nonparametric bayesian inference for the spectral density function of a random field a powerful technique for inference concerning spatial dependence in a random field is to use spectral methods based on frequency domain analysis here we develop a nonparametric bayesian approach to statistical inference for the spectral density of a random field we construct a multi dimensional bernstein polynomial prior for the spectral density and devise a markov chain monte carlo algorithm to simulate from the posterior of the spectral density the posterior sampling enables us to obtain a smoothed estimate of the spectral density as well as credible bands at desired levels simulation shows that our proposed method is more robust than a parametric approach for illustration we analyse a soil data example

correlated random measures abstractwe develop correlated random measures random measures where the atom weights can exhibit a flexible pattern of dependence and use them to develop powerful hierarchical bayesian nonparametric models hierarchical bayesian nonparametric models are usually built from completely random measures a poisson process based construction in which the atom weights are independent completely random measures imply strong independence assumptions in the corresponding hierarchical model and these assumptions are often misplaced in real world settings correlated random measures address this limitation they model correlation within the measure by using a gaussian process in concert with the poisson process with correlated random measures for example we can develop a latent feature model for which we can infer both the properties of the latent features and their dependency pattern we develop several other examples as well we study a correlated random measure model of pairwise count data we derive an eff

steady states in the scheduling of discrete time systems abstract steady solutions to a two sided max min linear system of equations with real coefficients are considered the problem is motivated by the demand to schedule cyclically repeated activities with deterministic processing times the maximum steady solutions are characterized as min eigenvectors of a special matrix q this condition is a necessary but not a sufficient one it has also been proven that the general problem of the recognition of solvability of this two sided system is np complete

lattice permutations and poisson dirichlet distribution of cycle lengths we study random spatial permutations on 3 where each jump x x is penalized by a factor mathrm e t x pi x 2 the system is known to exhibit a phase transition for low enough t where macroscopic cycles appear we observe that the lengths of such cycles are distributed according to poisson dirichlet this can be explained heuristically using a stochastic coagulation fragmentation process for long cycles which is supported by numerical data

an infinite dimensional analogue of the lebesgue measure and distinguished properties of the gamma process abstract we define a one parameter family l of sigma finite finite on compact sets measures in the space of distributions these measures are equivalent to the laws of the classical gamma processes and invariant under an infinite dimensional abelian group of certain positive multiplicators this family of measures was first discovered by gelfand graev vershik in the context of the representation theory of current groups here we describe it in direct terms using some remarkable properties of the gamma processes we show that the class of multiplicative measures coincides with the class of zero stable measures which is introduced in the paper we give also a new construction of the canonical representation of the current group sl 2 r x

subspace methods for blind estimation of time varying fir channels novel linear algorithms are proposed in this paper for estimating time varying fir systems without resorting to higher order statistics the proposed methods are applicable to systems where each time varying tap coefficient can be described with respect to time as a linear combination of a finite number of basis functions examples of such channels include almost periodically varying ones fourier series description or channels locally modeled by a truncated taylor series or by a wavelet expansion it is shown that the estimation of the expansion parameters is equivalent to estimating the second order parameters of an unobservable fir single input many output simo process which are directly computed under some assumptions from the observation data by exploiting this equivalence a number of different blind subspace methods are applicable which have been originally developed in the context of time invariant simo systems identifiability issues are investigated and some illustrative simulations are presented

polynomials of meixner s type in infinite dimensions jacobi fields and orthogonality measures abstract the classical polynomials of meixner s type hermite charlier laguerre meixner and meixner pollaczek polynomials are distinguished through a special form of their generating function which involves the laplace transform of their orthogonality measure in this paper we study analogs of the latter three classes of polynomials in infinite dimensions we fix as an underlying space a non compact riemannian manifold x and an intensity measure on it we consider a jacobi field in the extended fock space over l 2 x whose field operator at a point x x is of the form x x x x x x x where is a real parameter here x and x are respectively the annihilation and creation operators at the point x we then realize the field operators as multiplication operators in l 2 d where d is the dual of d c 0 x and is the spectral measure of the jacobi field we show that is a gamma measure for 2 a pascal measure for 2 and a meixner measure for is a levy noise measure the isomorphism between the extended fock space and l 2 d is carried out by infinite dimensional polynomials of meixner s type we find the generating function of these polynomials and using it we study the action of the operators x and x in the functional realization

