on fractional powers of generators of fractional resolvent families abstract we show that if a generates a bounded times resolvent family for some 0 2 then a generates an analytic times resolvent family for 0 2 2 and 0 2 and a generalized subordination principle is derived in particular if a generates a bounded times resolvent family for some 1 2 then a 1 generates an analytic c 0 semigroup such relations are applied to study the solutions of cauchy problems of fractional order and first order

cauchy problems for fractional differential equations with riemann liouville fractional derivatives abstract in this paper we are concerned with cauchy problems of fractional differential equations with riemann liouville fractional derivatives in infinite dimensional banach spaces we introduce the notion of fractional resolvent obtain some its properties and present a generation theorem for exponentially bounded fractional resolvents moreover we prove that a homogeneous order cauchy problem is well posed if and only if its coefficient operator is the generator of an order fractional resolvent and we give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of an inhomogeneous order cauchy problem

approachability and fixed points for non convex set valued maps this paper studies the approachability of upper semicontinuous nonconvex set valued maps by single valued continuous functions and its applications to fixed point theory the use of approximate selections was initiated by j von neumann 41 in the proof of his well known minimax principle this remarkable property was extended to the normed space setting by cellina s and cellina and lasota 9 in the context of a degree theory for upper semicontinuous convex compact valued maps it also holds for maps with compact contractible values defined on finite polyhedra of iw ma cole11 40 and more generally defined on compact anrs mclennan 39 it was recently taken up by gbrniewicz granas and kryszewski 22 241 in the context of an index theory for non convex maps defined on compact anrs the content of this paper is divided into three parts the first part is devoted to background material concerning the types of spaces and set valued maps studied herein in the second part we define the abstract class d of approachable set valued maps that is the class of maps a x y

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

full predictivistic modeling of stock market data application to change point problems in change point problems in general we should answer three questions how many changes are there where are they and what is the distribution of the data within the blocks in this paper we develop a new full predictivistic approach for modeling observations within the same block of observation and consider the product partition model ppm for treating the change point problem the ppm brings more flexibility into the change point problem because it considers the number of changes and the instants when the changes occurred as random variables a full predictivistic characterization of the model can provide a more tractable way to elicit the prior distribution of the parameters of interest once prior opinions will be required only about observable quantities we also present an application to the problem of identifying multiple change points in the mean and variance of a stock market return time series

note to the asymptotic behaviour of solutions of damped pendulum equations under forcing although the mathematical or the physical pendulum seems to be one of the most popular objects in modelling see the nice exposition lo and therefore no wonder that for the related autonomous equations studied by means of the planar geometrical methods a vast literature exists see the monographs 2 3 151 or more recently the beautiful modern article 4 there are still several white places of its study in the case of forcing recently the big activity is devoted for proving the existence of harmonics to its equation for the survey of results in this field see s lo or chaotic behaviour of the dynamics see e g 6 or the different approaches in 12 is nevertheless we have found only one reference 16 on the asymptotic behaviour of solutions of the pendulum type equations under forcing which is already 30 years old hence our aim is to extend the results in this field for the equation

on the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces abstract the main purpose of this paper is to deal with almost automorphic and asymptotically almost automorphic solutions of the initial value problem as well as the nonlinear volterra integral equation in banach spaces we obtain a collection of existence results of such solutions to these equations we investigate also a topological structure of such solution sets moreover we prove aronszajn type theorems for solutions of the initial value problem as well as the nonlinear volterra integral equation defined on the whole real line

