for fleming viot operators with brownian drift abstract this article is a supplement to the paper of d a dawson and p march j funct anal 132 1995 417 472 we define a two parameter scale of banach spaces of functions defined on m 1 r d the space of probability measures on d dimensional euclidean space using weighted sums of the classical sobolev norms we prove that the resolvent of the fleming viot operator with constant diffusion coefficient and brownian drift acts boundedly between certain members of the scale these estimates gauge the degree of smoothing performed by the resolvent and separate the contribution due to the diffusion coefficient and that due to the drift coefficient

penalized clustering of large scale functional data with multiple covariates in this article we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach in our proposed method responses and covariates are linked together through nonparametric multivariate functions fixed effects which have great flexibility in modeling various function features such as jump points branching and periodicity functional anova is used to further decompose multivariate functions in a reproducing kernel hilbert space and provide associated notions of main effect and interaction parsimonious random effects are used to capture various correlation structures the mixed effects models are nested under a general mixture model in which the heterogeneity of functional data is characterized we propose a penalized henderson s likelihood approach for model fitting and design a rejection controlled em algorithm for the estimation our method selects smoothing parameters through generalized cross validation furthermore bayesian confidence in

an analytic approach to fleming viot processes with interactive selection we study a class of nonsymmetric dirichlet forms e d e having a space of measures as state space e and derive some general results about them we show that under certain conditions they generate diffusion processes m in particular if m is ergodic and e d e is symmetric w r t quasi every starting point the large deviations of the empirical distribution of m are governed by e we apply all of this to construct fleming viot processes with interactive selection and prove some results on their behavior among other things we show some support properties for these processes using capacitary methods

inference in molecular population genetics full likelihood based inference for modern population genetics data presents methodological and computational challenges the problem is of considerable practical importance and has attracted recent attention with the development of algorithms based on importance sampling is and markov chain monte carlo mcmc sampling here we introduce a new is algorithm the optimal proposal distribution for these problems can be characterized and we exploit a detailed analysis of genealogical processes to develop a practicable approximation to it we compare the new method with existing algorithms on a variety of genetic examples our approach substantially outperforms existing is algorithms with efficiency typically improved by several orders of magnitude the new method also compares favourably with existing mcmc methods in some problems and less favourably in others suggesting that both is and mcmc methods have a continuing role to play in this area we offer insights into the relative advantages of each approach and we discuss diagnostics in the is framework

dynamic conditional independence models and markov chain monte carlo methods abstract in dynamic statistical modeling situations observations arise sequentially causing the model to expand by progressive incorporation of new data items and new unknown parameters for example in clinical monitoring patients and data arrive sequentially and new patient specific parameters are introduced with each new patient markov chain monte carlo mcmc might be used for continuous updating of the evolving posterior distribution but would need to be restarted from scratch at each expansion stage thus mcmc methods are often too slow for real time inference in dynamic contexts by combining mcmc with importance resampling we show how real time sequential updating of posterior distributions can be effected the proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded such as when a patient dies or is discharged we apply the

segmentation of macular fluorescein angiographies a statistical approach this paper is concerned with the use of bayesian methods in the segmentation of macular uorescein angiographies fluorescein angiography is used in ophthalmic practice to evaluate vascular retinopathies and choroidopathies sodium uorescein is injected in the arm s cubital vein of the patient and its distribution is observed along retinal vessels at certain times in this task a previous and essential step is the segmentation of the image into its relevant components in order to obtain this segmentation bayesian methods can be used because a previous knowledge about the spatial structure of the scene to be segmented is available in this kind of images the stochastic model assumed for the observed intensities is a simple model with a gaussian noise process which is statiscally independent between pixels the process of labels x is modelled as a markov random eld with a space dependent external eld expressing the anatomy of the ocular fundus and higher order interactions encouraging blood vessels to be thin and large this procedure is applied to di erent cases of diabetic retinophaty and vein occlusions two algorithms have been used to estimate x simulated annealing and iterated conditional modes in order to evaluate the accuracy of the estimation several error measures have been calculated 2001 pattern recognition society published by elsevier science ltd all rights reserved

