on the uniform consistency of bayes estimates for multinomial probabilities a k sided die is thrown n times to estimate the probabilities 1 k of landing on the various sides the mle of is the vector of empirical proportions p p 1 p k consider a set of bayesians that put uniformly positive prior mass on all reasonable subsets of the parameter space their posterior distributions will be uniformly concentrated near p sharp bounds are given using entropy these bounds apply to all sample sequences there are no exceptional null sets

the truncated complex moment problem let 2n denote a sequence of complex numbers 00 01 10 0 2n 2n 0 00 0 ij ji and let k denote a closed subset of the complex plane c the truncated complex k moment problem for entails determining whether there exists a positive borel measure on c such that ij zizj d 0 i j 2n and supp k for k kp a semi algebraic set determined by a collection of complex polynomials p pi z z mi 1 we characterize the existence of a finitely atomic representing measure with the fewest possible atoms in terms of positivity and extension properties of the moment matrix m n and the localizing matrices mpi we prove that there exists a rankm n atomic representing measure for 2n supported in kp if and only if m n 0 and there is some rankpreserving extension m n 1 for which mpi n ki 0 where deg pi 2ki or 2ki 1 1 i m

levy khintchine formulas independent of a levy function abstract in this paper we obtain integral representations independent of a levy function for negative definite functions with real part bounded below defined on a commutative involutive semigroup and for continuous negative definite functions defined on the group r n

short run and long run causality in time series theory causality in the sense of granger is typically defined in terms of predictibility of a vector of variables one period ahead recently liitkepohl 1993 proposed to define noncausality between two variables in terms of nonpredictibility at any number of periods ahead when more than two vectors are considered i e when the information set contains auxiliary variables these two notions are not equivalent in this paper we first generalize the notion of causality by considering causality at a given arbitrary horizon h then we derive necessary and sufficient conditions for noncausality between vectors of variables inside a larger vector up to any given horizon h where h can be infinite in particular for general possibly nonstationary processes with finite second moments relatively simple exhaustivity and separation conditions which are sufficient for noncausality at all horizons are provided to deal with cases where such conditions do not apply we consider a more specific although still very wide class of vector autoregressive processes possibly of infinite order stationary or nonstationary which include multivariate arima processes and we derive general parametric characterizations of noncausality at various horizons for this class including a causality chain characterization we also observe that the coefficients of lagged variables in forecasts at various horizons h 1 can be interpreted as generalized impulse response coefficients which yield a complete picture of linear causality properties in contrast with usual response coefficients which can be quite misleading in this respect

inference in linear time series models with some unit roots this paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots our motivating example is a vector autoregression with some unit roots in the companion matrix which might include polynomials in time as regressors in the general formulation the variable might be integrated or cointegrated of arbitrary orders and might have drifts as well we show that parameters that can be written as coefficients on mean zero nonintegrated regressors have jointly normal asymptotic distributions converging at the rate t 2 in general the other coefficients including the coefficients on polynomials in time will have nonnormal asymptotic distributions the results provide a formal characterization of which t or f tests such as granger causality tests will be asymptotically valid and which will have nonstandard limiting distributions

on comparability and permutation graphs this paper presents a technique for orienting a comparability graph transitively in o n 2 time the best previous algorithm for this problem required omega n 3 time when combined with a result in sp we can recognize permutation graphs in o n 2 time and determine in the same time complexity whether two permutation graphs are isomorphic the orientation algorithm can also be used to reduce the problem of recognizing comparability graphs to that of recognizing transitive graphs this gives an upper bound of o n 2 49 for comparability graph recognition while the fastest previous algorithms required omega n 3 time

some recent development in a concept of causality abstract the paper considers three separate but related topics i what is the relationship between causation and co integration if a pair of i 1 series are co integration there must be causation in at least one direction an implication is that some tests of causation based on different series may have missed one source of causation ii is there a need for a definition of instantaneous causation in a decision science it is argued that no such definition is required iii can causality tests be used for policy evaluation it is suggested that these tests are useful but that they should be evaluated with care

primitivity is hereditary for 2 structures abstract it is proved that each primitive 2 structure on n elements n 3 contains a primitive substructure on either n 1 or n 2 elements

on moment sequences and infinitely divisible sequences we consider infinitely divisible sequences in the context of moment sequences in the same vein as r a horn j math anal appl 31 1970 130 135 considered renewal sequences and we compare the results