how should trends in hydrological extremes be estimated 1 a comparison of six procedures for estimating the linear trend parameter in annual maximum 1 day river flows at five sites in southern brazil showed marked differences between on the one hand estimates obtained by incorporating trend into the generalized extreme value gev location parameter with all parameters estimated by maximum likelihood ml and on the other hand estimates found by least squares trend removal prior to fitting the gev by ml boot strap sampling and theil sen estimation ml estimates of trend were considerably smaller than those given by all other procedures the same was true where trend had been incorporated into the gumbel location parameter where 95 confidence intervals were calculated for the true trend by different procedures some confidence intervals bracketed zero indicating that the trend was not significant at the 5 level but there was no consistency between results from different procedures theil sen confidence intervals always bracketed zero confidence intervals given by detrending never did it is concluded that not only do different estimation procedures give different measures of trend uncertainty as reported elsewhere but the estimated trends themselves may differ and the paper suggests an explanation why this may occur some philosophical issues relating to estimation of trend in climatological and hydrological extremes are discussed and it is concluded that selection of a method to estimate trend must depend on context

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

linearized stability in periodic functional differential equations with state dependent delays in this paper we study stability of periodic solutions of a class of nonlinear functional differential equations fdes with state dependent delays using the method of linearization we show that a periodic solution of the nonlinear fde is exponentially stable if the zero solution of an associated linear periodic linear homogeneous fde is exponentially stable

bayesian multivariate linear regression with application to change point models in hydrometeorological variables 1 multivariate linear regression is one of the most popular modeling tools in hydrology and climate sciences for explaining the link between key variables piecewise linear regression is not always appropriate since the relationship may experiment sudden changes due to climatic environmental or anthropogenic perturbations to address this issue a practical and general approach to the bayesian analysis of the multivariate regression model is presented the approach allows simultaneous single change point detection in a multivariate sample and can account for missing data in the response variables and or in the explicative variables it also improves on recently published change point detection methodologies by allowing a more flexible and thus more realistic prior specification for the existence of a change and the date of change as well as for the regression parameters the estimation of all unknown parameters is achieved by monte carlo markov chain simulations it is shown that the developed approach is able to reproduce the results of rasmussen 2001 as well as those of perreault et al 2000a 2000b furthermore two of the examples provided in the paper show that the proposed methodology can readily be applied to some problems that cannot be addressed by any of the above mentioned approaches because of limiting model structure and or restrictive prior assumptions the first of these examples deals with single change point detection in the multivariate linear relationship between mean basin scale precipitation at different periods of the year and the summer autumn flood peaks of the broadback river located in northern quebec canada the second one addresses the problem of missing data estimation with uncertainty assessment in multisite streamflow records with a possible simultaneous shift in mean streamflow values that occurred at an unknown date

a new positivity condition for the curvature of hermitian manifolds in this note we introduce a new type of positivity condition for the curvature of a hermitian manifold which generalizes the notion of nonnegative quadratic orthogonal bisectional curvature to the non kahler case we derive a bochner formula for closed 1 1 forms from which this condition appears naturally and prove that if a hermitian manifold satisfies our positivity condition then any class alpha in h 1 1 bc x can be represented by a closed 1 1 form which is parallel with respect to the bismut connection lastly we show that such a curvature positivity condition holds on certain generalized hopf manifolds and on certain vaisman manifolds

a priori bounds for degenerate and singular evolutionary partial integro differential equations we study quasilinear evolutionary partial integro differential equations of second order which include time fractional p laplace equations of time order less than one by means of suitable energy estimates and de giorgi s iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these problems we also show that a maximum principle is valid for such equations

boundary value problems on infinite intervals and semiconductor devices the nonlinear differential equation y f x y y 0 x f satisfying bernstein type growth conditions we also examine an important application which occurs in the theory of semiconductor devices

a topological method for bounded solutions of nonautonomous ordinary differential equations the existence of bounded solutions to nonlinear nonautonomous ordinary differential equations is studied this is done by associating the given equation to nonlinear autonomous ones by means of a family of skew product flows related by homotopy the existence of a bounded solution to the original differential equation is then related to the nontriviality of a certain conley index associated with the autonomous differential equations the existence of nontrivial bounded solutions is also considered the differential equations studied are perturbations of homogeneous ones