universal first passage properties of discrete time random walks and levy flights on a line statistics of the global maximum and records abstract in these lecture notes i will discuss the universal first passage properties of a simple correlated discrete time sequence x 0 0 x 1 x 2 x n up to n steps where x i represents the position at step i of a random walker hopping on a continuous line by drawing independently at each time step a random jump length from an arbitrary symmetric and continuous distribution it includes e g the levy flights i will focus on the statistics of two extreme observables associated with the sequence i its global maximum and the time step at which the maximum occurs and ii the number of records in the sequence and their ages i will demonstrate how the universal statistics of these observables emerge as a consequence of pollaczek spitzer formula and the associated sparre andersen theorem

entropic measure and wasserstein diffusion we construct a new random probability measure on the circle and on the unit interval which in both cases has a gibbs structure with the relative entropy functional as hamiltonian it satisfies a quasi invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interval respectively the associated integration by parts formula is used to construct two classes of diffusion processes on probability measures on the sphere or the unit interval by dirichlet form methods the first one is closely related to malliavin s brownian motion on the homeomorphism group the second one is a probability valued stochastic perturbation of the heat flow whose intrinsic metric is the quadratic wasserstein distance it may be regarded as the canonical diffusion process on the wasserstein space

bayesian entropy estimation for countable discrete distributions we consider the problem of estimating shannon s entropy h from discrete data in cases where the number of possible symbols is unknown or even countably infinite the pitman yor process a generalization of dirichlet process provides a tractable prior distribution over the space of countably infinite discrete distributions and has found major applications in bayesian non parametric statistics and machine learning here we show that it provides a natural family of priors for bayesian entropy estimation due to the fact that moments of the induced posterior distribution over h can be computed analytically we derive formulas for the posterior mean bayes least squares estimate and variance under dirichlet and pitman yor process priors moreover we show that a fixed dirichlet or pitman yor process prior implies a narrow prior distribution over h meaning the prior strongly determines the entropy estimate in the under sampled regime we derive a family of continuous measures for mixing pitman yor processes to produce an approximately flat prior over h we show that the resulting pitman yor mixture pym entropy estimator is consistent for a large class of distributions finally we explore the theoretical properties of the resulting estimator and show that it performs well both in simulation and in application to real data

random subcubes as a toy model for constraint satisfaction problems we present an exactly solvable random subcube model inspired by the structure of hard constraint satisfaction and optimization problems our model reproduces the structure of the solution space of the random k satisfiability and k coloring problems and undergoes the same phase transitions as these problems the comparison becomes quantitative in the large k limit distance properties as well the x satisfiability threshold are studied the model is also generalized to define a continuous energy landscape useful for studying several aspects of glassy dynamics

about thinning invariant partition structures bernoulli p thinning has been well studied for point processes here we consider three other cases 1 sequences x 1 x 2 2 gaps of such sequences x n 1 x 1 n 3 partition structures for the first case we characterize the distributions which are simultaneously invariant under bernoulli p thinning for all p 0 1 based on this we make conjectures for the latter two cases and provide a potential approach for proof we explain the relation to spin glasses which is complementary to important previous work of aizenman and ruzmaikina arguin and shkolnikov

size biased sampling of poisson point processes and excursions some general formulae are obtained for size biased sampling from a poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function these formulae explain why in certain cases gamma and stable the size biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking residual allocation scheme defined by independent beta random variables an application is made to length biased sampling of excursions of a markov process away from a recurrent point of its statespace with emphasis on the brownian and bessel cases when the associated inverse local time is a stable subordinator results in this case are linked to generalizations of the arcsine law for the fraction of time spent positive by brownian motion

the convex minorant of a levy process we offer a unified approach to the theory of convex minorants of levy processes with continuous distributions new results include simple explicit constructions of the convex minorant of a levy process on both finite and infinite time intervals and of a poisson point process of excursions above the convex minorant up to an independent exponential time the poisson dirichlet distribution of parameter 1 is shown to be the universal law of ranked lengths of excursions of a levy process with continuous distributions above its convex minorant on the interval 0 1

