maximum entropy and the lottery abstract the distribution on m tuples of the first m integers is estimated from marginals of the distribution this problem is of interest in determining unpopular numbers in lotto games in canada s lotto 6 49 the proportion of tickets purchased in previous games containing each number is available under certain conditions the limiting distribution subject to the observed marginals is the constrained maximum entropy distribution this distribution is estimated and monte carlo methods are used to estimate the expected return of various lottery strategies tickets consisting of unpopular numbers may have expected return greater than their cost when the weekly sales are large or there are large carryover prizes prizes not won in earlier games the maximum entropy distribution is a rough approximation of the true distribution of tickets purchased certain aspects of the empirical distribution are not consistent with the maximum entropy distribution alternative methods which attempt to model the behavio

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

hyper markov laws in the statistical analysis of decomposable graphical models this paper introduces and investigates the notion of a hyper markov law which is a probability distribution over the set of probability measures on a multivariate space that i is concentrated on the set of markov probabilities over some decomposable graph and ii satisfies certain conditional independence restrictions related to that graph a stronger version of this hyper markov property is also studied our analysis starts by reconsidering the properties of markov probabilities using an abstract approach which thereafter proves equally applicable to the hyper markov case next it is shown constructively that hyper markov laws exist that they appear as sampling distributions of maximum likelihood estimators in decomposable graphical models and also that they form natural conjugate prior distributions for a bayesian analysis of these models as examples we construct a range of specific hyper markov laws including the hyper multinomial hyper dirichlet and the hyper wishart and inverse wishart laws these laws occur naturally in connection with the analysis of decomposable log linear and covariance selection models

classification and unfoldings of degenerate hopf bifurcations abstract this paper initiates the classification up to symmetry covariant contact equivalence of perturbations of local hopf bifurcation problems which do not satisfy the classical non degeneracy conditions the only remaining hypothesis is that i should be simple eigenvalues of the linearized right hand side at criticality then the lyapunov schmidt method allows a reduction to a scalar equation g x 0 where g x g x a definition is given of the codimension of g and a complete classification is obtained for all problems with codimension 3 together with the corresponding universal unfoldings the perturbed bifurcation diagrams are given for the cases with codimension 2 and for one case with codimension 3 for this last case one of the unfolding parameters is a modal parameter such that the topological codimension equals in fact 2 formulas are given for the calculation of the taylor coefficients needed for the application of the results and finally the results are applied to two simple problems a model of glycolytic oscillations and the fitzhugh nerve equations

central limit theorem for triangular arrays of non homogeneous markov chains in this paper we obtain the central limit theorem for triangular arrays of non homogeneous markov chains under a condition imposed to the maximal coefficient of correlation the proofs are based on martingale techniques and a sharp lower bound estimate for the variance of partial sums the results complement an important central limit theorem of dobrushin based on the contraction coefficient

small covering designs by branch and cut a branch and cut algorithm for finding covering designs is presented its originality resides in the use of isomorphism pruning of the enumeration tree a proof that no 4 10 5 1 covering design with less than 51 sets exists is obtained together with all non isomorphic 4 10 5 1 covering designs with 51 sets

optimal monte carlo updating based on peskun s theorem it is shown that optimal transition matrices in markov chain monte carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight we will compare the statistical efficiency of this sampler to existing algorithms such as heat bath updating and the metropolis algorithm we provide numerical results for the potts model as an application in classical physics as an application in quantum physics we consider the spin 3 2xy model and the bose hubbard model which have been simulated by the directed loop algorithm in the stochastic series expansion framework

on random and systematic scan samplers we introduce a simple time homogeneous markov embedding of a class of time inhomogeneous markov chains widely used in the context of monte carlo sampling algorithms such as systematic scan metropolis within gibbs samplers this allows us to establish that systematic scan samplers involving two factors are always better than their random scan counterparts when asymptotic variance is the criterion of interest we also show that this embedding sheds some light on the result of maire et al 2014 and discuss the scenario involving more than two factors

