periodic solutions for a class of non autonomous second order systems abstract the purpose of this paper is to study the existence of periodic solutions of non autonomous second order systems u t f t u t a e t 0 t u 0 u t u 0 u t 0 some new existence theorems are obtained by the least action principle

order based dependent dirichlet processes in this article we propose a new framework for bayesian nonparametric modeling with continuous covariates in particular we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick breaking representation we focus mostly on the class of random distributions that induces a dirichlet process at each covariate value we derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering two main constructions with analytically known correlation structures are proposed practical and efficient computational methods are introduced we apply our framework through mixtures of these processes to regression modeling the modeling of stochastic volatility in time series data and spatial geostatistical modeling

nonparametric bayes conditional distribution modeling with variable selection this article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors goals are 1 to estimate the conditional response distribution addressing the distributional changes across the predictor space and 2 to identify important predictors for the response distribution change both within local regions and globally we first introduce the probit stick breaking process psbp as a prior for an uncountable collection of predictor dependent random distributions and propose a psbp mixture psbpm of normal regressions for modeling the conditional distributions a global variable selection structure is incorporated to discard unimportant predictors while allowing estimation of posterior inclusion probabilities local variable selection is conducted relying on the conditional distribution estimates at different predictor points an efficient stochastic search sampling algorithm is proposed for posterior computation the methods are illustrated through simulation and applied to an epidemiologic study

existence of periodic solutions for ordinary differential systems in musielak orlicz sobolev spaces abstract in this paper we study the periodic solutions for the ordinary differential systems in musielak orlicz sobolev spaces we get some propositions of the musielak orlicz sobolev space w t 1 which are used to get the existence results using variational methods we have some existence results of the periodic solutions for the ordinary differential systems in musielak orlicz sobolev spaces

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

on adaptive extensions of group sequential trials for clinical investigations in group sequential trials it is important to obtain adequate data to assess overall benefits and risks of an experimental treatment for patients to achieve this goal we provide a general formal framework for adaptively extending a group sequential trial to stop at any interim analysis time often after a significance boundary for a clinical endpoint is crossed for statistical inference we propose to order the sample space by a class of well ordered group sequential tests on this basis we develop a unified sequential statistical inference approach that is applicable to both interim monitoring and final analysis we also show that the new ordering provides the foundation for the repeated confidence intervals procedure of jennison and turnbull

sequential ordinal modeling with applications to survival data summary this paper considers the class of sequential ordinal models in relation to other models for ordinal response data markov chain monte carlo mcmc algorithms based on the approach of albert and chib 1993 journal of the american statistical association88 669 679 are developed for the fitting of these models the ideas and methods are illustrated in detail with a real data example on the length of hospital stay for patients undergoing heart surgery a notable aspect of this analysis is the comparison based on marginal likelihoods and training sample priors of several nonnested models such as the sequential model the cumulative ordinal model and weibull and log logistic models

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

optimal sobolev imbeddings involving rearrangement invariant quasinorms let m and n be positive integers with n 2 and 1 m n 1 we study rearrangement invariant quasinorms r and d on functions f 0 1 view the mathml source such that to each bounded domain in view the mathml sourcen with lebesgue measure there corresponds c c 0 for which one has the sobolev imbedding inequality r u t c d mu t u cm0 involving the nonincreasing rearrangements of u and a certain mth order gradient of u when m 1 we deal in fact with a closely related imbedding inequality of talenti in which d need not be rearrangement invariant r u t c d d dt x view the mathml sourcen u x u t u x dx u c10 in both cases we are especially interested in when the quasinorms are optimal in the sense that r cannot be replaced by an essentially larger quasinorm and d cannot be replaced by an essentially smaller one our results yield best possible refinements of such limiting sobolev inequalities as those of trudinger strichartz hansson brezis and wainger