rank tests for changepoint problems summary we consider procedures based on quadratic form rank statistics to test for one or more changepoints in a series of independent observations models incorporating both smooth and abrupt changes are introduced various test statistics are suggested their asymptotic null distributions are derived and tables of significance points are given a monte carlo study shows that the asymptotic significance points are applicable to moderately sized samples

controlling the reinforcement in bayesian non parametric mixture models summary the paper deals with the problem of determining the number of components in a mixture model we take a bayesian non parametric approach and adopt a hierarchical model with a suitable non parametric prior for the latent structure a commonly used model for such a problem is the mixture of dirichlet process model here we replace the dirichlet process with a more general non parametric prior obtained from a generalized gamma process the basic feature of this model is that it yields a partition structure for the latent variables which is of gibbs type this relates to the well known exchangeable product partition models if compared with the usual mixture of dirichlet process model the advantage of the generalization that we are examining relies on the availability of an additional parameter belonging to the interval 0 1 it is shown that such a parameter greatly influences the clustering behaviour of the model a value of that is close to 1 generates a large number of clusters most of which are of small size then a reinforcement mechanism which is driven by acts on the mass allocation by penalizing clusters of small size and favouring those few groups containing a large number of elements these features turn out to be very useful in the context of mixture modelling since it is difficult to specify a priori the reinforcement rate it is reasonable to specify a prior for hence the strength of the reinforcement mechanism is controlled by the data

the conley index and the method of averaging in particular one useful theorem see e g hale s for details states roughly that if f satisfies certain uniformity hypotheses and the averaged equation has x 0 as a hyperbolic equilibrium point then the timedependent equation has a unique almost periodic solution in a neighborhood of zero for sufficiently small e 0 this solution is uniformly asymptotically stable if in addition x 0 is asymptotically stable for the averaged equation the hyperbolicity of x 0 is clearly crucial even for autonomous equations for example consider f x e x3 x2 we obtain fo x x3

compact kahler manifolds with nonpositive bisectional curvature in this article we prove that for any compact kahler manifold mn with real analytic metric and nonpositive bisectional curvature there exists a finite cover m of m such that m is a holomorphic and metric fiber bundle over a compact kahler manifold n with nonpositive bisectional curvature and c1 n 0 and the fiber is a flat complex torus this partially confirms a conjecture of yau

periodicity in a food limited population model with toxicants and state dependent delays abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a food limited population model with toxicant and state dependent delays that is du t dt u t r t a t u t j 1 m b j t u t j t u t k t c t u t j 1 m d j t u t j t u t where r t k t a t bj t dj t j 1 2 m are continuous real valued periodic functions with period 0 and r t k t a t 0 bj t dj t 0 j 1 2 m are periodic continuous functions with period 0 j j are periodic with respect to their first arguments some new results are obtained

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

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 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

existence of periodic solutions for delay differential equations with state dependent delay abstract in this paper we study the existence of periodic solutions of a delay differential equation with delay depending indirectly on the state a fixed point problem related to a poincare operator is constructed and solved using an ejective fixed point theorem

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 uniqueness theorem in kahler geometry we consider compact kahler manifolds with their kahler ricci tensor satisfying f ric constant under the nonnegative bisectional curvature assumption and certain conditions on f we prove that such metrics are in fact kahler einstein

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

existence of positive solutions to some singular and nonsingular second order boundary value problems abstract the topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y f t y y 0 0 t t 0 t 1 y 0 and or y 0 the principal tools are the arzela ascoli theorem essential maps and a priori bounds on solutions

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

multipath time delay estimation using change point technique consider a multipath signal whose individual signals are deterministic known pulses our problem is to estimate the amplitudes and delay times of individual signals several methods have been devoted to solution of these unknown parameters the maximum likelihood estimation and the estimate maximize algorithm are commonly used but they are computationally intensive we consider the multipath signal as a changing linear model and use a change point technique to obtain a quick and accurate estimate of the amplitudes and arrival delay times we detect the pulse in a multipath signal which first arrives and then finish one by one in a sequence until no pulse appears therefore by using the change point procedure the number of individual pulses need not be known the results of a monte carlo simulation study with trapezoidal and sinusoidal pulses are presented to demonstrate a quick and accurate estimate of arrival times and amplitudes

