asymptotic behavior of solutions of δv qv λv and the distance of λ to the essential spectrum dans l 2 r n n 2 on etudie l operateur q defini sur co r n avec q l 2 loc r n a valeurs reelles on etablit le lien entre la decroissance des fonctions propres et la distance de au spectre essentiel

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

stepwise signal extraction via marginal likelihood this article studies the estimation of a stepwise signal to determine the number and locations of change points of the stepwise signal we formulate a maximum marginal likelihood estimator which can be computed with a quadratic cost using dynamic programming we carry out an extensive investigation on the choice of the prior distribution and study the asymptotic properties of the maximum marginal likelihood estimator we propose to treat each possible set of change points equally and adopt an empirical bayes approach to specify the prior distribution of segment parameters a detailed simulation study is performed to compare the effectiveness of this method with other existing methods we demonstrate our method on single molecule enzyme reaction data and on dna array comparative genomic hybridization cgh data our study shows that this method is applicable to a wide range of models and offers appealing results in practice supplementary materials for this article are available online

on the essential spectrum of schrodinger operators with spherically symmetric potentials on determine le spectre essentiel des operateurs de schrodinger avec un potentiel a symetrie spherique v x q x

product partition models for normal means abstract i consider probability models for the estimation of normal means that allow for some of the means to be equal these probability models called product partition models specify prior probabilities for a random partition the posterior probability of the partition given the observations has the same form the resulting estimate of the means the product estimate is obtained by conditioning on the partition and summing over all possible partitions the large number of computations involved leads to the use of markov sampling to compute the product estimate i compare the product estimate to other estimates of normal means both in a simulation study and in the prediction of baseball batting averages

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

mixture models with a prior on the number of components abstracta natural bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric dirichlet weights and put a prior on the number of components that is to use a mixture of finite mixtures mfm the most commonly used method of inference for mfms is reversible jump markov chain monte carlo but it can be nontrivial to design good reversible jump moves especially in high dimensional spaces meanwhile there are samplers for dirichlet process mixture dpm models that are relatively simple and are easily adapted to new applications it turns out that in fact many of the essential properties of dpms are also exhibited by mfms an exchangeable partition distribution restaurant process random measure representation and stick breaking representation and crucially the mfm analogues are simple enough that they can be used much like the corresponding dpm properties consequently many of the powerful methods developed for inference in dpms

mode localization phenomena in large space structures the possibility of localization or confinement of vibratory modes in large space structures is investigated theoretically and numerically these structures belong to a class of periodic structures that have recently been shown to be sensitive to periodicity b reaking disorder or imperfections when localization occurs the modal amplitude of a global mode becomes confined to a local region of the structure with serious implications for the control problem the results of this study indicate that mode localization is most likely to occur in structures consisting of a large number of weakly coupled substructures certain large space structures with high modal densities fall in this category and it is therefore important to include the effect of structural imperfections and disorder when designing control systems for shape or directional control of such structures k kh kw ku k k m m m n n p qi qt t u v w uf 8fj e 6

factorization for efficient solution of eigenproblems of adjacency and laplacian matrices for graph products many structural models can be generated as the graph products of two or three subgraphs known as their generators the main types of graph products consist of cartesian strong cartesian direct and lexicographic products in this paper a general method is presented for the factorization of these graph products such that the eigenvalues of the entire graph are obtained as the union of the eigenvalues of the weighted subgraphs defined here the adjacency and laplacian matrices for each graph product are studied separately for graphs with missing elements cut outs the eigenvalues are calculated with the additional use of the rayleigh quotient approach the main idea stems from the rules recently developed by the authors for block diagonalization of matrices these products have many applications in computational mechanics such as ordering graph partitioning dynamic analysis and stability analysis of structures some of these applications are addressed in this paper copyright 2007 john wiley sons ltd