regenerative composition structures a new class of random composition structures the ordered analog of kingman s partition structures is defined by a regenerative description of component sizes each regenerative composition structure is represented by a process of random sampling of points from an exponential distribution on the positive halfline and separating the points into clusters by an independent regenerative random set examples are composition structures derived from residual allocation models including one associated with the ewens sampling formula and composition structures derived from the zero set of a brownian motion or bessel process we provide characterisation results and formulas relating the distribution of the regenerative

random fractal strings their zeta functions complex dimensions and spectral asymptotics in this paper a string is a sequence of positive non increasing real numbers which sums to one for our purposes a fractal string is a string formed from the lengths of removed sub intervals created by a recursive decomposition of the unit interval by using the so called complex dimensions of the string the poles of an associated zeta function it is possible to obtain detailed information about the behaviour of the asymptotic properties of the string we consider random versions of fractal strings we show that by using a random recursive self similar construction it is possible to obtain similar results to those for deterministic self similar strings in the case of strings generated by the excursions of stable subordinators we show that the complex dimensions can only lie on the real line the results allow us to discuss the geometric and spectral asymptotics of one dimensional domains with random fractal boundary

estimation of communications channels using discrete wavelet transform based deconvolution in this paper a technique for the deconvolution of signals in the wavelet domain is presented it makes use of the discrete wavelet transform dwt implemented with filter banks and is based on expressing the convolution of two signals using the forward merge approach for dwt based convolution the dwt based deconvolution technique is then applied to the problem of pilot based channel estimation which can be used in the design of wavelet based agile radio systems par dwt based deconvolution is first described analytically and is then implemented in matlab to validate the theory and evaluate its performance monte carlo simulations of dwt based deconvolution of transmitted signals from received signals both known a priori are performed to estimate channel impulse responses transmitted signals are corrupted by additive white gaussian noise awgn resulting in e b n 0 ratios ranging from 0 db to 30 db fast fading channels with gaussian and hilly area power delay profiles pdps are used along with four different wavelets for the dwts the results of the simulations show that dwt based deconvolution is a viable technique and its performance in some cases is comparable to direct discrete time domain deconvolution

a rademacher type theorem on l2 wasserstein spaces over closed riemannian manifolds abstract let p be any borel probability measure on the l 2 wasserstein space p 2 m w 2 over a closed riemannian manifold m we consider the dirichlet form e induced by p and by the wasserstein gradient on p 2 m under natural assumptions on p we show that w 2 lipschitz functions on p 2 m are contained in the dirichlet space d e and that w 2 is dominated by the intrinsic metric induced by e we illustrate our results by giving several detailed examples

gibbs states over the cone of discrete measures we construct gibbs perturbations of the gamma process on r d which may be used in applications to model systems of densely distributed particles first we propose a definition of gibbs measures over the cone of discrete radon measures on r d and then analyze conditions for their existence our approach works also for general levy processes instead of gamma measures to this end we need only the assumption that the first two moments of the involved levy intensity measures are finite also uniform moment estimates for the gibbs distributions are obtained which are essential for the construction of related diusions moreover we prove a mecke type characterization for the gamma measures on the cone and an fkg inequality for them

power laws for family sizes in a duplication model qian luscombe and gerstein j molecular biol 313 2001 673 681 introduced a model of the diversification of protein folds in a genome that we may formulate as follows consider a multitype yule process starting with one individual in which there are no deaths and each individual gives birth to a new individual at rate 1 when a new individual is born it has the same type as its parent with probability 1 r and is a new type different from all previously observed types with probability r we refer to individuals with the same type as families and provide an approximation to the joint distribution of family sizes when the population size reaches n we also show that if 1 s n 1 r then the number of families of size at least s is approximately cns 1 1 r while if n 1 r s the distribution decays more rapidly than any power

poisson calculus for spatial neutral to the right processes neutral to the right ntr processes were introduced by doksum in 1974 as bayesian priors on the class of distributions on the real line since that time there have been numerous applications to models that arise in survival analysis subject to possible right censoring however unlike the dirichlet process the larger class of ntr processes has not been used in a wider range of more complex statistical applications here to circumvent some of these limitations we describe a natural extension of ntr processes to arbitrary polish spaces which we call spatial neutral to the right processes our construction also leads to a new rich class of random probability measures which we call ntr species sampling models we show that this class contains the important two parameter extension of the dirichlet process we provide a posterior analysis which yields tractable ntr analogues of the blackwell macqueen distribution our analysis turns out to be closely related to the study of regenerative composition structures a new computational scheme which is an ordered variant of the general chinese restaurant processes is developed this can be used to approximate complex posterior quantities we also discuss some relationships to results that appear outside of bayesian nonparametrics