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

conditional simulation of max stable processes summary since many environmental processes such as heat waves or precipitation are spatial in extent it is likely that a single extreme event affects several loca tions and the areal modelling of extremes is therefore essential if the spatial dependence of e xtremes has to be appropriately taken into account this paper proposes a framework for conditional simulations of max stable processes and give closed forms for brown resnick and schlather processes we test the method on simulated data and give an application to extreme rainfall around zurich and extreme temperature in switzerland results show that the proposed framework provides accurate conditional simulations and can handle real sized problems

polytopes associated with symmetry handling this paper investigates a polyhedral approach to handle symmetries in mixed binary programs we study symretopes i e the convex hulls of all binary vectors that are lexicographically maximal in their orbit with respect to the symmetry group these polytopes turn out to be quite complex for practical use we therefore develop an integer programming formulation with ternary coefficients based on knapsack polytopes arising from a single lexicographic order enforcing inequality we show that for these polytopes the optimization as well as the separation problem of minimal cover inequalities can be solved in almost linear time we demonstrate the usefulness of this approach by computational experiments showing that it is competitive with state of the art methods and is considerably faster for specific problem classes

bayesian models for multiple local sequence alignment and gibbs sampling strategies abstract a wealth of data concerning life s basic molecules proteins and nucleic acids has emerged from the biotechnology revolution the human genome project has accelerated the growth of these data multiple observations of homologous protein or nucleic acid sequences from different organisms are often available but because mutations and sequence errors misalign these data multiple sequence alignment has become an essential and valuable tool for understanding structures and functions of these molecules a recently developed gibbs sampling algorithm has been applied with substantial advantage in this setting in this article we develop a full bayesian foundation for this algorithm and present extensions that permit relaxation of two important restrictions we also present a rank test for the assessment of the significance of multiple sequence alignment as an example we study the set of dinucleotide binding proteins and predict binding segments for dozens of its members

markov chain monte carlo methods for lattice gaussian sampling convergence analysis and enhancement sampling from lattice gaussian distribution has emerged as an important problem in coding decoding and cryptography in this paper the classic gibbs algorithm from markov chain monte carlo mcmc methods is demonstrated to be geometrically ergodic for lattice gaussian sampling which means that the markov chain arising from it converges exponentially fast to the stationary distribution meanwhile the exponential convergence rate of the markov chain is also derived through the spectral radius of the forward operator then a comprehensive analysis of the convergence rate is carried out and two sampling schemes are proposed to further enhance the convergence performance the first one referred to as a metropolis within gibbs mwg algorithm improves the convergence by refining the state space of the univariate sampling the second is a blocked strategy of the gibbs algorithm which performs sampling over multivariates at each markov move and is shown to yield a better convergence rate than the traditional univariate sampling in order to perform blocked sampling efficiently the gibbs klein gk algorithm is proposed which samples block by block using the kleins algorithm furthermore the validity of the gk algorithm is demonstrated by showing its ergodicity simulation results based on mimo detections are presented to confirm the convergence gain brought by the proposed gibbs sampling schemes

weighted finite population sampling to maximize entropy summary attention is drawn to a method of sampling a finite population of n units with unequal probabilities and without replacement the method was originally proposed by stern cover 1989 as a model for lotteries the method can be characterized as maximizing entropy given coverage probabilities 7ci or equivalently as having the probability of a selected sample proportional to the product of a set of weights wi we show the essential uniqueness of the wi given the 7i and describe practical geometrically convergent algorithms for computing the wi from the 7i we present two methods for stepwise selection of sampling units and corresponding schemes for removal of units that can be used in connection with sample rotation inclusion probabilities of any order can be written explicitly in closed form second order inclusion probabilities 7rij satisfy the condition 0 ij 7ic 7j which guarantees yates grundy s variance estimator to be unbiased definable for all samples and always nonnegative for any sample size

hopf bifurcation at a degenerate stationary pitchfork soit e un espace de hilbert reel on considere l existence de petites solutions periodiques pour une equation d evolution sur e donnee par du dt g u u e r avec g 0 0 r