block diagonalization of adjacency and laplacian matrices for graph product applications in structural mechanics eigenvalues and eigenvectors of graphs have many applications in structural mechanics and combinatorial optimization for a regular space structure the visualization of its graph model as the product of two simple graphs results in a substantial simplification in the solution of the corresponding eigenproblems in this paper the adjacency and laplacian matrices of four graph products namely cartesian strong cartesian direct and lexicographic products are diagonalized and efficient methods are obtained for calculating their eigenvalues and eigenvectors an exceptionally efficient method is developed for the eigensolution of the laplacian matrices of strong cartesian and direct products special attention is paid to the lexicographic product which is not studied in the past as extensively as the other three graph products examples are provided to illustrate some applications of the methods in structural mechanics copyright 2006 john wiley sons ltd

computation of isotopisms of algebras over finite fields by means of graph invariants in this paper we define a pair of faithful functors that map isomorphic and isotopic finite dimensional algebras over finite fields to isomorphic graphs these functors reduce the cost of computation that is usually required to determine whether two algebras are isomorphic in order to illustrate their efficiency we determine explicitly the classification of two and three dimensional partial quasigroup rings

joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a bayesian sampling approach we propose a joint segmentation algorithm for piecewise constant autoregressive ar processes recorded by several independent sensors the algorithm is based on a hierarchical bayesian model appropriate priors allow us to introduce correlations between the change locations of the observed signals numerical problems inherent to bayesian inference are solved by a gibbs sampling strategy the proposed joint segmentation methodology yields improved segmentation results when compared with parallel and independent individual signal segmentations the initial algorithm is derived for piecewise constant ar processes whose orders are fixed on each segment however an extension to models with unknown model orders is also discussed theoretical results are illustrated by many simulations conducted with synthetic signals and real arc tracking and speech signals

eigensolution of augmented graph products using shifted inverse iteration method two important matrices associated with graphs are adjacency and laplacian matrices in this paper efficient methods are presented for eigensolution of graph products augmented by other graphs for augmentations that do not destroy the symmetry of the graph products a method is proposed for decomposition of matrices resulting in considerable simplification of their eigensolution for graphs composed of two non overlapping graph products joined through a small number of link members a method based on shifted inverse iteration is proposed which utilizes all eigenvalues and eigenvectors of each individual graph products owing to the availability of fast methods for eigensolution of graph products this method simplifies the eigensolution of a variety of graph models and proves to be very efficient in determining the few smallest eigenpairs of these models with high levels of accuracy

bayesian inference on changes in response densities over predictor clusters in epidemiology it often is of interest to assess how individuals with different trajectories over time in an environmental exposure or biomarker differ with respect to a continuous response for ease in interpretation and presentation of results epidemiologists typically categorize predictors before analysis to extend this approach to time varying predictors individuals can be clustered by their predictor trajectory with the cluster index included as a predictor in a regression model for the response this article develops a semiparametric bayes approach that avoids assuming a prespecified number of clusters and allows the response to vary nonparametrically over predictor clusters this methodology is motivated by interest in relating trajectories in weight gain during pregnancy to the distribution of birth weight adjusted for gestational age at delivery in this setting the proposed approach allows the tails of the birth weight density to vary flexibly over weight gain clusters

separation measures and the geometry of bayes factor selection for classification conjugacy assumptions are often used in bayesian selection over a partition because they allow the otherwise unfeasibly large model space to be searched very quickly the implications of such models can be analysed algebraically we use the explicit forms of the associated bayes factors to demonstrate that such methods can be unstable under common settings of the associated hyperparameters we then prove that the regions of instability can be removed by setting the hyperparameters in an unconventional way under this family of assignments we prove that model selection is determined by an implicit separation measure a function of the hyperparameters and the sufficient statistics of clusters in a given partition we show that this family of separation measures has plausible properties the methodology proposed is illustrated through the selection of clusters of longitudinal gene expression profiles

restricted rank modification of the symmetric eigenvalue problem theoretical considerations the problem is considered how to obtain the eigenvalues and vectors of a matrix a vvt where a is a symmetric matrix with known spectral decomposition and vvt is a positive semidefinite matrix of low rank it is shown that the eigenvalues of a vvt can easily be located to any desired accuracy by means of the inertia of the matrix i vt a 1v the problem of determining the eigenvalues of a restricted to r v can be treated likewise