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

are gibbs type priors the most natural generalization of the dirichlet process discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in bayesian inference here we focus on the family of gibbs type priors a recent elegant generalization of the dirichlet and the pitman yor process priors these random probability measures share properties that are appealing both from a theoretical and an applied point of view i they admit an intuitive predictive characterization justifying their use in terms of a precise assumption on the learning mechanism ii they stand out in terms of mathematical tractability iii they include several interesting special cases besides the dirichlet and the pitman yor processes the goal of our paper is to provide a systematic and unified treatment of gibbs type priors and highlight their implications for bayesian nonparametric inference we deal with their distributional properties the resulting estimators frequentist asymptotic validation and the construction of time dependent versions applications mainly concerning mixture models and species sampling serve to convey the main ideas the intuition inherent to this class of priors and the neat results they lead to make one wonder whether it actually represents the most natural generalization of the dirichlet process

plurisubharmonic functions and the structure of complete kahler manifolds with nonnegative curvature in this paper we study global properties of continuous plurisubharmonic functions on complete noncompact kahler manifolds with nonnegative bisectional curvature and their applications to the structure of such manifolds we prove that continuous plurisubharmonic functions with reasonable growth rate on such manifolds can be approximated by smooth plurisubharmonic functions through the heat flow deformation optimal liouville type theorem for the plurisubharmonic functions as well as a splitting theorem in terms of harmonic functions and holomorphic functions are established the results are then applied to prove several structure theorems on complete noncompact kahler manifolds with nonnegative bisectional or sectional curvature

using solution sets for solving boundary value problems for ordinary differential equations where f e c i x r r s c c z r consists of finding fixed points of a solution map e for a suitable linearized problem associated to bv see e g 2 5 6 71 in these problems the map x is either continuous and single valued or upper semicontinuous set valued with convex values these are rather strong restrictions because the set of solutions of a general boundary value problem may well be neither a singleton nor a convex set the case in which the solution map is upper semicontinuous but with nonnecessarily convex values is considered in this paper more precisely we want to consider the case when the values of x form an acyclic set and the case when the values of c are sets with a finite number of elements an application to the existence of periodic solutions for a licnard type equation is also given moreover an existence theorem for a boundary value problem of the following form f l x x x teicr x e r

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

estimation and comparison of multiple change point models this paper provides a new bayesian approach for models with multiple change points the centerpiece of the approach is a formulation of the change point model in terms of a latent discrete state variable that indicates the regime from which a particular observation has been drawn this state variable is specified to evolve according to a discrete time discrete state markov process with the transition probabilities constrained so that the state variable can either stay at the current value or jump to the next higher value this parameterization exactly reproduces the change point model the model is estimated by markov chain monte carlo methods using an approach that is based on chib 1996 this methodology is quite valuable since it allows for the fitting of more complex change point models than was possible before methods for the computation of bayes factors are also developed all the techniques are illustrated using simulated and real data sets

abstract fractional cauchy problems with almost sectorial operators abstract of concern are the cauchy problems for linear and semilinear time fractional evolution equations involving in the linear part a linear operator a whose resolvent satisfies the estimate of growth 1 0 in a sector of the complex plane which occurs when one considers for instance the partial differential operators in the limit domain of dumb bell with a thin handle or in the space of holder continuous functions by constructing a pair of families of operators in terms of the generalized mittag leffler type functions and the resolvent operators associated with a for the first time and a deep analysis on the properties for these families we obtain the existence and uniqueness of mild solutions and classical solutions to the cauchy problems moreover we present three examples to illustrate the feasibility of our results

positivity and regularity of hyperbolic volterra equations in banach spaces soit x un espace de banach a un operateur lineaire clos non borne dans x a domaine dense d a a l loc 1 r f c j x avec j 0 t et on considere l equation de volterra de type scalaire u t f t 0 t a t au d t j on etudie l existence la positivite la regularite et la compacite ainsi que l integrabilite de l operateur resolvant s t defini par s t x x 0 t a t as xd t 0 x d a pour deux classes particulieres de noyaux a et d operateurs a