powerful short cuts for multiple testing procedures with special reference to gatekeeping strategies in this paper we present a general testing principle for a class of multiple testing problems based on weighted hypotheses under moderate conditions this principle leads to powerful consonant multiple testing procedures furthermore short cut versions can be derived which simplify substantially the implementation and interpretation of the related test procedures it is shown that many well known multiple test procedures turn out to be special cases of this general principle important examples include gatekeeping procedures which are often applied in clinical trials when primary and secondary objectives are investigated and multiple test procedures based on hypotheses which are completely ordered by importance we illustrate the methodology with two real clinical studies

a note on testing families of hypotheses using graphical procedures regulatory guidelines for drug development suggest a strong control of the familywise error rate when multiple hypotheses are simultaneously tested in confirmatory clinical trials accordingly a variety of multiple test procedures exist for pharmaceutical trial applications which are typically defined on a single structured family of null hypotheses for some confirmatory clinical trials with multiple objectives however it is advantageous to address the arising multiplicity problems via grouped families of hypotheses graphical test procedures have been developed to construct visualize and perform multiple test procedures that are tailored to either a single or multiple families of structured hypotheses of interest this note complements the existing literature by introducing a general algorithm to calculate adjusted p values for any sequentially rejective graphical test procedure where the test procedures within the individual families of hypotheses are not necessarily graphical

a simple and efficient simulation smoother for state space time series analysis a simulation smoother in state space time series analysis is a procedure for drawing samples from the conditional distribution of state or disturbance vectors given the observations we present a new technique for this which is both simple and computationally efficient the treatment includes models with diffuse initial conditions and regression effects computational comparisons are made with the previous standard method two applications are provided to illustrate the use of the simulation smoother for gibbs sampling for bayesian inference and importance sampling for classical inference 2002 biometrika trust

anisotropic orlicz sobolev spaces of vector valued functions and lagrange equations abstract in this paper we study some properties of anisotropic orlicz and orlicz sobolev spaces of vector valued functions for a special class of g functions we introduce a variational setting for a class of lagrangian systems we give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on orlicz sobolev space

a semiparametric bayesian model for randomised block designs summary a model is proposed for a bayesian semiparametric analysis of randomised block experiments the model is a hierarchical model in which a dirichlet process is inserted at the middle stage for the distribution of the block effects this model allows an arbitrary distribution of block effects and it results in effective estimates of treatment contrasts block effects and the distribution of block effects an effective computational strategy is presented for describing the posterior distribution

bayesian modeling of temporal dependence in large sparse contingency tables it is of interest in many applications to study trends over time in relationships among categorical variables such as age group ethnicity religious affiliation political party and preference for particular policies at each time point a sample of individuals provides responses to a set of questions with different individuals sampled at each time in such settings there tend to be an abundance of missing data and the variables being measured may change over time at each time point we obtained a large sparse contingency table with the number of cells often much larger than the number of individuals being surveyed to borrow information across time in modeling large sparse contingency tables we propose a bayesian autoregressive tensor factorization approach the proposed model relies on a probabilistic parafac factorization of the joint pmf characterizing the categorical data distribution at each time point with autocorrelation included across times we develop efficient computational methods th

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

a recycling framework for the construction of bonferroni based multiple tests in this paper we describe bonferroni based multiple testing procedures mtps as strategies to split and recycle test mass here test mass refers to parts of the nominal level alpha at which the family wise error rate is controlled briefly test mass is split between different null hypotheses and whenever a null hypothesis is rejected the part of alpha allocated to it may be recycled to the testing of other hypotheses these recycling mtps are closed testing procedures based on raw p values associated with testing the individual null hypotheses and the class of such mtps includes for example serial and parallel gatekeeping fallback and holm procedures graphical displays and a concise algebraic notation are provided for such mtps this recycling approach has pedagogical advantages and may facilitate the tailoring of mtps for different purposes

periodic solutions of non autonomous second order systems with a p laplacian abstract in this paper we investigate non autonomous second order systems with a p laplacian and obtain existence results for periodic solutions with the dual least action principle