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

sampling for conditional inference on network data random graphs with given vertex degrees have been widely used as a model for many real world complex networks however both statistical inference and analytic study of such networks present great challenges in this article we propose a new sequential importance sampling method for sampling networks with a given degree sequence these samples can be used to approximate closely the null distributions of a number of test statistics involved in such networks and provide an accurate estimate of the total number of networks with given vertex degrees we study the asymptotic behavior of the proposed algorithm and prove that the importance weight remains bounded as the size of the graph grows this property guarantees that the proposed sampling algorithm can still work efficiently even for large sparse graphs we apply our method to a range of examples to demonstrate its efficiency in real problems

reformulations in mathematical programming automatic symmetry detection and exploitation if a mathematical program has many symmetric optima solving it via branch and bound techniques often yields search trees of disproportionate sizes thus finding and exploiting symmetries is an important task we propose a method for automatically finding the formulation group of any given mixed integer nonlinear program and for reformulating the problem by means of static symmetry breaking constraints the reformulated problem which is likely to have fewer symmetric optima can then be solved via standard branch and bound codes such as cplex for linear programs and couenne for nonlinear programs our computational results include formulation group tables for the miplib3 miplib2003 globallib and minlplib instance libraries and solution tables for some instances in the aforementioned libraries

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

extended formulations for packing and partitioning orbitopes we give compact extended formulations for the packing and partitioning orbitopes with respect to the full symmetric group described and analyzed in kaibel and pfetsch kaibel v m e pfetsch 2008 packing and partitioning orbitopes math programming ser a114 1 1 36 these polytopes are the convex hulls of all 0 1 matrices with lexicographically sorted columns and at most respectively exactly one 1 entry per row they are important objects for symmetry reduction in certain integer programs using the extended formulations we also derive a rather simple proof of the fact established in the paper mentioned above that basically shifted column inequalities suffice to describe those orbitopes linearly

exact tests for the rasch model via sequential importance sampling rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability this paper furthers rasch s approach by 1 providing an efficient monte carlo methodology for accurately approximating the required probability and 2 illustrating the usefulness of rasch s approach for several important testing problems through simulation studies our monte carlo methodology is shown to compare favorably to other monte carlo methods proposed for this problem in two respects it is considerably faster and it provides more reliable estimates of the monte carlo standard error

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea

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

bayesian estimation of switching arma models abstract switching arma processes have recently appeared as an efficient modelling to nonlinear time series models because they can represent multiple or heterogeneous dynamics through simple components the levels of dependence between the observations are double at a first level the parameters of the model are selected by a markovian procedure at a second level the next observation is generated according to a standard time series model when the model involves a moving average structure the complexity of the resulting likelihood function is such that simulation techniques like those proposed by shephard 1994 biometrika 81 115 131 and billio and monfort 1998 journal of statistical planning and inference 68 65 103 are necessary to derive an inference on the parameters of the model we propose in this paper a bayesian approach with a non informative prior distribution developed in mengersen and robert 1996 bayesian statistics 5 oxford university press oxford pp 255 276 and robert and titterington 1998 statistics and computing 8 2 145 158 in the setup of mixtures of distributions and hidden markov models respectively the computation of the bayes estimates relies on mcmc techniques which iteratively simulate missing states innovations and parameters until convergence the performances of the method are illustrated on several simulated examples this work also extends the papers by chib and greenberg 1994 journal of econometrics 64 183 206 and chib 1996 journal of econometrics 75 1 79 97 which deal with arma and hidden markov models respectively