boundary driven zero range processes in random media the stationary states of boundary driven zero range processes in random media with quenched disorder are examined and the motion of a tagged particle is analyzed for symmetric transition rates also known as the random barrier model the stationary state is found to be trivial in absence of boundary drive out of equilibrium two further cases are distinguished according to the tail of the disorder distribution for strong disorder the fugacity profiles are found to be governed by the paths of normalized stable subordinators the expectations of integrated functions of the tagged particle position are calculated for three types of routes

markov chain monte carlo in approximate dirichlet and beta two parameter process hierarchical models summary we present some easy to construct random probability measures which approximate the dirichlet process and an extension which we will call the beta two parameter process the nature of these constructions makes it simple to implement markov chain monte carlo algorithms for fitting nonparametric hierarchical models and mixtures of nonparametric hierarchical models for the dirichlet process we consider a truncation approximation as well as a weak limit approximation based on a mixture of dirichlet processes the same type of truncation approximation can also be applied to the beta two parameter process both methods lead to posteriors which can be fitted using markov chain monte carlo algorithms that take advantage of blocked coordinate updates these algorithms promote rapid mixing of the markov chain and can be readily applied to normal mean mixture models and to density estimation problems we prefer the truncation approximations since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the gibbs sampler furthermore for the dirichlet process the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort we also find that a certain beta two parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution

on the length of the longest excursion summary a lower limit of the length of the longest excursion of a symmetric random walk is given certain related problems are also discussed it is shown e g that for any a 0 and all sufficiently large n there are c e loglogn excursions in the interval 0 n with total length greater than n l a with probability 1

self similar fragmentations derived from the stable tree i the basic object we consider is a certain model of continuum random tree called the stable tree we construct a fragmentation process f t t 0 out of this tree by removing the vertices located under height t thanks to a self similarity property of the stable tree we show that the fragmentation process is also self similar the semigroup and other features of the fragmentation are given explicitly asymptotic results are given as well as a couple of related results on continuous state branching processes

hierarchical exchangeability of pure states in mean field spin glass models the main result in this paper is motivated by the mezard parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models such as the random k sat model at positive temperature using the fact that one can safely assume the validity of the ghirlanda guerra identities in these models we prove hierarchical exchangeability of pure states for the asymptotic gibbs measures which allows us to apply a representation result for hierarchically exchangeable arrays recently proved in austin and panchenko in probab theory relat fields 2013 comparing this representation with the predictions of the mezard parisi ansatz one can see that the key property still missing is that the multi overlaps between pure states depend only on their overlaps

multiresolution sequence detection in rapidly fading channels based on focused wavelet decompositions the problem of detecting a sequence using the maximum likelihood strategy when the time varying multipath channel is unknown can be in principle solved using the generalized likelihood detector gld the gld metric involves finding the orthogonal projection of the received signal onto the subspace of the transmitted signal distorted by the multipath channel the faded signal corresponding to one of the transmitted sequences is in fact known to lie in a subspace but its exact location is not known because the channel parameters are unknown this detector which in the case of a static channel collapses to the per survivor processing method is also called a matched subspace detector because its statistic is matched to the a priori known signal subspace unfortunately the computation of the perfectly matched orthogonal projection of the received signal onto the multipath faded signal subspace is in the general time varying case impossible we introduce in this work the idea of using new wavelet based subspaces that approximate the original signal subspace the nested sequence of linear vector spaces defined by a wavelet based multiresolution decomposition of the fading channel time variations provides a set of subspaces that at an increasingly high level of detail are efficient representations of the original signal subspace for each of these representations sequence detection at different levels of resolution can be performed

time varying system identification and model validation using wavelets parametric identification of time varying tv systems is possible if each tv coefficient can be expanded onto a finite set of basis sequences the problem then becomes time invariant with respect to the parameters of the expansion the authors address the question of selecting this set of basis sequences they advocate the use of a wavelet basis because of its flexibility in capturing the signal s characteristics at different scales and discuss how to choose the optimal wavelet basis for a given system trajectory they also develop statistical tests to keep only the basis sequences that significantly contribute to the description of the system s time variation by formulating the problem as a regressor selection problem they apply an p test and an aic based approach for multiresolution analysis of tv systems the resulting algorithm can estimate tv ar or armax models and determine their orders they apply this algorithm to both synthetic and real speech data and compare it with the kalman filtering tv parameter estimator