river stream flows in the northern quebec labrador region a multivariate change point analysis via maximum likelihood 1 spring stream flows of six rivers that flow in the northern quebec labrador region are modeled in a multivariate gaussian framework and have been analyzed for possible change points in their average flows the multivariate formulation takes into account correlations among the flows of the six rivers that flow in the same region significant change was detected in the multivariate mean vector and the unknown change point is estimated by the method of maximum likelihood estimation we then establish the asymptotic distribution of the change point maximum likelihood estimate wherein we show that the multivariate case can be transformed into an equivalent univariate problem a simulation study is carried out to investigate the robustness of the asymptotic distribution to departures from normality and independence as well as its closeness to finite samples the asymptotic distribution allowed us to compute confidence interval estimates of the change point in the river flows a decrease in the mean river flows in 1984 identified by the methodology may have been a consequence of a sharp decline in the region s snow cover that occurred about a year or two ahead

multiple changepoint fitting via quasilikelihood with application to dna sequence segmentation summary we consider situations where a step function with a variable number of steps provides an adequate model for a regression relationship while the variance of the observations depends on their mean this model provides for discontinuous jumps at changepoints and for constant means and error variances in between changepoints the basic statistical problem consists of identification of the number of changepoints their locations and the levels the function assumes in between we embed this problem into a quasilikelihood formulation and utilise the minimum deviance criterion to fit the model for the choice of the number of changepoints we discuss a modified schwarz criterion a dynamic programming algorithm makes the segmentation feasible for sequences of moderate length the performance of the segmentation method is demonstrated in an application to the segmentation of the bacteriophage l sequence

perfect sampling for the wavelet reconstruction of signals the coupling from the past cftp procedure is a protocol for finite state markov chain monte carlo mcmc methods whereby the algorithm itself can determine the necessary runtime to convergence in this paper we demonstrate how this protocol can be applied to the problem of signal reconstruction using bayesian wavelet analysis where the dimensionality of the wavelet basis set is unknown and the observations are distorted by gaussian white noise of unknown variance mcmc simulation is used to account for model uncertainty by drawing samples of wavelet bases for approximating integrals or summations on the model space that are either too complex or too computationally demanding to perform analytically we extend the cftp protocol by making use of the central limit theorem to show how the algorithm can also monitor its own approximation error induced by mcmc in this way we can assess the number of mcmc samples needed to approximate the integral to within a user specified tolerance level hence the method automatically ensures convergence and determines the necessary number of iterations needed to meet the error criteria

bayesian multiple change points and segmentation application to homogenization of climatic series 1 in this paper we describe a new multiple change point detection technique based on segmenting the time series under study into subsequences these segments correspond to the episodes that are likely to contain a unique jump they are found by applying bayesian decision theory through the minimization of simple cost functions all calculations can be performed explicitly without falling back on markov chain monte carlo methods and resulting in particularly light implementation through prior distributions derived from a stochastic renewal process description of jump occurrences expert knowledge of jump amplitude and return period is also introduced in our decision process comparison to several multiple change point methods on simulated series lead to similar or better performance achieved at lower computational cost

estimation in dirichlet random effects models we develop a new gibbs sampler for a linear mixed model with a dirich let process random effect term which is easily extended to a generalized linear mixed model with a probit link function our gibbs sampler exploits the properties of the multinomial and dirichlet distributions and is shown to be an improvement in terms of operator norm and efficiency over other commonly used mcmc algorithms we also investigate methods for the estimation of the precision parameter of the dirichlet process finding that maximum likelihood may not be desirable but a posterior mode is a reasonable approach examples are given to show how these models perform on real data our results complement both the theoretical basis of the dirichlet process nonparametric prior and the computational work that has been done to date

exact bayesian curve fitting and signal segmentation we consider regression models where the underlying functional relationship between the response and the explanatory variable is modeled as independent linear regressions on disjoint segments we present an algorithm for perfect simulation from the posterior distribution of such a model even allowing for an unknown number of segments and an unknown model order for the linear regressions within each segment the algorithm is simple can scale well to large data sets and avoids the problem of diagnosing convergence that is present with monte carlo markov chain mcmc approaches to this problem we demonstrate our algorithm on standard denoising problems on a piecewise constant ar model and on a speech segmentation problem