nonparametric bayes modeling of multivariate categorical data modeling of multivariate unordered categorical nominal data is a challenging problem particularly in high dimensions and cases in which one wishes to avoid strong assumptions about the dependence structure commonly used approaches rely on the incorporation of latent gaussian random variables or parametric latent class models the goal of this article is to develop a nonparametric bayes approach which defines a prior with full support on the space of distributions for multiple unordered categorical variables this support condition ensures that we are not restricting the dependence structure a priori we show this can be accomplished through a dirichlet process mixture of product multinomial distributions which is also a convenient form for posterior computation methods for nonparametric testing of violations of independence are proposed and the methods are applied to model positional dependence within transcription factor binding motifs

lattice reduction aided gibbs algorithm for lattice gaussian sampling convergence enhancement and decoding optimization sampling from the lattice gaussian distribution has emerged as an important problem in coding decoding and cryptography in this paper lattice reduction technique is adopted to gibbs sampler for lattice gaussian sampling first with respect to lattice gaussian distribution we show the convergence rate of systematic scan gibbs sampling is characterized by the hirschfeld gebelein renyi maximal correlation among the multivariate of being sampled then lattice reduction aided gibbs algorithm is proposed to sample from an equivalent lattice gaussian distribution but with less correlated multivariate thus leading to a better markov mixing after that we extend the proposed lattice reduction aided gibbs sampling to lattice decoding where the choice of the standard deviation for the sampling is fully investigated a customized solution that suits for each specific decoding case by euclidean distance is given which results in a better tradeoff between markov mixing and sampler decoding based on it a startup mechanism is also proposed for gibbs sampler decoding where decoding complexity can be reduced without performance loss moreover the recycling gibbs sampling that exploits the potential of samples is also considered to improve the decoding performance in lattice decoding simulation results based on large scale uncoded multiple input multiple output detection are presented to confirm the performance gain and complexity reduction

sequential monte carlo methods for statistical analysis of tables we describe a sequential importance sampling sis procedure for analyzing two way zero one or contingency tables with fixed marginal sums an essential feature of the new method is that it samples the columns of the table progressively according to certain special distributions our method produces monte carlo samples that are remarkably close to the uniform distribution enabling one to approximate closely the null distributions of various test statistics about these tables our method compares favorably with other existing monte carlo based algorithms and sometimes is a few orders of magnitude more efficient in particular compared with markov chain monte carlo mcmc based approaches our importance sampling method not only is more efficient in terms of absolute running time and frees one from pondering over the mixing issue but also provides an easy and accurate estimate of the total number of tables with fixed marginal sums which is far more difficult for an mcmc method to achieve

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

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

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

packing and partitioning orbitopes we introduce orbitopes as the convex hulls of 0 1 matrices that are lexicographically maximal subject to a group acting on the columns special cases are packing and partitioning orbitopes which arise from restrictions to matrices with at most or exactly one 1 entry in each row respectively the goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints e g for a well known formulation of the graph coloring problem we provide a thorough polyhedral investigation of packing and partitioning orbitopes for the cases in which the group acting on the columns is the cyclic group or the symmetric group our main results are complete linear inequality descriptions of these polytopes by facet defining inequalities for the cyclic group case the descriptions turn out to be totally unimodular while for the symmetric group case both the description and the proof are more involved the associated separation problems can be solved in linear time

imperfection sensitivity of interacting hopf and steady state bifurcations and their classification abstract the bifurcation problem of interacting time periodic and stationary solutions of nonlinear evolution equations with double degeneracy is discussed in terms of singularity and imperfect bifurcation theory a complete classification up to symmetry covariant contact equivalence and codimension three of generic perturbations of interacting hopf and steady state bifurcations is presented the sensitivity of the bifurcation diagrams to imperfections is analyzed normal forms describing sequences of secondary and tertiary bifurcations leading to motions on tori are determined a variety of phenomena such as gaps in hopf branches periodic motions not stably connected to steady states and the formation of islands is discovered which one can expect to find in perturbed evolution equations on pure geometric grounds implications for physical systems are discussed