the equation a x b y over max for the two sided homogeneous linear equation system a x b y over max with no infinite rows or columns in a or b an algorithm is presented which converges to a finite solution from any finite starting point whenever a finite solution exists if the finite elements of a b are all integers convergence is in a finite number of steps for which a precise bound can be calculated if moreover one of a b has only finite elements the algorithm is thus pseudopolynomial in complexity

invariant measures for the continual cartan subgroup abstract we construct and study the one parameter semigroup of finite measures l 0 on the space of schwartz distributions that have an infinite dimensional abelian group of linear symmetries this group is a continual analog of the classical cartan subgroup of diagonal positive matrices of the group sl n r the parameter is the degree of homogeneity with respect to homotheties of the space we prove uniqueness theorem for measures with given degree of homogeneity and call the measure with degree of homogeneity equal to one the infinite dimensional lebesgue measure l the structure of these measures is very closely related to the so called poisson dirichlet measures pd and to the well known gamma process the nontrivial properties of the lebesgue measure are related to the superstructure of the measure pd 1 which is called the conic poisson dirichlet measure cpd this is the most interesting finite measure on the set of positive convergent monotonic real series

statistical mechanics of the chinese restaurant process lack of self averaging anomalous finite size effects and condensation the pitman yor or chinese restaurant process is a stochastic process that generates distributions following a power law with exponents lower than 2 as found in numerous physical biological technological and social systems we discuss its rich behavior with the tools and viewpoint of statistical mechanics we show that this process invariably gives rise to a condensation i e a distribution dominated by a finite number of classes we also evaluate thoroughly the finite size effects finding that the lack of stationary state and self averaging of the process creates realization dependent cutoffs and behavior of the distributions with no equivalent in other statistical mechanical models

the two parameter poisson dirichlet distribution derived from a stable subordinator the two parameter poisson dirichlet distribution denoted mathsf pd alpha theta is a probability distribution on the set of decreasing positive sequences with sum 1 the usual poisson dirichlet distribution with a single parameter theta introduced by kingman is mathsf pd 0 theta known properties of mathsf pd 0 theta including the markov chain description due to vershik shmidt and ignatov are generalized to the two parameter case the size biased random permutation of mathsf pd alpha theta is a simple residual allocation model proposed by engen in the context of species diversity and rediscovered by perman and the authors in the study of excursions of brownian motion and bessel processes for 0 alpha 1 mathsf pd alpha 0 is the asymptotic distribution of ranked lengths of excursions of a markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index alpha formulae in this case trace back to work of darling lamperti and wendel in the 1950s and 1960s the distribution of ranked lengths of excursions of a one dimensional brownian motion is mathsf pd 1 2 0 and the corresponding distribution for a brownian bredge is mathsf pd 1 2 1 2 the mathsf pd alpha 0 and mathsf pd alpha alpha distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable markov process whose zero set is the range of a stable subordinator of index alpha

frequency of frequencies distributions and size dependent exchangeable random partitions abstractmotivated by the fundamental problem of modeling the frequency of frequencies fof distribution this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions a cluster structure naturally arising from a completely random measure mixed poisson process allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size a distinct and motivated feature that makes it more flexible than a partition structure this allows it to model an entire fof distribution whose structural properties change as the population size varies a fof vector can be simulated by drawing an infinite number of poisson random variables or by a stick breaking construction with a finite random number of steps a generalized negative binomial process model is proposed to generate a cluster structure where in the prior the number of clusters is f

iterates of the infinitesimal generator and space time harmonic polynomials of a markov process we relate iterates of the infinitesimal generator of a markov process to space time harmonic functions first we develop the theory for a general markov process and create a family a space time martingales next we investigate the special class of subordinators combinatorics results on space time harmonic polynomials and generalized stirling numbers are developed and interpreted from a probabilistic point of view finally we introduce the notion of pairs of subordinators in duality investigate the implications on the associated martingales and consider some explicit examples