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

kernel stick breaking processes we propose a class of kernel stick breaking processes for uncountable collections of dependent random probability measures the process is constructed by first introducing an infinite sequence of random locations independent random probability measures and beta distributed random weights are assigned to each location predictor dependent random probability measures are then constructed by mixing over the locations with stick breaking probabilities expressed as a kernel multiplied by the beta weights some theoretical properties of the process are described including a covariate dependent prediction rule a retrospective markov chain monte carlo algorithm is developed for posterior computation and the methods are illustrated using a simulated example and an epidemiological application

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

markovian structures in biological sequence alignments abstract the alignment of multiple homologous biopolymer sequences is crucial in research on protein modeling and engineering molecular evolution and prediction in terms of both gene function and gene product structure in this article we provide a coherent view of the two recent models used for multiple sequence alignment the hidden markov model hmm and the block based motif model to develop a set of new algorithms that have both the sensitivity of the block based model and the flexibility of the hmm in particular we decompose the standard hmm into two components the insertion component which is captured by the so called propagation model and the deletion component which is described by a deletion vector such a decomposition serves as a basis for rational compromise between biological specificity and model flexibility furthermore we introduce a bayesian model selection criterion that in combination with the propagation model genetic algorithm and other computational aspects forms the cor

eigenvalue reanalysis of locally modified structures using a generalized rayleigh s method in this paper we introduce approximate reanalysis methods based on the generalized rayleigh s quotient with these methods the fundamental eigenvalue of a locally modified system can be computed readily using the fundamental mode as well as the static solution of the original system following a general development of theory several special cases of in terest in design are derived here and then tabulated numerical examples illustrate the accuracy of the new formulations

generalized ewens pitman model for bayesian clustering we propose a bayesian method for clustering from discrete data structures that commonly arise in genetics and other applications this method is equivariant with respect to relabelling units unsampled units do not interfere with sampled data and missing data do not hinder inference cluster inference using the posterior mode performs well on simulated and real datasets and the posterior predictive distribution enables supervised learning based on a partial clustering of the sample

domain decomposition methods for eigenvalue problems abstract this paper proposes several domain decomposition methods to compute the smallest eigenvalue of linear self adjoint partial differential operators let us be given a partial differential operator on a domain which consists of two nonoverlapping subdomains suppose a fast eigenvalue solver is available for each of these subdomains but not for the union of them the first proposed method is a scheme which determines an appropriate boundary condition at the interface separating the two regions this boundary condition can be derived from the zero of a nonlinear operator which plays the same role for the eigenvalue problem as the steklov poincare operator for the linear equation an iterative method can be used to solve this nonlinear equation yielding the exact boundary condition at the interface this enables the determination of the eigenpair on the whole domain the same concept can be applied to a schwarz alternating method for the eigenvalue problem in case the subdomains overlap a nonoverlapping scheme in the spirit of schur complement will also be discussed these ideas are also applicable to a domain imbedding algorithm

exact filtering for partially observed continuous time models summary the forward backward algorithm is an exact filtering algorithm which can efficiently calculate likelihoods and which can be used to simulate from posterior distributions using a simple result which relates gamma random variables with different rates we show how the forward backward algorithm can be used to calculate the distribution of a sum of gamma random variables and to simulate from their joint distribution given their sum one application is to calculating the density of the time of a specific event in a markov process as this time is the sum of exponentially distributed interevent times this enables us to apply the forward backward algorithm to a range of new problems we demonstrate our method on three problems calculating likelihoods and simulating allele frequencies under a non neutral population genetic model analysing a stochastic epidemic model and simulating speciation times in phylogenetics

clustering from categorical data sequences the three parameter cluster model is a combinatorial stochastic process that generates categorical response sequences by randomly perturbing a fixed clustering parameter this clear relationship between the observed data and the underlying clustering is particularly attractive in cluster analysis in which supervised learning is a common goal and missing data is a familiar issue the model is well equipped for this task as it can handle missing data perform out of sample inference and accommodate both independent and dependent data sequences moreover its clustering parameter lies in the unrestricted space of partitions so that the number of clusters need not be specified beforehand we establish these and other theoretical properties and also demonstrate the model on datasets from epidemiology genetics political science and legal studies