constructions of random distributions via sequential barycenters this article introduces and develops a constructive method for generating random probability measures with a prescribed mean or distribution of the means the method involves sequentially generating an array of barycenters which uniquely defines a probability measure basic properties of the generated measures are presented including conditions under which almost all the generated measures are continuous or almost all are purely discrete or almost all have finite support applications are given to models for average optimal control problems and to experimental approximation of universal constants 1 introduction the purpose of this note is to introduce a general and natural method for constructing random probability measures with any prescribed mean or distribution of the means this method complements classical and recent constructions e g dubins and freedman 1967 ferguson 1973 1974 graf mauldin and williams 1986 mauldin sudderth and williams 1992 and monticino 1996 none of which generates random measures with a priori specified means in fact even the calculation of the distribution of the means for those constructions is difficult cf cifarelli and regazzani 1990 and monticino 1995 the new method presented here which is based on sequential barycenters satisfies ferguson s 1974 two basic requirements that such constructions have large support and be analytically manageable the construction is easy to implement and is robust allowing generation of random measures which are either almost surely discrete or continuous as desired since many problems in probability and analysis involve distributions with given means the new construction will perhaps prove a useful tool in a variety of applications 2 sequential barycenter arrays this section introduces the notion of a sequential barycenter array sba and develops some basic properties of the probability measures defined by the arrays these sba s although not named as such are used in standard proofs of skorohod s embedding theorems e g billingsley 1986 section 37 and it is the reversal of this standard procedure which is the foundation for the construction of the random measures given in the next section

theory and numerical analysis for exact distributions of functionals of a dirichlet process the distribution of a mean or more generally of a vector of means of a dirichlet process is considered some characterizing aspects of this paper are i a review of a few basic results providing new formulations free from many of the extra assumptions considered to date in the literature and giving essentially new simpler and more direct proofs ii new numerical evaluations with any prescribed error of approximation of the distribution at issue iii a new form for the law of a vector of means moreover as applications of these results we give iv the sharpest condition sufficient for the distribution of a mean to be symmetric v forms for the probability distribution of the variance of the dirichlet random measure vi some hints for determining the finite dimensional distributions of a random function connected with bayesian methods for queuing models

the markov moment problem and de finetti s theorem part ii the markov moment problem is to characterize sequences admitting the representation s n 0 1 x nf x dx where f x is a probability density on 0 1 and 0 f x c for almost all x there are well known characterizations through complex systems of non linear inequalities on s n necessary and sufficient linear conditions are the following s 0 1 and for all and here is the forward difference operator this result is due to hausdorff we give a new proof with some ancillary results for example characterizing monotone densities then we make the connection to de finetti s theorem with characterizations of the mixing measure

functionals of dirichlet processes the cifarelli regazzini identity and beta gamma processes suppose that p g is a linear functional of a dirichlet process with shape oh where 0 0 is the total mass and h is a fixed probability measure this paper describes how one can use the well known bayesian prior to posterior analysis of the dirichlet process and a posterior calculus for gamma processes to ascertain properties of linear functionals of dirichlet processes in particular in conjunction with a gamma identity we show easily that a generalized cauchy stieltjes transform of a linear functional of a dirichlet process is equivalent to the laplace functional of a class of what we define as beta gamma processes this represents a generalization of an identity due to cifarelli and regazzini which is also known as the markov krein identity for mean functionals of dirichlet processes these results also provide new explanations and interpretations of results in the literature the identities are analogues to quite useful identities for beta and gamma random variables we give a result which can be used to ascertain specifications on h such that the dirichlet functional is beta distributed this avoids the need for an inversion formula for these cases and points to the special nature of the dirichlet process and indeed the functional beta gamma calculus developed in this paper

hierarchical mixture modeling with normalized inverse gaussian priors in recent years the dirichlet process prior has experienced a great success in the context of bayesian mixture modeling the idea of overcoming discreteness of its realizations by exploiting it in hierarchical models combined with the development of suitable sampling techniques represent one of the reasons of its popularity in this article we propose the normalized inverse gaussian n ig process as an alternative to the dirichlet process to be used in bayesian hierarchical models the n ig prior is constructed via its finite dimensional distributions this prior although sharing the discreteness property of the dirichlet prior is characterized by a more elaborate and sensible clustering which makes use of all the information contained in the data whereas in the dirichlet case the mass assigned to each observation depends solely on the number of times that it occurred for the n ig prior the weight of a single observation depends heavily on the whole number of ties in the sample moreover expressio

existence uniqueness and a constructive solution algorithm for a class of finite markov moment problems we consider a class of finite markov moment problems with an arbitrary number of positive and negative branches we show criteria for the existence and uniqueness of solutions and we characterize in detail the nonunique solution families moreover we present a constructive algorithm to solve the moment problems numerically and prove that the algorithm computes the right solution