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

periodic solutions for some nonautonomous second order hamiltonian systems the existence and multiplicity of periodic solutions are obtained for nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

simplex factor models for multivariate unordered categorical data gaussian latent factor models are routinely used for modeling of dependence in continuous binary and ordered categorical data for unordered categorical variables gaussian latent factor models lead to challenging computation and complex modeling structures as an alternative we propose a novel class of simplex factor models in the single factor case the model treats the different categorical outcomes as independent with unknown marginals the model can characterize flexible dependence structures parsimoniously with few factors and as factors are added any multivariate categorical data distribution can be accurately approximated using a bayesian approach for computation and inferences a markov chain monte carlo mcmc algorithm is proposed that scales well with increasing dimension with the number of factors treated as unknown we develop an efficient proposal for updating the base probability vector in hierarchical dirichlet models theoretical properties are described and we evaluate the appr

some existence results on periodic solutions of euler lagrange equations in an orlicz sobolev space setting abstract in this paper we consider the problem of finding periodic solutions of certain euler lagrange equations we employ the direct method of the calculus of variations i e we obtain solutions minimizing certain functional i we give conditions which ensure that i is finitely defined and differentiable on certain subsets of orlicz sobolev spaces w 1 l associated to an n function we show that in some sense it is necessary for the coercivity that the complementary function of satisfy the 2 condition we conclude by discussing conditions for the existence of minima of i

existence and multiplicity results for some nonlinear problems with singular phi laplacian using leray schauder degree theory we obtain various existence and multiplicity results for nonlinear boundary value problems phi u f t u u l u u 0 where l u u 0 denotes the dirichlet periodic or neumann boundary conditions on 0 t phi a a r is an increasing homeomorphism phi 0 0 the difichlet problem is always solvable for neumann or periodic boundary conditions we obtain in particular existence conditions for nonlinearities which satisfy some sign conditions upper and lower solutions theorems ambrosetti prodi type results we prove lazer solimini type results for singular nonlinearities and periodic boundary conditions c 2007 elsevier inc all rights reserved

dynamic nonparametric bayesian models for analysis of music the dynamic hierarchical dirichlet process dhdp is developed to model complex sequential data with a focus on audio signals from music the music is represented in terms of a sequence of discrete observations and the sequence is modeled using a hidden markov model hmm with time evolving parameters the dhdp imposes the belief that observations that are temporally proximate are more likely to be drawn from hmms with similar parameters while also allowing for innovation associated with abrupt changes in the music texture the sharing mechanisms of the time evolving model are derived and for inference a relatively simple markov chain monte carlo sampler is developed segmentation of a given musical piece is constituted via the model inference detailed examples are presented on several pieces with comparisons to other models the dhdp results are also compared with a conventional music theoretic analysis all the supplemental materials used by this paper are available online

periodic solutions of a class of non autonomous second order systems some existence theorems are obtained by the least action principle for periodic solutions of nonautonomous second order systems with a potential which is the sum of a subconvex function and a subquadratic function

nonhomogeneous boundary value problems for some nonlinear equations with singular phi laplacian using leray schauder degree theory we obtain various existence results for the quasilinear equation problems phi u f t u u submitted to nonhomogeneous dirichlet or nonlinear neumann steklov boundary conditions on 0 t when phi a a r is an increasing homeomorphism phi 0 0 we compare the results with the ones proved earlier in the homogeneous case c 2008 elsevier inc all rights reserved

some existence results on periodic solutions of ordinary p laplacian systems some existence theorems are obtained for periodic solutions of ordinary p laplacian systems by the minimax methods in critical point theory

mountain pass type periodic solutions for euler lagrange equations in anisotropic orlicz sobolev space abstract using the mountain pass theorem we establish the existence of periodic solution for euler lagrange equation lagrangian consists of kinetic part an anisotropic g function potential part k w and a forcing term we consider two situations g satisfying 2 2 at infinity and globally we give conditions on the growth of the potential near zero for both situations