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

convergence rate of markov chain methods for genomic motif discovery we analyze the convergence rate of a popular gibbs sampling method used for statistical discovery of gene regulatory binding motifs in dna sequences this sampler satisfies a very strong form of ergodicity uniform however we show that due to multimodality of the posterior distribution the rate of convergence often decreases exponentially as a function of the length of the dna sequence specifically we show that this occurs whenever there is more than one true repeating pattern in the data in practice there are typically multiple even numerous such patterns in biological data the goal being to detect the most well conserved and frequently occurring of these our findings match empirical results in which the motif discovery gibbs sampler has exhibited such poor convergence that it is used only for finding modes of the posterior distribution candidate motifs rather than for obtaining samples from that distribution ours appear to be the first meaningful bounds on the convergence rate of a markov chain method for sampling from a multimodal posterior distribution as a function of statistical quantities like the number of observations

a jackknife variance estimator for unistage stratified samples with unequal probabilities summary existing jackknife variance estimators used with sample surveys can seriously overestimate the true variance under unistage stratified sampling without replacement with unequal probabilities a novel jackknife variance estimator is proposed which is as numerically simple as existing jackknife variance estimators under certain regularity conditions the proposed variance estimator is consistent under stratified sampling without replacement with unequal probabilities the high entropy regularity condition necessary for consistency is shown to hold for the rao sampford design an empirical study of three unequal probability sampling designs supports our findings

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

applying the horvitz thompson criterion in complex designs a computer intensive perspective for estimating inclusion probabilities a modification of the horvitz thompson estimator is proposed for complex sampling designs the inclusion probabilities are estimated by means of independent replications of the sampling scheme the properties of the resulting estimator are derived guidelines for choosing the appropriate number of replications are given and some applications are considered

hopf bifurcation from a turning point on considere une equation d evolution du dt g u 0 dans un espace de hilbert reel e dependant d un parametre reel variant dans un intervalle r on etudie la bifurcation des solutions periodiques a partir d un point de rebroussement

antithetic coupling of two gibbs sampler chains two coupled gibbs sampler chains both with invariant probability density are run in parallel so that the chains are negatively correlated we define an asymptotically unbiased estimator of the expectation e f x which achieves significant variance reduction with respect to the usual gibbs sampler at comparable computational cost the variance of the estimator based on the new algorithm is always smaller than the variance of a single gibbs sampler chain if is attractive and f is monotone nondecreasing in all components of x for nonattractive targets our results are not complete the new antithetic algorithm outperforms the standard gibbs sampler when is a multivariate normal density or the ising model more generally nonrigorous arguments and numerical experiments support the usefulness of the antithetically coupled gibbs samplers also for other nonattractive models in our experiments the variance is reduced to at least a third and the efficiency also improves significantly

coincident bifurcation of equilibrium and periodic solutions of evolution equations abstract bifurcation of equilibrium and periodic solutions of nonlinear evolution equations is considered in the neighbourhood of an equilibrium solution for which the corresponding linear problem admits both non zero equilibrium and non constant periodic solutions these solutions of the linear problem are related to those of the nonlinear equation by deriving bifurcation equations possessing a simple symmetry property this results in a simplification of the bifurcation analysis illustrated by a discussion of two important special cases exhibiting secondary bifurcation of periodic solutions author

a bayesian insertion deletion algorithm for distant protein motif searching via entropy filtering bayesian models have been developed that find ungapped motifs in multiple protein sequences in this article we extend the model to allow for deletions and insertions in motifs direct generalization of the ungapped algorithm based on gibbs sampling proved unsuccessful because the configuration space became much larger to alleviate the convergence difficulty a two stage procedure is introduced at the first stage we develop a method called entropy filtering which quickly searchs good starting points for the alignment approach without the concern of deletion insertion patterns at the second stage we switch to an algorithm that generates both a random vector that represents insertion deletion patterns and a random variable of motif locations after the two steps gapped motif alignments are obtained for multiple sequences when applied to datasets that consist of helix loop helix proteins and high mobility group proteins respectively our methods show great improvements over those that produce u