component mode iteration for frequency calculations this paper presents component mode iteration a new method for carrying out a form of subspace iteration on the substructure level for structures composed of substructures in component mode iteration substructure displacement is in terms of component modes with the interface displacements as coefficients component modes are chosen such that exact compatibility is assured throughout the structure the reduced structure eigenvalue problem is assembled and solved for lower mode approximations the resulting estimates of lower mode interface motion are used to refine the component modes by approximating the dynamic response of substructures to interface motion with a vector iteration process for this step the substructures are independent and can be processed in parallel reassembly and solution of the reduced structure problem yields improved lower mode estimates further iterations of refinement and reassembly are performed until convergence takes place the initial component modes are generated automatically and at negligible expense and numerical examples show that convergence with these is excellent yielding very accurate results after only one iteration indeed convergence is shown to be significantly faster than in the standard subspace iteration method

a smooth transition model for multiple regime time series this study deals with the problem of fitting a time series modeled by a smooth transition regression function this model extends the standard linear piecewise model within the piecewise model the regression function parameters change abruptly at the changepoints in the smooth transition model parametric transition functions are introduced that allow for gradual changes of the regression function around the changepoints this model can very accurately reproduce both nonregular and smooth random processes moreover it allows the extraction of information about the changes in the regression function through the transition function parameters the estimation of the model is performed through a fully bayesian framework prior distributions are set for each parameter and the full joint posterior distribution is expressed the computation of standard bayesian estimates involves intractable multi dimensional integrals therefore a reversible jump markov chain monte carlo algorithm is derived to sample the joint posterior distributions a comparative simulation study shows that the smooth transition approach achieves competitive performances and provides more sparse representations of standard test functions finally the smooth transition framework is applied to estimate real world electrical transients which allows the extraction of the relevant features for signal classification

a dual craig bampton method for dynamic substructuring a novel component mode synthesis method for dynamic analysis of structures is presented it is based on free interface vibration modes and residual flexibility components although the ingredients are the same as in previously published procedures e g macneal or rubin our method is fundamentally different in that it assembles the substructures using interface forces dual assembly and enforces only weak interface compatibility the new formulation is based on a fully consistent reduction approach and the reduced matrices so obtained are exactly dual to the craig bampton reduced matrices the new free interface substructuring method proposed here is thus more natural then classical free interface synthesis procedures and leads to simpler reduced matrices we illustrate the efficiency of the dual craig bampton approach for reducing the dynamical representation on a three dimensional frame

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

exponential bounds and absence of positive eigenvalues for n body schrodinger operators for a large class ofn body potentialsv we prove that if is an eigenfunction of v with eigenvaluee then sup 2 e 0 exp x l2 is either a threshold or consequences of this result are the absence of positive eigenvalues and optimal l2 exponential lower bounds

joint segmentation of multivariate astronomical time series bayesian sampling with a hierarchical model astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series this paper approaches such problems using bayesian priors to represent relationships between signals with various degrees of certainty and not just rigid constraints the segmentation is conducted by using a hierarchical bayesian approach to a piecewise constant poisson rate model a gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters results obtained with synthetic and real photon counting data illustrate the performance of the proposed algorithm

kron s method for symmetric eigenvalue problems kron s method has been used successfully by engineers for over 30 years to find eigenvalues of large symmetric matrices these matrices arise from domain decomposition of nonoverlapping domains of self adjoint partial differential operators this paper discusses some theoretical aspects of kron s method specifically the poles and zeroes of eigenvalues of the kron matrix and their relationships with the eigenvalues of the original matrix are given

the lanczos algorithm applied to kron s method in this paper kron s primitive composite system matrix is shown to be reducible to a symmetric indefinite matrix this matrix although never formed explicitly can then be transformed to a tridiagonal matrix of reduced order by the lanczos algorithm eigenvalue solutions of this partially tridiagonalized matrix give very good approximations to the eigenvalues of the composite system the method has multiplication counts which are over 90 per cent lower than when the condensed kron matrix is solved by the newton raphson iteration applied to the kron scalar equation numerical examples illustrating the kron lanczos method when solving for the natural frequencies of frames with large numbers of degrees of freedom are presented