periodic solutions of nonlinear perturbations of phi laplacians with possibly bounded phi using leray schauder degree theory we obtain various existence and multiplicity results for nonlinear periodic boundary value problems of the form phi u f t u u u 0 u t 0 u 0 u t where phi r a a 0 r is a continuous function c 2007 elsevier ltd all rights reserved

retrospective markov chain monte carlo methods for dirichlet process hierarchical models inference for dirichlet process hierarchical models is typically performed using markov chain monte carlo methods which can be roughly categorized into marginal and conditional methods the former integrate out analytically the infinite dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the gibbs sampler conditional methods impute the dirichlet process and update it as a component of the gibbs sampler since this requires imputation of an infinite dimensional process implementation of the conditional method has relied on finite approximations in this paper we show how to avoid such approximations by designing two novel markov chain monte carlo algorithms which sample from the exact posterior distribution of quantities of interest the approximations are avoided by the new technique of retrospective sampling we also show how the algorithms can obtain samples from functionals of the dirichlet process the marginal and the conditional methods are compared and a careful simulation study is included which involves a non conjugate model different datasets and prior specifications

tensor decompositions and sparse log linear models contingency table analysis routinely relies on log linear models with latent structure analysis providing a common alternative latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data while log linear models achieve dimensionality reduction through sparsity little is known about the relationship between these notions of dimensionality reduction in the two paradigms we derive several results relating the support of a log linear model to nonnegative ranks of the associated probability tensor motivated by these findings we propose a new collapsed tucker class of tensor decompositions which bridge existing parafac and tucker decompositions providing a more flexible framework for parsimoniously characterizing multivariate categorical data taking a bayesian approach to inference we illustrate empirical advantages of the new decompositions

periodic solutions of non autonomous second order systems with γ quasisubadditive potential abstract the existence of periodic solutions to non autonomous second order systems with quasisubadditive potential is proved with classical theorems of variational calculus

the simulation smoother for time series models summary recently suggested procedures for simulating from the posterior density of states given a gaussian state space time series are refined and extended we introduce and study the simulation smoother which draws from the multivariate posterior distribution of the disturbances of the model so avoiding the degeneracies inherent in state samplers the technique is important in gibbs sampling with non gaussian time series models and for performing bayesian analysis of gaussian time series

testing strategies in multi dose experiments including active control inferential test strategies for multi arm trials are adapted or proposed for the special situation when more than one dose of a test treatment placebo and active control s are compared this includes between doses dose placebo and dose active control comparisons the procedures refer to situations when detailed comparisons make sense only if the sensitivity of the trial has been shown for example if a dose response relationship or a difference between active control and placebo has been established split strategies hierarchical assuming an order restriction among doses or linked procedures are introduced in linked procedures equivalence to the active control will be established only if the dose is also shown to be effective as compared to placebo all the inferential procedures control the experimentwise error rate in the strong sense for the respective sets of null hypotheses considered

a graphical approach to sequentially rejective multiple test procedures for clinical trials with multiple treatment arms or endpoints a variety of sequentially rejective weighted bonferroni type tests have been proposed such as gatekeeping procedures fixed sequence tests and fallback procedures they allow to map the difference in importance as well as the relationship between the various research questions onto an adequate multiple test procedure since these procedures rely on the closed test principle they usually require the explicit specification of a large number of intersection hypotheses tests the underlying test strategy may therefore be difficult to communicate we propose a simple iterative graphical approach to construct and perform such bonferroni type tests the resulting multiple test procedures are represented by directed weighted graphs where each node corresponds to an elementary hypothesis together with a simple algorithm to generate such graphs while sequentially testing the individual hypotheses the approach is illustrated with the visualization of several common gatekeeping strategies a case study is used to illustrate how the methods from this article can be used to tailor a multiple test procedure to given study objectives