conditioning likelihood and coherence a review of some foundational concepts 2000 conditioning likelihood and coherence a review of some foundational concepts journal of the american statistical association vol 95 no 452 pp 1340 1346

on generating functions of hausdorff moment sequences the class of generating functions for completely monotone se quences moments of finite positive measures on 0 1 has an elegant char acterization as the class of pick functions analytic and positive on 1 we establish this and another such characterization and develop a variety of consequences in particular we characterize generating functions for moments of convex and concave probability distribution functions on 0 1 also we provide a simple analytic proof that for any real p and r with p 0 the fuss catalan or raney numbers r pn r pn r

asymptotic normality of semiparametric and nonparametric posterior distributions in this article it is shown that the marginal semiparametric and nonparametric posterior distributions for a parameter of interest behave like an ordinary parametric posterior distribution this in practice provides support of the utility of marginal semiparametric and nonparametric posterior distributions in particular the marginal semiparametric and nonparametric posterior distributions are asymptotically normal and centered at the corresponding maximum likelihood estimates mles or posterior means with covariance matrix the inverse of the fisher information additionally the semiparametric and nonparametric mles for the parameter of interest and the marginal posterior means are asymptotically normal and centered at the true parameter with the same covariance matrix the results are a semiparametric version and a nonparametric version of the parametric bayesian central limit theorem that establish a connection between the semiparametric and the nonparametric bayesian inference and their frequentis

large deviations for random power moment problem we consider the set mn of all n truncated power moment sequences of probability measures on 0 1 we endow this set with the uniform probability picking randomly a point in mn we show that the upper canonical measure associated with this point satisfies a large deviation principle moderate deviation are also studied completing earlier results on asymptotic normality given by chang kemperman and studden ann probab 21 1993 1295 1309 surprisingly our large deviations results allow us to compute explicitly the n 1 th moment range size of the set of all probability measures having the same n first moments the main tool to obtain these results is the representation of mn on canonical moments see the book of dette and studden

exact multivariate bayesian bootstrap distributions of moments the common unknown probability law p of a random sample y 1 y n is assigned a dirichlet process prior with index it is shown that the posterior joint density of several moments of p converges as r 0 to a multivariate b spline which is therefore the bayesian bootstrap joint density of the moments the result provides the basis for possible default nonparametric bayesian inference on unknown moments

fundamental study the modular decomposition of countable graphs definition and construction in monadic second order logic we consider the notion of modular decomposition for countable graphs the modular decomposition of a graph given with an enumeration of its set of vertices can be defined by formulas of monadic second order logic another result is the definition of a representation of modular decompositions by low degree relational structures such relational structures can also be defined in the considered graph by monadic second order formulas

incremental modular decomposition modular decomposition is a form of graph decomposition that has been discovered independently by researchers in graph theory game theory network theory and other areas this paper reduces the time needed to find the modular decomposition of a graph from o n 3 to o n 2 together with a new algorithm for transitive orientation given in 21 this leads to fast new algorithms for a number of problems in graph recognition and isomorphism including recognition of comparability graphs and permutation graphs the new algorithm works by inserting each vertex successively into the decomposition tree using o n time to insert each vertex

free self decomposability and unimodality of the fuss catalan distributions we study properties of the fuss catalan distributions mu p r p ge 1 0 1 there exists r 0 p with p 1 r 0 p p such that the fuss catalan distribution mu p r is unimodal if and only if either r p or 0 r le r 0 p we prove rigorously some partial results

superresolution in the markov moment problem abstract suppose that bar x is a characteristic function and a 1 a 2 a n are weight functions on a finite measure space recent work of gamboa and gassiat observed conditions guaranteeing that x bar x 1 is small whenever 0 x 1 a e and the moment errors int x bar x a i are small i 1 2 n using concise and elementary techniques we obtain similar results under very mild assumptions we also provide precise error bounds

shape from moments an estimation theory perspective this paper discusses the problem of recovering a planar polygon from its measured complex moments these moments correspond to an indicator function defined over the polygon s support previous work on this problem gave necessary and sufficient conditions for such successful recovery process and focused mainly on the case of exact measurements being given in this paper we extend these results and treat the same problem in the case where a longer than necessary series of noise corrupted moments is given similar to methods found in array processing system identification and signal processing we discuss a set of possible estimation procedures that are based on the prony and the pencil methods relate them one to the other and compare them through simulations we then present an improvement over these methods based on the direct use of the maximum likelihood estimator exploiting the above methods as initialization finally we show how regularization and thus maximum a posteriori probability estimator could be applied to reflect prior knowledge about the recovered polygon