approximate eigensolution of laplacian matrices for locally modified graph products laplacian matrices and their spectrum are of great importance in algebraic graph theory there exist efficient formulations for eigensolutions of the laplacian matrices associated with a special class of graphs called product graphs in this paper the problem of determining a few approximate smallest eigenvalues and eigenvectors of large scale product graphs modified through the addition or deletion of some nodes and or members is investigated the eigenproblem associated with a modified graph model is reduced using the set of master eigenvectors and linear approximated slave eigenvectors from the original model implicitly restarted lanczos method is employed to obtain the required eigenpairs of the reduced problem examples of large scale models are included to demonstrate the efficiency of the proposed method compared to the direct application of the irl method

bayesian disease mapping using product partition models our objective is to develop a model to estimate the relative risk of disease in each area a i i 1 n of a region and to identify areas of unusually high or low risk we use a product partition model ppm in which we assume that the true relative risks can be partitioned into a number of components or sets of areas where the relative risks are equal the ppm allows the data to weight those partitions likely to hold and inference about particular parameters may be made by first conditioning on the partition and then averaging over all partitions we develop markov chain monte carlo mcmc techniques to approximate the posterior distributions of the partitions and the parameters we first test the method in a simulation study and then apply it to data for two separate groups of different types of cancer in the mid western health board region in ireland the results are compared with those obtained using the standardized mortality ratio method an empirical bayes method a spatial scan method and a nonparametric bayesian method

automatic bayesian curve fitting summary a method of estimating a variety of curves by a sequence of piecewise polynomials is proposed motivated by a bayesian model and an appropriate summary of the resulting posterior distribution a joint distribution is set up over both the number and the position of the knots defining the piecewise polynomials throughout we use reversible jump markov chain monte carlo methods to compute the posteriors the methodology has been successful in giving good estimates for smooth functions i e continuous and differentiable as well as functions which are not differentiable and perhaps not even continuous at a finite number of points the methodology is extended to deal with generalized additive models

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

bayesian tree structured image modeling using wavelet domain hidden markov models wavelet domain hidden markov models have proven to be useful tools for statistical signal and image processing the hidden markov tree hmt model captures the key features of the joint probability density of the wavelet coefficients of real world data one potential drawback to the hmt framework is the need for computationally expensive iterative training to fit an hmt model to a given data set e g using the expectation maximization algorithm we greatly simplify the hmt model by exploiting the inherent self similarity of real world images the simplified model specifies the hmt parameters with just nine meta parameters independent of the size of the image and the number of wavelet scales we also introduce a bayesian universal hmt uhmt that fixes these nine parameters the uhmt requires no training of any kind while extremely simple we show using a series of image estimation denoising experiments that these new models retain nearly all of the key image structure modeled by the full hmt finally we propose a fast shift invariant hmt estimation algorithm that outperforms other wavelet based estimators in the current literature both visually and in mean square error

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

bayesian clustering and product partition models summary we present a decision theoretic formulation of product partition models ppms that allows a formal treatment of different decision problems such as estimation or hypothesis testing and clustering methods simultaneously a key observation in our construction is the fact that ppms can be formulated in the context of model selection the underlying partition structure in these models is closely related to that arising in connection with dirichlet processes this allows a straightforward adaptation of some computational strategies originally devised for nonparametric bayesian problems to our framework the resulting algorithms are more flexible than other competing alternatives that are used for problems involving ppms we propose an algorithm that yields bayes estimates of the quantities of interest and the groups of experimental units we explore the application of our methods to the detection of outliers in normal and student t regression models with clustering structure equivalent to that induced by a dirichlet process prior we also discuss the sensitivity of the results considering different prior distributions for the partitions