a distance based point reassignment heuristic for the k hyperplane clustering problem abstract we consider the k hyperplane clustering problem where given a set of m points in r n we have to partition the set into k subsets clusters and determine a hyperplane for each of them so as to minimize the sum of the squares of the euclidean distances between the points and the hyperplane of the corresponding clusters we give a nonconvex mixed integer quadratically constrained quadratic programming formulation for the problem since even very small size instances are challenging for state of the art spatial branch and bound solvers like couenne we propose a heuristic in which many critical points are reassigned at each iteration such points which are likely to be ill assigned in the current solution are identified using a distance based criterion and their number is progressively decreased to zero our algorithm outperforms the best available one proposed by bradley and mangasarian on a set of real world and structured randomly generated instances for the largest instances we obtain an average improvement in the solution quality of 54

a prediction based test for multiple endpoints this article introduces a global hypothesis test intended for studies with multiple endpoints our test makes use of a priori predictions about the direction of the result of each endpoint and we weight these predictions using the sample correlation matrix the global alternative hypothesis concerns a parameter defined as the researcher s ability to correctly predict the direction of each measure essentially a binomial parameter this allows for the test to include expected effects that are all positive all negative or both while still using the cumulative information across those endpoints a rejection of the null hypothesis h0 0 provides evidence that the researcher s underlying theory about the natural process provides a better prediction of the observed results relative to the null hypothesized predictive ability thus indicating the theory is worthy of further study we compare our test to o brien s ordinary least squares ols test and show that for small samples and situations where the effect is not in the same direction across all endpoints our approach has better power while if the effect is equidirectional across all endpoints the ols test can have greater power

on the principle of reduced stability abstract the principle of reduced stability says that the stability of bifurcating stationary or periodic solutions is given by the finite dimensional bifurcation equation obtained by the method of lyapunov schmidt to be more precise the linearized stability is governed by the linearization of the bifurcation equation about the bifurcating branch of solutions and in particular by the signs of the real parts of the perturbation of the eigenvalues along this branch this principle is true for simple eigenvalue bifurcation whereas it may be false for higher dimensional bifurcation equations a condition for the validity of that principle is given a counterexample shows that it cannot be dropped in general

covariance structure and convergence rate of the gibbs sampler with various scans this paper presents results on covariance structure and convergence for the gibbs sampler with both systematic and random scans it is shown that under conditions that guarantee the compactness of the markov forward operator and irreducibility of the corresponding chain the gibbs sampling scheme converges geometrically in terms of pearson 2 distance in particular for the random scan the autocovariance can be expressed as variances of iterative conditional expectations as a consequence the autocorrelations are all positive and decrease monotonically

modified orbital branching for structured symmetry with an application to unit commitment the past decade has seen advances in general methods for symmetry breaking in mixed integer linear programming these methods are advantageous for general problems with general symmetry groups some important classes of mixed integer linear programming problems such as bin packing and graph coloring contain highly structured symmetry groups this observation has motivated the development of problem specific techniques in this paper we show how to strengthen orbital branching in order to exploit special structures in a problem s symmetry group the proposed technique to which we refer as modified orbital branching is able to solve problems with structured symmetry groups more efficiently one class of problems for which this technique is effective is when the solution variables can be expressed as 0 1 matrices where the problem s symmetry group contains all permutations of the columns we use the unit commitment problem an important problem in power systems to demonstrate the strength of modified orbital branching

variable selection in regression mixture modeling for the discovery of gene regulatory networks the profusion of genomic data through genome sequencing and gene expression microarray technology has facilitated statistical research in determining gene interactions regulating a biological process current methods generally consist of a two stage procedure clustering gene expression measurements and searching for regulatory switches typically short conserved sequence patterns motifs in the dna sequence adjacent to the genes this process often leads to misleading conclusions as incorrect cluster selection may lead to missing important regulatory motifs or making many false discoveries treating cluster memberships as known rather than estimated introduces bias into analyses preventing uncertainty about cluster parameters further there is underutilization of the available data as the sequence information is ignored for purposes of expression clustering and vice versa we propose a way to address these issues by combining gene clustering and motif discovery in a unified framework a mixture