means of a dirichlet process and multiple hypergeometric functions the lauricella theory of multiple hypergeometric functions is used to shed some light on certain distributional properties of the mean of a dirichlet process this approach leads to several results which are illustrated here among these are a new and more direct procedure for determining the exact form of the distribution of the mean a correspondence between the distribution of the mean and the parameter of a dirichlet process a characterization of the family of cauchy distributions as the set of the fixed points of this correspondence and an extension of the markov krein identity moreover an expression of the characteristic function of the mean of a dirichlet process is obtained by resorting to an integral representation of a confluent form of the fourth lauricella function this expression is then employed to prove that the distribution of the mean of a dirichlet process is symmetric if and only if the parameter of the process is symmetric and to provide a new expression of the moment generating function of the variance of a dirichlet process

using k branch entropy solutions for multivalued geometric optics computations this paper is devoted to a numerical simulation of the classical wkb system arising in geometric optics expansions it contains the nonlinear eikonal equation and a linear conservation law whose coefficient can be discontinuous we address the problem of treating it in such a way that superimposed signals can be reproduced by means of the kinetic formulation of multibranch solutions originally due to brenier and corrias some existence and uniqueness results are given together with computational test cases of increasing difficulty displaying up to five multivaluations

hydrological natural inflow and climate variables time and frequency causality analysis numbers of studies have proved the significant influence of climate variables on hydrologicalseries considering the pivotal role of the hydroelectric power plants play in the electricity production in brazil this paper considers the natural hydrological inflow data from 15 major basins and 8 climate variables containing 7 el ni no southern oscillation proxies and the sunspot numbers the causal relationships between hydrological natural inflows and climate variables are investigated by adopting and comparing 5 different causality detection methods granger causality test frequency domain causality test convergent cross mapping causality test single spectrum analysis ssa causality test and periodic autoregressive model causality test that cover both well established and novel empirical approaches both time domain and frequency domain causality tests gain valid evidences of unidirectional causality for a group of series ccm achieved unidirectional causality for 18 of pairs and overwhelmingly indicated the opposite direction of causality a mixture of results are concluded by ssa causality test par based causality test obtained six unidirectional causality but only one is really significant

the recognition of series parallel digraphs we present a linear time algorithm to recognize the class of vertex series parallel vsp digraphs our method is based on the relationship between vsp digraphs and the class of edge series paralle

filtered variate prior distributions for histogram smoothing abstract we develop prior distributions for histogram inference favoring smooth population frequencies that is probability vectors with small differences for neighboring categories we give a theory of prior random probability vectors representable as a linear transform or filter of a standard random probability vector or equivalently a random weighted average of nonrandom smooth probability vectors promising methods of prior assessment are given based on elicitation of a list of typically smooth probability vectors the empirical moments of which can then be matched by the mean vector and variance matrix of a constructed continuous type filtered variate prior distribution

theory of 2 structures part i clans basic subclasses and morphisms abstract the notion of a 2 structure is more general than the notion of a graph and less general than the notion of a relational structure this paper develops the theory of 2 structures and in particular it demonstrates that each 2 structure can be constructed from decomposed into three sorts of basic 2 structures this result is obtained through a hierarchical representation of 2 structures by trees

theory of 2 structures part ii representation through labeled tree families abstract this paper which is the second part of a whole consisting of two parts continues the investigation of the theory of 2 structures initiated in part i in particular we investigate hierarchical representations of 2 structures through trees where the local relationship between direct descendants of an inner node of a tree is given through a 2 structure the main result of the paper is that for such hierarchical definition it suffices to consider trees where these local relationships are given by either a primitive 2 structure or a complete 2 structure or a linear 2 structure hence each 2 structure can be constructed from decomposed into primitive complete and linear 2 structures

self similar spreading in a merging splitting model of animal group size in a recent study of certain merging splitting models of animal group size degond et al in j nonlinear sci 27 2 379 424 2017 it was shown that an initial size distribution with infinite first moment leads to convergence to zero in weak sense corresponding to unbounded growth of group size in the present paper we show that for any such initial distribution with a power law tail the solution approaches a self similar spreading form a one parameter family of such self similar solutions exists with densities that are completely monotone having power law behavior in both small and large size regimes with different exponents