on the pitman yor process with spike and slab base measure summaryfor the most popular discrete nonparametric models beyond the dirichlet process the prior guess at the shape of the data generating distribution also known as the base measure is assumed to be diffuse such a specification greatly simplifies the derivation of analytical results allowing for a straightforward implementation of bayesian nonparametric inferential procedures however in several applied problems the available prior information leads naturally to the incorporation of an atom into the base measure and then the dirichlet process is essentially the only tractable choice for the prior in this paper we fill this gap by considering the pitman yor process with an atom in its base measure we derive computable expressions for the distribution of the induced random partitions and for the predictive distributions these findings allow us to devise an effective generalized polya urn gibbs sampler applications to density estimation clustering and curve estimation with both simulated and real data serve as an illustration of our results and allow comparisons with existing methodology in particular we tackle a functional data analysis problem concerning basal body temperature curves

arcsine laws and interval partitions derived from a stable subordinator levy discovered that the fraction of time a standard one dimensional brownian motion b spends positive before time t has arcsine distribution both for a fixed time when b t 0 almost surely and for t an inverse local time when b t 0 almost surely this identity in distribution is extended from the fraction of time spent positive to a large collection of functionals derived from the lengths and signs of excursions of b away from 0 similar identities in distribution are associated with any process whose zero set is the range of a stable subordinator for instance a bessel process of dimension d for 0 d 2

on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations in this paper we study systems of fuzzy relation inequalities and equations of the form u v i v i u i i where u is an unknown and v i i i are given fuzzy relations the dual systems v i u u v i i i their conjunctions the systems of the form u v i v i u i i and certain special types of these systems we call them weakly linear systems for each weakly linear system with a complete residuated lattice as the underlying structure of truth values we prove the existence of the greatest solution and we provide an algorithm for computing the greatest solution which works whenever the underlying complete residuated lattice is locally finite otherwise we determine some sufficient conditions under which the algorithm works the algorithm is iterative and each its single step can be viewed as solving of a particular linear system weakly linear systems emerged from the fuzzy automata theory but we show that they also have important applications in other fields e g in the concurrency theory and social network analysis

studying the sinr process of the typical user in poisson networks using its factorial moment measures based on a stationary poisson point process a wireless network model with random propagation effects shadowing and or fading is considered in order to examine the process formed by the signal to interference plus noise ratio sinr values experienced by a typical user with respect to all the base stations in the down link channel this sinr process is completely characterized by deriving its factorial moment measures which involve numerically tractable explicit integral expressions this novel framework naturally leads to expressions for the k coverage probability including the case of random sinr threshold values considered in multi tier network models while the k coverage probabilities correspond to the marginal distributions of the order statistics of the sinr process a more general relation is presented connecting the factorial moment measures of the sinr process to the joint densities of these order statistics this gives a way for calculating the exact values of the coverage probabilities arising in a general scenario of signal combination and interference cancellation between base stations the presented framework consisting of the mathematical representations of sinr characteristics with respect to the factorial moment measures holds for the whole domain of sinr and is amenable to considerable model extension

the genealogy of branching brownian motion with absorption we consider a system of particles which perform branching brownian motion with negative drift and are killed upon reaching zero in the near critical regime where the total population stays roughly constant with approximately n particles we show that the characteristic time scale for the evolution of this population is of order logn 3 in the sense that when time is measured in these units the scaled number of particles converges to a variant of neveu s continuous state branching process furthermore the genealogy of the particles is then governed by a coalescent process known as the bolthausen sznitman coalescent this validates the non rigorous predictions by brunet derrida muller and munier for a closely related model

nonparametric bayes local partition models for random effects this paper focuses on the problem of choosing a prior for an unknown random effects distribution within a bayesian hierarchical model the goal is to obtain a sparse representation by allowing a combination of global and local borrowing of information a local partition process prior is proposed which induces dependent local clustering subjects can be clustered together for a subset of their parameters and one learns about similarities between subjects increasingly as parameters are added some basic properties are described including simple two parameter expressions for marginal and conditional clustering probabilities a slice sampler is developed which bypasses the need to approximate the countably infinite random measure in performing posterior computation the methods are illustrated using simulation examples and an application to hormone trajectory data