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

general type token distribution the problem of estimating the number of unique types or dis tinct species in a group occurs in many fields but is not a straightforward one given an arbitrary probabilistic distribution of entries to be sam pled this study shows in exact and approximated forms the conditional probabilistic distribution of unique entries sampled independently given the number of samples the numerical evaluation validates the proposed ap proximation finally we discuss a theory that unifies the related approaches regarding estimation of the number of classes ams 2000 subject classifications primary 60c05 62p99 secondary 62f10

covariance structure of the gibbs sampler with applications to the comparisons of estimators and augmentation schemes summary we study the covariance structure of a markov chain generated by the gibbs sampler with emphasis on data augmentation when applied to a bayesian missing data problem the gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector the empirical distribution based on the sampled values of the parameter vector and a mixture of complete data posteriors we prove that rao blackwellization causes a one lag delay for the autocovariances among dependent samples obtained from data augmentation and consequently the mixture approximation produces estimates with smaller variances than the empirical approximation the covariance structure results are used to compare different augmentation schemes it is shown that collapsing and grouping random components in a gibbs sampler with two or three components usually result in more efficient sampling schemes

interaction of periodic and stationary bifurcation from multiple eigenvalues on considere des equations d evolution non lineaires du dt g u o dependant d un parametre reel dans un espace de hilbert reel e

algorithms for highly symmetric linear and integer programs this paper deals with exploiting symmetry for solving linear and integer programming problems basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of lower dimension combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension

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

pruning by isomorphism in branch and cut the paper presents a branch and cut for solving 0 1 integer linear programs having a large symmetry group the group is used for pruning the enumeration tree and for generating cuts the cuts are non standard cutting integer feasible solutions but leaving the optimal value of the problem unchanged pruning and cut generation are performed by backtracking procedures using a schreier sims table for representing the group applications to hard set covering problems and to the generation of covering designs and error correcting codes are presented

simple design efficient calibration estimators for rejective and high entropy sampling summary for survey calibration consider the situation where the population totals of auxiliary variables are known or where auxiliary variables are measured for all population units for each situation wedevelopdesign efficientcalibrationestimatorsunderrejectiveorhigh entropysampling a general approach is to extend efficient estimators for missing data problems with independent and identically distributed data to the survey setting we show that this approach effectively resolves two long standing issues in existing approaches how to achieve design efficiency regardless of a linear superpopulation model in generalized regression and calibration estimation and how to find a simple approximation in optimal regression estimation moreover the proposed approach sheds light on several issues that seem not to be well studied in the literature examples include use of the weighted kullback leibler distance in calibration estimation and efficient estimation allowing for misspecification of a nonlinear superpopulation model

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

decomposing matrices into blocks in this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so called bordered block diagonal form more precisely given some matrix a we try to assign as many rows as possible to some number beta of blocks of size kappa such that no two rows assigned to different blocks intersect in a common column bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems we show that various matrices from the linear programming and mixed integer programming libraries netlib and miplib can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality these computations are done with a branch and cut algorithm based on polyhedral investigations of the matrix decomposition problem in practice however one would use heuristics to find a good decomposition we present several heuristic ideas and test their performance finally we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch and cut code for general mixed integer programs

peskun s theorem and a modified discrete state gibbs sampler attention is drawn to the use of peskun s theorem in improving statistical efficiency of discretestate gibbs sampling