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

multiple change points estimation in linear regression models via sparse group lasso we consider linear regression problems for which the underlying model undergoes multiple changes our goal is to estimate the number and locations of change points that segment available data into different regions and further produce sparse and interpretable models for each region to address challenges of the existing approaches and to produce interpretable models we propose a sparse group lasso based approach for linear regression problems with change points under certain mild assumptions and a properly chosen regularization term we prove that the solution of the proposed approach is asymptotically consistent in particular we show that the estimation error of linear coefficients diminishes and the locations of the estimated change points are close to those of true change points we further propose a method to choose the regularization term so that the results mentioned above hold in addition we show that the complexity of the proposed algorithm is much smaller than those of existing approaches numerical examples are provided to validate the analytical results

a global continuation theorem and bifurcation from infinity for infinite dimensional dynamical systems a general continuation theorem for isolated sets in infinite dimensional dynamical systems is proved for a class of semiflows this result is then used to prove the existence of continua of full bounded solutions bifurcating from infinity for systems of reaction diffusion equations

long time behavior of nonlinear integro differential evolution equations abstract we study the long time behavior as time tends to infinity of globally bounded strong solutions to certain integro differential equations in hilbert spaces based on an appropriate new lyapunov function and the ojasiewicz simon inequality we prove that any globally bounded strong solution converges to a steady state in a real hilbert space

a bayesian method for combining results from several binomial experiments abstract the problem of combining information related to i binomial experiments each having a distinct probability of success i is considered instead of using a standard exchangeable prior for 1 i we propose a more flexible distribution that takes into account various degrees of similarity among the i s using ideas developed by malec and sedransk we consider a partition g of the experiments and take the i s belonging to the same partition subset to be exchangeable and the i s belonging to distinct subsets to be independent next we perform bayesian inference on conditional on g of course one is typically uncertain about which partition to use and so a prior distribution is assigned on a set of plausible partitions g the final inference on is obtained by combining the conditional inferences according to the posterior distribution of g the methodology adopted in this article offers a wide flexibility in structuring the dependence among the i s this allows the

on the structure of fixed point sets of compact maps in b0 spaces with applications to integral and differential equations in unbounded domain abstract in this paper we present certain applications of the topological degree theory in locally convex linear topological spaces as a result we obtain two generalizations of the krasnosielski perov rabinovitz theorem on the characterization of sets of solutions of functional equations known for the banach space case onto the case of a locally convex space on the other hand we make use of such consequences of the degree theory as the borsuk theorem and browder domain invariance theorem in order to reach a certain generalization of the lasota opial covering theorem and a new theorem on the characterization of sets of solutions of functional equations at the end we apply the abstract topological theorems to study the structure of sets of solutions of a certain integral equation and the darboux problem for a hyperbolic equation in an unbounded domain a general assumption is that the kernel of the integral equation and the right hand side of the hyperbolic equation satisfy the caratheodory conditions

a note of sasakian metrics with constant scalar curvature in this paper we consider compact sasakian manifolds with constant scalar curvature under some positive curvature assumption we prove that such sasakian metrics must be einstein metrics

on evolutionary volterra equations with state dependent delay abstract in this work we study topological properties of the solution set of abstract volterra equations with state dependent delay particularly we ensure that such a set is a nonempty compact and connected set as application we consider our abstract results in the framework of integro differential equations coming from viscoelasticity theory