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

bayesian analysis of isochores statistical identification of isochore structure the variation in large scale gc composition proportion of dna bases that are g or c as opposed to a or t of mammalian genomes is a necessary requirement for understanding both the evolution of base composition and the many genomic features such as mutation and recombination rates which covary with base composition we have developed a bayesian method for isochore analysis that we demonstrate to be more accurate than the commonly used binary segmentation approach implemented within the program isofinder the method accounts for both fine scale and large scale structure we adapt direct simulation methods to allow for iid samples from the posterior distribution of our model and provide an accurate approximation to this that can analyze data from a chromosome in a matter of seconds we apply our method to human chromosome 1 the resulting estimate of how gc content varies across this region is shown to be a better predictor of local recombination rates t

on line inference for hidden markov models via particle filters we consider the on line bayesian analysis of data by using a hidden markov model where inference is tractable conditional on the history of the state of the hidden component a new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type the algorithm is similar to the mixture kalman filter but uses a different resampling algorithm we prove that this resampling algorithm is computationally efficient and optimal among unbiased resampling algorithms in terms of minimizing a squared error loss function in a practical example that of estimating break points from well log data our new particle filter outperforms two other particle filters one of which is the mixture kalman filter by between one and two orders of magnitude

semi markov models with phase type sojourn distributions continuous time multistate models are widely used for categorical response data particularly in the modeling of chronic diseases however inference is difficult when the process is only observed at discrete time points with no information about the times or types of events between observation times unless a markov assumption is made this assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state such a formulation results in a semi markov model we show that the computational problems associated with fitting semi markov models to panel observed data can be alleviated by considering a class of semi markov models with phase type sojourn distributions this allows methods for hidden markov models to be applied in addition extensions to models where observed states are subject to classification error are given the methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post lung transplantation patients

blind restoration of linearly degraded discrete signals by gibbs sampling this paper addresses the problem of simultaneous parameter estimation and restoration of discrete valued signals that are blurred by an unknown fir filter and contaminated by additive gaussian white noise with unknown variance assuming that the signals are stationary markov chains with known state space but unknown initial and transition probabilities bayesian inference of all unknown quantities is made from the blurred and noisy observations a monte carlo procedure called the gibbs sampler is employed to calculate the bayesian estimates simulation results are presented to demonstrate the effectiveness of the method

tree valued resampling dynamics martingale problems and applications the measure valued fleming viot process is a diffusion which models the evolution of allele frequencies in a multi type population in the neutral setting the kingman coalescent is known to generate the genealogies of the individuals in the population at a fixed time the goal of the present paper is to replace this static point of view on the genealogies by an analysis of the evolution of genealogies we encode the genealogy of the population as an isometry class of an ultra metric space which is equipped with a probability measure the space of ultra metric measure spaces together with the gromov weak topology serves as state space for tree valued processes we use well posed martingale problems to construct the tree valued resampling dynamics of the evolving genealogies for both the finite population moran model and the infinite population fleming viot diffusion we show that sufficient information about any ultra metric measure space is contained in the distribution of the vector of subtree lengths obtained by sequentially sampled individuals we give explicit formulas for the evolution of the laplace transform of the distribution of finite subtrees under the tree valued fleming viot dynamics

long time behaviour and regularity properties of transition semigroups of fleming viot processes let a be a feller generator on a compact space and l be the corresponding fleming viot fv operator with no selection and no recombination in this paper we give conditions on a implying that the semigroup t t generated by l i converges towards equilibrium with exponential rate moreover we determine explicit bounds on the rate of convergence in terms of a ii is hypercontractive iii is strong feller and iv is compact we give applications of the last result to the existence of invariant measures for fv operators with interactive selection