fuss catalan matrices their weighted sums and stabilizer subgroups of the riordan group abstract in this paper we present the riordan arrays called fuss catalan matrices which are constructed by the convolutions of the generating functions of the fuss catalan numbers we also discuss weighted sums of the fuss catalan matrices using such matrices as transformations of recursive sequences and their connection with stabilizer subgroups of the riordan group

measurement of linear dependence and feedback between multiple time series abstract measures of linear dependence and feedback for multiple time series are defined the measure of linear dependence is the sum of the measure of linear feedback from the first series to the second linear feedback from the second to the first and instantaneous linear feedback the measures are nonnegative and zero only when feedback causality of the relevant type is absent the measures of linear feedback from one series to another can be additively decomposed by frequency a readily usable theory of inference for all of these measures and their decompositions is described the computations involved are modest

stationary distributions for a class of generalized fleming viot processes we identify stationary distributions of generalized fleming viot processes with jump mechanisms specified by certain beta laws together with a parameter measure each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a dirichlet random measure with the same parameter measure the calculations are based primarily on the well known relationship to measure valued branching processes with immigration

t structures t functions and texts the theory of 2 structures see e g ehrenfeucht and rozenberg 1990 provides a convenient framework for investigating various mathematical structures encountered in computer science this paper investigates a subclass of 2 structures called t structures which turned out to be important in the investigation of basic properties of 2 structures see ehrenfeucht and rozenberg 1992 we prove that t structures are a natural generalization of linear orders in particular we prove that a t structure can be represented by two linear orders based on this result the notion of a text is introduced which generalizes the notion of a word as used in formal language theory a text may be seen as a word with a structure spanned on it this structure may be a tree but it may also be more general than a tree basic properties of the class of texts corresponding to trees are investigated

a k structure generalization of the theory of 2 structures the prime tree decomposition of graphs facilitates the solution of a number of important combinatorial problems the decomposition is also known as modular decomposition and substitution decomposition it has been generalized to 2 structures and to k ary relations but while both of these generalizations give the decomposition on graphs as a special case neither is a generalization of the other in this paper we propose a type of edge colored hypergraph which we will call a k structure we define the modular decomposition of k structures and generalize the essential algebraic properties this unifies the prime tree decompositions on 2 structures and k ary relations by giving them as special cases and extends the decomposition to k structures that are neither 2 structures nor k ary relations in addition we show that any indecomposable k structure on n 3 nodes contains a smaller indecomposable substructure that has at least n k nodes this is a generalization of a previously known result on graphs and 2 structures that is where k 2 the generalization to k ary relations that it gives as a special case is also new

the markov power moment problem in problems of controllability and frequency extinguishing for the wave equation on a half axis in this paper necessary and sufficient conditions of null controllability and approximate null controllability are obtained for the wave equation on a half axis controls solving these problems are found explicitly moreover bang bang controls solving the approximate null controllability problem are constructed with the aid of solutions of a frequency extinguishing problem in the restricted band a a for this equation and the markov power moment problem

skew symmetric matrices and their principal minors abstract in this article we study the following problem given a positive integer k what is the relationship between two matrices with entries in a field k and having equal corresponding principal minors of order at most k our main theorem improves a result of loewy 13 for skew symmetric matrices all of whose off diagonal entries are nonzero

bayesian nonparametric inference for random distributions and related functions in recent years bayesian nonparametric inference both theoretical and computational has witnessed considerable advances however these advances have not received a full critical and comparative analysis of their scope impact and limitations in statistical modelling many aspects of the theory and methods remain a mystery to practitioners and many open guestions remain in this paper we discuss and illustrate the rich modelling and analytic possibilities that are available to the statistician within the bayesian nonparametric and or semiparametric framework

hierarchical statistical models and a generalized likelihood ratio test this paper deals with statistical inference for statistical models which have a nested structure the emphasis here is on the use of a classical test of significance and on a confidence set construction approach for model identification and the paper proposes a generalized likelihood ratio test with equal marginal error rate as a basic tool the power performance of this test is characterized and some applications are illustrated

testing for short and long run causality a frequency domain approach abstract the framework of geweke 1982 journal of the american statistical association 77 304 324 and hosoya 1991 probability theory and related fields 88 429 444 is adopted to construct a simple test for causality in the frequency domain this test can also be applied to cointegrated systems to study the large sample properties of the test we analyze the power against a sequence of local alternatives the finite sample properties are investigated by means of monte carlo simulations our methodology is applied to investigate the predictive content of the yield spread for future output growth using quarterly us data we observe reasonable leading indicator properties at frequencies around one year and typical business cycle frequencies