on the computational complexity of coalitional resource games we study coalitional resource games crgs a variation of qualitative coalitional games qcgs in which each agent is endowed with a set of resources and the ability of a coalition to bring about a set of goals depends on whether they are collectively endowed with the necessary resources we investigate and classify the computational complexity of a number of natural decision problems for crgs over and above those previously investigated for qcgs in general for example we show that the complexity of determining whether conflict is inevitable between two coalitions with respect to some stated resource bound i e a limit value for every resource is co np complete we then investigate the relationship between crgs and qcgs and in particular the extent to which it is possible to translate between the two models we first characterise the complexity of determining equivalence between crgs and qcgs we then show that it is always possible to translate any given crg into a succinct equivalent qcg and that it is not always possible to translate a qcg into an equivalent crg we establish some necessary and some sufficient conditions for a translation from qcgs to crgs to be possible and show that even where an equivalent crg exists it may have size exponential in the number of goals and agents of its source qcg

posterior simulation in countable mixture models for large datasets mixture models or convex combinations of a countable number of probability distributions offer an elegant framework for inference when the population of interest can be subdivided into latent clusters having random characteristics that are heterogeneous between but homogeneous within the clusters traditionally the different kinds of mixture models have been motivated and analyzed from very different perspectives and their common characteristics have not been fully appreciated the inferential techniques developed for these models usually necessitate heavy computational burdens that make them difficult if not impossible to apply to the massive data sets increasingly encountered in real world studies this paper introduces a flexible class of models called generalized polya urn gpu processes many common mixture models including finite mixtures hidden markov models and dirichlet processes are obtained as special cases of gpu processes other important special cases include finite dimensional

on max min linear inequalities and coalitional resource games with sharable resources abstract in a coalitional resource game crg for brief agents form coalitions to pool their resources in order to achieve certain goals requiring the expenditure of these resources a particular coalition is said to be successful if the common resources of its members enable to achieve a set of goals that satisfies all members of the coalition it is known that when resources are consumable it is np complete to decide whether a given coalition is successful in this paper we show a connection of crgs with sharable resources and max min linear systems of inequalities this correspondence leads to polynomial algorithms for checking whether a given crg admits a successful coalition and for several other problems whose counterparts for crgs with consumable resources are hard on the other hand we prove that some problems concerning the structure of successful coalitions are hard also in the case of sharable resources

stick breaking autoregressive processes this paper considers the problem of defining a time dependent nonparametric prior for use in bayesian nonparametric modelling of time series a recursive construction allows the definition of priors whose marginals have a general stick breaking form the processes with poisson dirichlet and dirichlet process marginals are investigated in some detail we develop a general conditional markov chain monte carlo mcmc method for inference in the wide subclass of these models where the parameters of the marginal stick breaking process are nondecreasing sequences we derive a generalised polya urn scheme type representation of the dirichlet process construction which allows us to develop a marginal mcmc method for this case we apply the proposed methods to financial data to develop a semi parametric stochastic volatility model with a time varying nonparametric returns distribution finally we present two examples concerning the analysis of regional gdp and its growth

exchangeable and partially exchangeable random partitions call a random partition of the positive integerspartially exchangeable if for each finite sequence of positive integersn1 nk the probability that the partition breaks the firstn1 nk integers intok particular classes of sizesn1 nk in order of their first elements has the same valuep n1 nk for every possible choice of classes subject to the sizes constraint a random partition is exchangeable iff it is partially exchangeable for a symmetric functionp n1 nk a representation is given for partially exchangeable random partitions which provides a useful variation of kingman s representation in the exchangeable case results are illustrated by the two parameter generalization of ewens partition structure

laplace operators on the cone of radon measures abstract we consider the infinite dimensional lie group g which is the semidirect product of the group of compactly supported diffeomorphisms of a riemannian manifold x and the commutative multiplicative group of functions on x the group g naturally acts on the space m x of radon measures on x we would like to define a laplace operator associated with a natural representation of g in l 2 m x here is assumed to be the law of a measure valued levy process a unitary representation of the group cannot be determined since the measure is not quasi invariant with respect to the action of the group g consequently operators of a representation of the lie algebra and its universal enveloping algebra in particular a laplace operator are not defined nevertheless we determine the laplace operator by using a special property of the action of the group g a partial quasi invariance we further prove the essential self adjointness of the laplace operator finally we explicitly construct a diffusion process on m x whose generator is the laplace operator