poisson representations of branching markov and measure valued branching processes representations of branching markov processes and their measure valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates each particle has a location and a level but unlike earlier constructions the levels change with time in fact death of a particle occurs only when the level of the particle crosses a specified level r or for the limiting models hits infinity for branching markov processes at each time t conditioned on the state of the process the levels are independent and uniformly distributed on 0 r for the limiting measure valued process at each time t the joint distribution of locations and levels is conditionally poisson distributed with mean measure k t x lambda where lambda denotes lebesgue measure and k is the desired measure valued process the representation simplifies or gives alternative proofs for a variety of calculations and results including conditioning on extinction or nonextinction harris s convergence theorem for supercritical branching processes and diffusion approximations for processes in random environments

pattern statistics and vandermonde matrices in this paper we determine some limit distributions of pattern statistics in rational stochastic models we present a general approach to analyze these statistics in rational models having an arbitrary number of strongly connected components we explicitly establish the limit distributions in most significant cases they are characterized by a family of unimodal density functions defined by means of confluent vandermonde matrices

association pattern discovery via theme dictionary models summary discovering patterns from a set of text or more generally categorical data is an important problem in many disciplines such as biomedical research linguistics artificial intelligence and sociology we consider here the well known market basket problem that is often discussed in the data mining community and is also quite ubiquitous in biomedical research the data under consideration are a set of baskets where each basket contains a list of items our goal is to discover themes which are defined as subsets of items that tend to co occur in a basket we describe a generative model i e the theme dictionary model for such data structures and describe two likelihood based methods to infer themes that are hidden in a collection of baskets we also propose a novel sequential monte carlo method to overcome computational challenges using both simulation studies and real applications we demonstrate that the new approach proposed is significantly more powerful than existing methods such as association rule mining and topic modelling in detecting weak and subtle interactions in the data

model guided labeling of coronary structure assigning anatomic labels to coronary arteries in x ray angiograms is an important task in medical imaging motivated by the desire to standardize the assessment of coronary artery disease and to facilitate the three dimensional 3 d reconstruction and visualization of the coronary vasculature however automatic labeling poses a number of significant challenges including the presence of noise artifacts competing structures misleading visual cues and other difficulties associated with a dynamic and inherently complex structure the authors have developed a model guided approach that addresses these challenges and automatically labels the vascular structure in coronary angiographic images the approach consists of two models 1 a symbolic model represented through a directed acyclic graph that captures vascular tree hierarchies and branch interrelationships and 2 a generalized 3 d model that captures spatial and geometric relationships importantly the approach detects ambiguities such as vessel overlaps that may be found in a frame of a cine sequence and resolves these ambiguities by considering the information derived from other unambiguous frames in the temporal sequence employing dynamic programming methods to match the image features found in the different ambiguous and unambiguous frames this paper presents this model guided labeling algorithm and discusses the experimental results obtained from implementing and applying the resulting labeling system to a variety of clinical images the results indicate the feasibility of achieving robust and consistently accurate image labeling through this model guided temporal disambiguation method

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

fleming viot processes in population genetics fleming and viot indiana univ math j 28 1979 pp 817 843 introduced a class of probability measure valued diffusion processes that has attracted the interest of both pure and applied probabilists this paper surveys the subject of fleming viot processes as it relates to population genetics topics include 1 introduction 2 some measure valued markov chains 2 1 a diploid model 2 2 the wright fisher model 2 3 a moran model 3 the fleming viot process characterization 4 convergence 5 ergodicity 6 an infinite particle system 7 bounded mutation operators 8 reversibility 9 examples 9 1 continuous state stepwise mutation model 9 2 infinitely many neutral alleles model 9 3 infinitely many neutral alleles model with ages 9 4 two locus model with recombination 9 5 n locus model with gene conversion 9 6 infinitely many sites model without recombination 9 7 infinitely many neutral alleles model with allelic genealogies