the effect of filtering on granger causality based multivariate causality measures in the past causality measures based on granger causality have been suggested for assessing directionality in neural signals in frequency domain analyses power or coherence of neural data it is common to preprocess the time series by filtering or decimating however in other fields it has been shown theoretically that filtering in combination with granger causality may lead to spurious or missed causalities we investigated whether this result translates to multivariate causality methods derived from granger causality with a a simulation study and b an application to magnetoencephalographic data to this end we performed extensive simulations of the effect of applying different filtering techniques and evaluated the performance of five different multivariate causality measures in combination with two numerical significance measures random permutation and leave one out method the analysis included three of the most widely used filters high pass low pass notch filter four different filter types butterworth chebyshev i and ii elliptic filter variation of filter order decimating and interpolation the simulation results suggest that preprocessing without a strong prior about the artifact to be removed disturbs the information content and time ordering of the data and leads to spurious and missed causalities only if apparent artifacts like a current or movement artifact are present filtering out the respective disturbance seems advisable while oversampling poses no problem decimation by a factor greater than the minimum time shift between the time series may lead to wrong inferences in general the multivariate causality measures are very sensitive to data preprocessing

large sample bayesian analysis for rm geo g 1 discrete time queueing models statistical inference for the probability generating function p g f of the equilibrium waiting time distribution is considered the consistency of the posterior distribution for such a p g f as well as the weak convergence to a gaussian process of a suitable rescaling are proved as by products results on statistical inference for queueing characteristics are also ob tained finally the problem of estimating the probability of a long delay is considered 1 introduction and preliminaries discrete time queueing models have recently received considerable attention mainly because of their appli cations to telecommunication systems based on asynchronous transfer mode atm which is the standard transport vehicle of the broadband integrated let t be the r v number of time slots between i 1 th and ith batches i ith interarrival time and let s be the r v ith service time i e the size of i the ith batch the hypotheses on r v s t s and s s are ii

some new results for dirichlet priors let p be a random probability measure chosen by a dirichlet process whose parameter a is a finite measure with support contained in 0 and suppose that v f x 2 p dx f xp dx 2 is a finite random variable this paper deals with the distribution of v which is given in a rather general case a simple application to bayesian bootstrap is also illustrated

distribution functions of means of a dirichlet process let be a random probability measure chosen by a dirichlet process on r b with parameter and such that x dx turns out to be a finite random variable the main concern of this paper is the statement of a suitable expression for the distribution function of that random variable such an expression is deduced through an extension of a procedure based on the use of generalized stieltjes transforms

inference on one way effect and evidence in japanese macroeconomic data this paper provides an approach to testing a variety of causal characteristics expressed in terms of the measures of one way effect for cointegrated vector time series for this purpose we propose wald tests and their computational algorithm by means of the measures of one way effect incorporating johansen s algorithm for the maximum likelihood estimates and the likelihood ratio tests using the wald test statistics the paper also provides a method of confidence set construction for the causal measures the approach proposed in the paper includes testing granger s non causality as an instance of its multiple applications as an illustration the paper presents a characterization of the causal structure of the recent japanese macroeconomy on the basis of the proposed method and the derived evidence

a de finetti type theorem with m dependent states in this paper certain translation invariant states on the infinite tensor productc algebra are considered form a state ona ism dependent if varphi a 1 otimes a 2 otimes otimes a l varphi a 1 otimes otimes a k varphi a k m 1 otimes otimes a l wheneverl k m andak 1 ak 2 ak m 1 the closed convex hull of the stationarym dependent states is characterized by a symmetry condition the case ofm 0 corresponds to independence and the result reduces to ac algebraic version due to e stormer of the classical de finetti s theorem on exchangeable sequences

a stable numerical method for inverting shape from moments we derive a stable technique based upon matrix pencils for the reconstruction of or approximation by polygonal shapes from moments we point out that this problem can be considered the dual of 2 d numerical quadrature over polygonal domains an analysis of the sensitivity of the problem is presented along with some numerical examples illustrating the relevant points finally an application to the problem of gravimetry is explored where the shape of a gravitationally anomalous region is to be recovered from measurements of its exterior gravitational field

bayesian posteriors for arbitrarily rare events we study how much data a bayesian observer needs to correctly infer the relative likelihoods of two events when both events are arbitrarily rare each period either a blue die or a red die is tossed the two dice land on side 1 with unknown probabilities p 1 and q 1 which can be arbitrarily low given a data generating process where p 1 c q 1 we are interested in how much data are required to guarantee that with high probability the observer s bayesian posterior mean for p 1 exceeds 1 c times that for q 1 if the prior densities for the two dice are positive on the interior of the parameter space and behave like power functions at the boundary then for every 0 there exists a finite n so that the observer obtains such an inference after n periods with probability at least 1 whenever n p 1 n the condition on n and p 1 is the best possible the result can fail if one of the prior densities converges to zero exponentially fast at the boundary