bayesian methods for hidden markov models markov chain monte carlo mcmc sampling strategies can be used to simulate hidden markov model hmm parameters from their posterior distribution given observed data some mcmc methods used in practice for computing likelihood conditional probabilities of hidden states and the most likely sequence of states can be improved by incorporating established recursive algorithms the most important of these is a set of forward backward recursions calculating conditional distributions of the hidden states given observed data and model parameters i show how to use the recursive algorithms in an mcmc context and demonstrate mathematical and empirical results showing a gibbs sampler using the forward backward recursions mixes more rapidly than another sampler often used for hmms iintroduce an augmented variables technique for obtaining unique state labels in hmms and finite mixture models i show how recursive computing allows the statistically efficient use of mcmc output when estimating the hidden states i

statistical inference in a stochastic epidemic seir model with control intervention ebola as a case study a stochastic discrete time susceptible exposed infectious recovered seir model for infectious diseases is developed with the aim of estimating parameters from daily incidence and mortality time series for an outbreak of ebola in the democratic republic of congo in 1995 the incidence time series exhibit many low integers as well as zero counts requiring an intrinsically stochastic modeling approach in order to capture the stochastic nature of the transitions between the compartmental populations in such a model we specify appropriate conditional binomial distributions in addition a relatively simple temporally varying transmission rate function is introduced that allows for the effect of control interventions we develop markov chain monte carlo methods for inference that are used to explore the posterior distribution of the parameters the algorithm is further extended to integrate numerically over state variables of the model which are unobserved this provides a realistic stochastic model that can be used by epidemiologists to study the dynamics of the disease and the effect of control interventions

an exact gibbs sampler for the markov modulated poisson process a markov modulated poisson process mmpp is a poisson process whose intensity varies according to a markov process we present a novel technique for simulating from the exact distribution of a continuous time markov chain over an interval given the start and end states and the infinitesimal generator and use this to create a gibbs sampler which samples from the exact distribution of the hidden markov chain in an mmpp we apply the gibbs sampler to modelling the occurrence of a rare dna motif the chi site and to inferring regions of the genome with evidence of high or low intensities for occurrences of this site

bayesian curve fitting using mcmc with applications to signal segmentation we propose some bayesian methods to address the problem of fitting a signal modeled by a sequence of piecewise constant linear in the parameters regression models for example autoregressive or volterra models a joint prior distribution is set up over the number of the changepoints knots their positions and over the orders of the linear regression models within each segment if these are unknown hierarchical priors are developed and as the resulting posterior probability distributions and bayesian estimators do not admit closed form analytical expressions reversible jump markov chain monte carlo mcmc methods are derived to estimate these quantities results are obtained for standard denoising and segmentation of speech data problems that have already been examined in the literature these results demonstrate the performance of our methods

product partition models for change point problems product partition models assume that observations in different components of a random partition of the data are independent if the probability distribution of random partitions is in a certain product form prior to making the observations it is also in product form given the observations the product model thus provides a convenient machinery for allowing the data to weight the partitions likely to hold and inference about particular future observations may then be made by first conditioning on the partition and then averaging over all partitions these models apply with special computational simplicity to change point problems where the partitions divide the sequence of observations into components within which different regimes hold we show with appropriate selection of prior product models that the observations can eventually determine approximately the true partition

a pairwise likelihood based approach for changepoint detection in multivariate time series models this paper develops a composite likelihood based approach for multiple changepoint estimation in multivariate time series we derive a criterion based on pairwise likelihood and minimum description length for estimating the number and locations of changepoints and for performing model selection in each segment the number and locations of the changepoints can be consistently estimated under mild conditions and the computation can be conducted efficiently with a pruned dynamic programming algorithm simulation studies and real data examples demonstrate the statistical and computational efficiency of the proposed method

a lanczos based method for structural dynamic reanalysis problems in this paper a new solution method for the modified eigenvalue problem with specific application to structural dynamic reanalysis is presented the method which is based on the block lanczos algorithm is developed for multiple low rank modifications to a system and calculates a few selected eigenpairs given the solution to the original system ax x procedures are developed for the modified standard eigenvalue problem a a x x where 1 a jbsjbt where sj s p p p n and b n p is constant for all the perturbations sj 2 a i jbisjbit where bi n p may vary with the pertubations sj the procedures are then extended for the reciprocal and generalized eigenvalue problems so that they are directly applicable to the structural dynamic reanalysis problem numerical examples are given to demonstrate the applications of the method