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

multivariate density estimation by bayesian sequential partitioning consider a class of densities that are piecewise constant functions over partitions of the sample space defined by sequential coordinate partitioning we introduce a prior distribution for a density in this function class and derive in closed form the marginal posterior distribution of the corresponding partition a computationally efficient method based on sequential importance sampling is presented for the inference of the partition from this posterior distribution compared to traditional approaches such as the kernel method or the histogram the bayesian sequential partitioning bsp method proposed here is capable of providing much more accurate estimates when the sample space is of moderate to high dimension we illustrate this by simulated as well as real data examples the examples also demonstrate how bsp can be used to design new classification methods competitive with the state of the art

rejection control and sequential importance sampling abstract we discuss ways of combining rejection sampling and importance sampling methods in monte carlo computations and demonstrate their usefulness in updating dynamic systems specifically we propose the rejection controlled sequential importance sampling rc sis algorithm which is designed to simultaneously reduce monte carlo variation and retain independent samples in sequential importance sampling the proposed method is demonstrated by three examples taken from econometrics hierarchical bayes analysis and digital telecommunications they all show significant improvements over previous results

empirical bayes confidence intervals based on bootstrap samples abstract consider the model with data generated by the following two stage process first a parameter is sampled from a prior distribution g and then an observation is sampled from the conditional distribution f y if the prior distribution is known then the bayes estimate under squared error loss is the posterior expectation of conditional on the data y for example if g is gaussian with mean and variance 2 and f y is gaussian with mean and variance 2 then the posterior distribution is gaussian with mean b 1 b y and variance 2 1 b where b 2 2 2 inferences about are based on this distribution we study the application of the bootstrap to situations where the prior must be estimated from the data empirical bayes methods for this model we observe data y t y 1 y k t each independent y k following the compound model described previously as first shown by james and stein 1961 setting each k equal to its estimated posterior mean where and pr

adapting the number of particles in sequential monte carlo methods through an online scheme for convergence assessment particle filters are broadly used to approximate posterior distributions of hidden states in state space models by means of sets of weighted particles while the convergence of the filter is guaranteed when the number of particles tends to infinity the quality of the approximation is usually unknown but strongly dependent on the number of particles in this paper we propose a novel method for assessing the convergence of particle filters in an online manner as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment the method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter we provide a rigorous theoretical analysis of the proposed methodology and as an example of its practical use we present simulations of a simple algorithm for the dynamic and online adaptation of the number of particles during the operation of a particle filter on a stochastic version of the lorenz 63 system

contour grouping based on contour skeleton duality in this paper we present a method for grouping relevant object contours in edge maps by taking advantage of contour skeleton duality regularizing contours and skeletons simultaneously allows us to combine both low level perceptual constraints as well as higher level model constraints in a very effective way the models are represented using paths in symmetry sets skeletons are treated as trajectories of an imaginary virtual robot in a discrete space of symmetric points obtained from pairs of edge segments boundaries are then defined as the maps obtained by grouping the associated pairs of edge segments along the trajectories casting the grouping problem in this manner makes it similar to the problem of simultaneous localization and mapping slam hence we adapt the state of the art probabilistic framework namely rao blackwellized particle filtering that has been successfully applied to slam we use the framework to maximize the joint posterior over skeletons and contours

finding words with unexpected frequencies in deoxyribonucleic acid sequences considering a markov chain model for deoxyribonucleic acid sequences this paper proposes two asymptotically normal statistics to test whether the frequency of a given word is concordant with the first order markov chain model or not the problem is to choose estimates w of the expectation of the frequency m w of a word w in the observed sequence such that the asymptotic variance of m w w is easily computable the first estimator is derived from the frequency of w 1 which is w with its last letter deleted the second following an idea of cowan is the conditional expectation m w given the observed frequencies of all two letter words two examples on phage lambda and phage t7 are shown