does sunspot numbers cause global temperatures a reconsideration using non parametric causality tests abstract in a recent paper gupta et al 2015 analyzed whether sunspot numbers cause global temperatures based on monthly data covering the period 1880 1 2013 9 the authors find that standard time domain granger causality test fails to reject the null hypothesis that sunspot numbers do not cause global temperatures for both full and sub samples namely 1880 1 1936 2 1936 3 1986 11 and 1986 12 2013 9 identified based on tests of structural breaks however frequency domain causality test detects predictability for the full sample at short 2 2 6 months cycle lengths but not the sub samples but since full sample causality cannot be relied upon due to structural breaks gupta et al 2015 conclude that the evidence of causality running from sunspot numbers to global temperatures is weak and inconclusive given the importance of the issue of global warming our current paper aims to revisit this issue of whether sunspot numbers cause global temperatures using the same data set and sub samples used by gupta et al 2015 based on an nonparametric singular spectrum analysis ssa based causality test based on this test we however show that sunspot numbers have predictive ability for global temperatures for the three sub samples over and above the full sample thus generally speaking our non parametric ssa based causality test outperformed both time domain and frequency domain causality tests and highlighted that sunspot numbers have always been important in predicting global temperatures

exponential functionals and means of neutral to the right priors summary the mean of a random distribution chosen from a neutral to the right prior can be represented as the exponential functional of an increasing additive process this fact is exploited in order to give sufficient conditions for the existence of the mean of a neutralto the right prior and for the absolute continuity of its probability distribution moreover expressions for its moments of any order are provided for illustrative purposes we consider a generalisation of the neutral to the right prior based on the gamma process and the beta stacy process finally by resorting to the maximum entropy algorithm we obtain an approximation to the probability density function of the mean of a neutral tothe right prior the arguments are easily extended to examine means of posterior quantities the numerical results obtained are compared to those yielded by the application of some well established simulation algorithms

solving composite sum of powers via pade approximation and orthogonal polynomials with application to optimal pwm problem abstract this paper presents methods for solving the polynomial system j 1 k x j i j k 1 n x j i p i i 1 2 n which is called the composite sum of powers it is shown that these polynomial equation can be reduced to a single variable polynomial equations by exploiting the modified newton s identities in this paper we generalize this identity and solve it via pade approximation theory and the related theory of formal orthogonal polynomials fops because the solution forms the roots of fops we present several interesting computational procedures such as the use of three term reccurence formulas determinantal formulations and the computation of the eigenvalues of tridiagonal matrices the computation of this special polynomial system arise in practical engineering task of solving optimal odd symmetry single phase pulse width modulated pwm problem

product of ginibre matrices fuss catalan and raney distributions squared singular values of a product of s square random ginibre matrices are asymptotically characterized by probability distributions p s x such that their moments are equal to the fuss catalan numbers of order s we find a representation of the fuss catalan distributions p s x in terms of a combination of s hypergeometric functions of the type s f s 1 the explicit formula derived here is exact for an arbitrary positive integer s and for s 1 it reduces to the marchenko pastur distribution using similar techniques involving the mellin transform and the meijer g function we find exact expressions for the raney probability distributions the moments of which are given by a two parameter generalization of the fuss catalan numbers these distributions can also be considered as a two parameter generalization of the wigner semicircle law

primitive 2 structures with the n 2 property a fundamental notion in the theory of 2 structures is that of a primitive 2 structure in ehrenfeucht rozenberg 1990 it is proved that primitivity is hereditary in the sense that each primitive 2 structure on n elements where n 3 contains a primitive substructure on either n 1 or n 2 elements in this paper we determine the class of primitive 2 structures on n elements that do not contain primitive substructures on n 1 elements these 2 structures are said to satisfy the n 2 property we show that for each n 3 there is a restricted number of primitive 2 structures on n elements satisfying this property in fact for each n 4 there are four different reversible 2 structures up to isomorphism satisfying the n 2 property while for n odd there are five different 2 structures with this property

optimal sequencing by modular decomposition polynomial algorithms we show that the combination of dynamic programming with partial order decomposition algorithms enables us to solve sequencing problems in polynomial time for substantially larger classes of precedence constraints than previously realized the algorithm s efficiency depends on the maximum number of jobs that are not related by the precedence constraints in certain subsets of the jobs we also demonstrate how to modify this general algorithm lo take advantage of special problem characteristics