improving samc using smoothing methods theory and applications to bayesian model selection problems stochastic approximation monte carlo samc has recently been proposed by liang liu and carroll j amer statist assoc 102 2007 305 320 as a general simulation and optimization algorithm in this paper we propose to improve its convergence using smoothing methods and discuss the application of the new algorithm to bayesian model selection problems the new algorithm is tested through a change point identification example the numerical results indicate that the new algorithm can outperform samc and reversible jump mcmc significantly for the model selection problems the new algorithm represents a general form of the stochastic approximation markov chain monte carlo algorithm it allows multiple samples to be generated at each iteration and a bias term to be included in the parameter updating step a rigorous proof for the convergence of the general algorithm is established under verifiable conditions this paper also provides a framework on how to improve efficiency of monte carlo simulations by incorporating some nonparametric techniques

structural learning with time varying components tracking the cross section of financial time series summary when modelling multivariate financial data the problem of structural learning is compounded by the fact that the covariance structure changes with time previous work has focused on modelling those changes by using multivariate stochastic volatility models we present an alternative to these models that focuses instead on the latent graphical structure that is related to the precision matrix we develop a graphical model for sequences of gaussian random vectors when changes in the underlying graph occur at random times and a new block of data is created with the addition or deletion of an edge we show how a bayesian hierarchical model incorporates both the uncertainty about that graph and the time variation thereof

existence of bounded solutions for multivalued differential systems on demontre l existence de solutions bornees pour le systeme x t a t x t f t x t x s sur un intervalle i reel non borne ou f est une application a valeur convexe semi continue superieurement a est une matrice n n avec conditions de caratheodory s est un sous ensemble d un espace de banach

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

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

multiscale generalised linear models for nonparametric function estimation summary we present a method for extracting information about both the scale and trend of local components of an inhomogeneous function in a nonparametric generalised linear model our multiscale framework combines recursive partitions which allow for the incorporation of scale in a natural manner with systems of piecewise polynomials supported on the partition intervals which serve to summarise the smooth trend within each interval our estimators are formulated as solutions of complexity penalised likelihood optimisations where the penalty seeks to limit the number of intervals used to model the data the actual calculation of the estimators may be accomplished using standard software routines for generalised linear models within the context of efficient tree based polynomial time algorithms a risk analysis shows that these estimators achieve the same asymptotic rates in the nonparametric generalised linear model as the classical wavelet based estimators in the gaussian function plus noise model for suitably defined ranges of besov spaces numerical simulations show that the method tends to perform at least as well as and often better than alternative wavelet based methodologies in the context of finite samples while applications to gamma ray burst data in astronomy and packet loss data in computer network traffic analysis confirm its practical relevance

estimates for the neumann problem and nonexistence of c 2 levi flat hypersurfaces in cp n letbe a pseudoconvex domain with c 2 boundary in cp n n 2 we prove that the neumann operator n exists for square integrable forms on furthermore there exists a number 0 0 such that the operators n n n and the bergman projection are regular in the sobolev space w for 0 and n 2 as a consequence we prove the nonexistence of c 2 levi flat hypersurfaces in cp n

asymptotic properties of solutions to quasi linear differential systems abstract using some previous author s results or their slight modifications two theorems concerning the existence of a bounded and a periodic solution are presented for the system whose one part of components is uniformly ultimately bounded while the other tends mostly to infinity this type of results seems to be new

use of fuzzy statistical technique in change periods detection of nonlinear time series many papers have been presented on the study of change points detection nonetheless we would like to point out that in dealing with the time series with switching regimes we should also take the characteristics of change periods into account because many patterns of change structure in time series exhibit a certain kind of duration those phenomena should not be treated as a mere sudden turning at a certain time in this paper we propose a procedure about change periods detection for nonlinear time series the detecting statistical method is an application of fuzzy classification and a generalization of inclan and tiao s result j am statist assoc 89 1994 913 simulation results show that the performance of the proposed procedure is efficient and successful finally an empirical application about change periods detecting for taiwan monthly visitor s arrival is demonstrated

on the qualitative theory of lower semicontinuous differential inclusions on etudie les proprietes qualitatives de l ensemble des solutions de caratheodory pour une inclusion differentielle de la forme x t f t x t t 0 t x 0 r n

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