rao blackwellisation of sampling schemes summary this paper proposes a post simulation improvement for two common monte carlo methods the accept reject and metropolis algorithms the improvement is based on a rao blackwellisation method that integrates over the uniform random variables involved in the algorithms and thus post processes the standard estimators we show how the rao blackwellised versions of these algorithms can be implemented and through examples illustrate the improvement in variance brought by these new procedures we also compare the improved version of the metropolis algorithm with ordinary and rao blackwellised importance sampling procedures for independent and general metropolis set ups

continuum sites stepping stone models coalescing exchangeable partitions and random trees analogues of stepping stone models are considered where the sitespace is continuous the migration process is a general markov process and the type space is infinite such processes were defined in previous work of the second author by specifying a feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing markov processes an alternative representation is obtained here in terms of a limit of interacting particle systems it is shown that under a mild condition on the migration process the continuum sites stepping stone process has continuous sample paths the case when the migration process is brownian motion on the circle is examined in detail using a duality relation between coalescing and annihilating brownian motion this duality relation is also used to show that a tree like random compact metric space that is naturally associated to an in nite family of coalescing brownian motions on the circle has hausdorff and packing dimension both almost surely equal to 1 2 and moreover this space is capacity equivalent to the middle 1 2 cantor set and hence also to the brownian zero set

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

on the number of occurrences of a symbol in words of regular languages we study the random variable yn representing the number of occurrences of a symbol a in a word of length n chosen at random in a regular language l a b where the random choice is defined via a non negative rational formal series r of support l assuming that the transition matrix associated with r is primitive we obtain asymptotic estimates for the mean value and the variance of yn and present a central limit theorem for its distribution under a further condition on such a matrix we also derive an asymptotic approximation of the discrete fourier transform of yn that allows to prove a local limit theorem for yn further consequences of our analysis concern the growth of the coefficients in rational formal series in particular it turns out that for a wide class of regular languages l the maximum number of words of length n in l having the same number of occurrences of a given symbol is of the order of growth n n for some constant 1

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

retina verification system based on biometric graph matching this paper presents an automatic retina verification framework based on the biometric graph matching bgm algorithm the retinal vasculature is extracted using a family of matched filters in the frequency domain and morphological operators then retinal templates are defined as formal spatial graphs derived from the retinal vasculature the bgm algorithm a noisy graph matching algorithm robust to translation non linear distortion and small rotations is used to compare retinal templates the bgm algorithm uses graph topology to define three distance measures between a pair of graphs two of which are new a support vector machine svm classifier is used to distinguish between genuine and imposter comparisons using single as well as multiple graph measures the classifier achieves complete separation on a training set of images from the varia database 60 of the data equaling the state of the art for retina verification because the available data set is small kernel density estimation kde of the genuine and imposter score distributions of the training set are used to measure performance of the bgm algorithm in the one dimensional case the kde model is validated with the testing set a 0 eer on testing shows that the kde model is a good fit for the empirical distribution for the multiple graph measures a novel combination of the svm boundary and the kde model is used to obtain a fair comparison with the kde model for the single measure a clear benefit in using multiple graph measures over a single measure to distinguish genuine and imposter comparisons is demonstrated by a drop in theoretical error of between 60 and more than two orders of magnitude

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

nonparametric hierarchical bayes via sequential imputations we consider the empirical bayes estimation of a distribution using binary data via the dirichlet process let d denote a dirichlet process with being a finite measure on 0 1 instead of having direct samples from an unknown random distribution f from d we assume that only indirect binomial data are observable this paper presents a new interpretation of lo s formula and thereby relates the predictive density of the observations based on a dirichlet process model to likelihoods of much simpler models as a consequence the log likelihood surface as well as the maximum likelihood estimate of c 0 1 is found when the shape of is assumed known together with a formula for the fisher information evaluated at the estimate the sequential imputation method of kong liu and wong is recommended for overcoming computational difficulties commonly encountered in this area the related approximation formulas are provided an analysis of the tack data of beckett and diaconis which motivated this study is supplemented to illustrate our methods