incorporation of a priori moment information into signal recovery and synthesis problems abstract the problem addressed is that of synthesizing a function subject to a priori moment constraints each moment constraint requires that the function to be synthesized lies in a closed convex set for r moment constraints the function must lie at the intersection of r convex sets the method of projections onto convex sets pocs is used to synthesize a function consistent with the moment constraints the algorithm has application in medical imaging especially in computer aided tomography

characterization and complexity of uniformly nonprimitive labeled 2 structures abstract according to the clan decomposition theorem of ehrenfeucht and rozenberg 1990 each labeled 2 structure has a decomposition into three types of basic 2 structures complete linear and primitive this decomposition can be expressed as a node labeled tree the shape of the 2 structure our main interest is in the uniformly nonprimitive 2 structures which do not have primitive substructures every directed graph can be considered as a restricted 2 structure with only two labels arc no arc it is proved that forbidding primitivity in the 2 structures gives a unified approach to some well known classes of graphs viz the cographs and the transitive vertex series parallel graphs we also study the parallel complexity of the decomposition of 2 structures it is shown that there is a logcf algorithm which recognizes the uniformly nonprimitive 2 structures and constructs their shapes we prove also that for every mso monadic second order definable property of 2 structures there is a logcf algorithm to decide whether or not a uniformly nonprimitive 2 structure has that property

nesting of prime substructures in k ary relations the modular decomposition of a graph or relation has a large number of combinatorial applications it divides the structure into a set of prime induced substructures which cannot be further decomposed recent work on graphs and k ary relations has focused on the discovery that prime induced substructures are densely nested when they occur lower bounds on the nesting density of prime substructures in graphs are used heavily in the only known linear time algorithm for directed graphs we improve on the previously known lower bounds for k ary relations and show that no further improvement is possible

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

un theoreme du type bochner godement et le probleme des moments abstract in this paper a bochner godement type result is proved some applications on a moment problem are given

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

steady state learning and nash equilibrium we study the steady states of a system in which players learn about the strategies their opponents are playing by updating their bayesian priors in light of their observations players are matched at random to play a fixed extensive form game and each player observes the realized actions in his own matches but not the intended off path play of his opponents or the realized actions in other matches because players are assumed to live finite lives there are steady states in which learning continually takes place if lifetimes are long and players are very patient the steady state distribution of actions approximates that of a nash equilibrium

angular 2 structures abstract the theory of 2 structures forms a convenient framework for investigating graphs in this paper we investigate the class of angular 2 structures which results by requiring that the primitivity is forbidden on the lowest possible level i e it is required that no substructure on three elements is primitive the paper presents the basic theory of angular 2 structures and in particular the theory of primitive angular 2 structures we demonstrate that the notion of an angular 2 structure is a well chosen generalization of the notions of a symmetric graph and a partial order

consistency of bernstein polynomial posteriors a bernstein prior is a probability measure on the space of all the distribution functions on 0 1 under very general assumptions it selects absolutely continuous distribution functions whose densities are mixtures of known beta densities the bemstein prior is of interest in bayesian nonparametric inference with continuous data we study the consistency of the posterior from a bernstein prior we first show that under mild assumptions the posterior is weakly consistent for any distribution function p o on 0 1 with continuous and bounded lebesgue density with slightly stronger assumptions on the prior the posterior is also hellinger consistent this implies that the predictive density from a bernstein prior which is a bayesian density estimate converges in the hellinger sense to the true density assuming that it is continuous and bounded we also study a sieve maximum likelihood version of the density estimator and show that it is also hellinger consistent under weak assumptions when the order of the bernstein polynomial i e the number of components in the beta distribution mixture is truncated we show that under mild restrictions the posterior concentrates on the set of pseudotrue densities finally we study the behaviour of the predictive density numerically and we also study a hybrid bayes maximum likelihood density estimator

the decomposition and measurement of the interdependency between second order stationary processes for a given pair of multivariate stationary processes the process of one way effect is extracted from each of the processes each process is decomposed into two orthogonal processes namely into the process generated by the one way effect of the other process and the process orthogonal to it based on the decomposition three measures characterizing the interdependency of the pair of processes are introduced they are the measure of association the measure of one way effect and the measure of reciprocity each of the measures is defined as overall as well as frequencywise measure the paper shows that the measure of association is equal to the sum of the others it discusses the relationships of those measures to the ones proposed by gel fand yaglom and by geweke