algebras on subintervals of pseudo hoops if a is a bounded email protected monoid or a pseudo bl algebra then it was proved that a subinterval a b of a can be endowed with a structure of an algebra of the same kind as a similar results were obtained if a is a residuated lattice and a b belong to the boolean center of a given a bounded pseudo hoop a in this paper we will give conditions for a email protected a for the subinterval a b of a to be endowed with a structure of a pseudo hoop we will introduce the notions of bosbach and riecan states on a pseudo hoop we study their properties and we prove that any bosbach state on a good pseudo hoop is a riecan state for the case of a bounded wajsberg pseudo hoop we prove that the two states coincide we also study the restrictions of bosbach states on subinterval algebras of a pseudo hoop

inference for mixtures of finite polya tree models mixtures of polya tree models provide a flexible alternative when a parametric model may only hold approximately i provide computational strategies for obtaining full semiparametric inference for mixtures of finite polya tree models given a standard parameterization including models that would be troublesome to fit using dirichlet process mixtures recommendations are put forth on choosing the level of a finite polya tree and model comparison is discussed several examples demonstrate the utility of finite polya tree modeling including data fit to generalized linear mixed models and several survival models

some aspects of polya tree distributions for statistical modelling the definition and elementary properties of polya tree distributions are reviewed two theorems are presented showing that polya trees can be constructed to concentrate arbitrarily closely about any desired pdf and that polya tree priors can put positive mass in every relative entropy neighborhood of every positive density with finite entropy thereby satisfying a consistency condition such theorems are false for dirichlet processes models are constructed combining partially specified polya trees with other information such as monotonicity or unimodality it is shown how to compute bounds on posterior expectations over the class of all priors with the given specifications a numerical example is given a theorem of diaconis and freedman about dirichlet processes is generalized to polya trees allowing polya trees to be the models for errors in regression problems finally empirical bayes models using dirichlet processes are generalized to polya trees an example from berry and christensen is reanalyzed with a polya tree model

some kinds of view the fuzzy filters of bl algebras the concepts of view the mathml source fuzzy implicative positive implicative and fantastic filters of bl algebras are introduced and some related properties are investigated some characterizations of these generalized fuzzy filters are derived in particular we describe the relationships among ordinary fuzzy implicative positive implicative and fantastic filters view the mathml source fuzzy implicative positive implicative and fantastic filters and view the mathml source fuzzy implicative positive implicative and fantastic filters of bl algebras finally we prove that a fuzzy set f of a bl algebra l is an view the mathml source fuzzy implicative filter of l if and only if it is both an view the mathml source fuzzy positive implicative filter and an view the mathml source fuzzy fantastic filter

a bayesian semiparametric survival model with longitudinal markers we consider inference for data from a clinical trial of treatments for metastatic prostate cancer patients joined the trial with diverse prior treatment histories the resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms inference is further complicated by the need to include a longitudinal marker as a covariate to address these challenges we develop a semiparametric model for joint inference of longitudinal data and an event time the proposed approach includes the possibility of cure for some patients the event time distribution is based on a nonparametric polya tree prior for the longitudinal data we assume a mixed effects model incorporating a regression on covariates in a nonparametric event time model in general and for a polya tree model in particular is a challenging problem we exploit the fact that the covariate itself is a random variable we achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time i e we implicitly model the desired regression by modeling the reverse conditional distribution

multiscale modeling and estimation of poisson processes with application to photon limited imaging many important problems in engineering and science are well modeled by poisson processes in many applications it is of great interest to accurately estimate the intensities underlying observed poisson data in particular this work is motivated by photon limited imaging problems this paper studies a new bayesian approach to poisson intensity estimation based on the haar wavelet transform it is shown that the haar transform provides a very natural and powerful framework for this problem using this framework a novel multiscale bayesian prior to model intensity functions is devised the new prior leads to a simple bayesian intensity estimation procedure furthermore we characterize the correlation behavior of the new prior and show that it has 1 f spectral characteristics the new framework is applied to photon limited image estimation and its potential to improve nuclear medicine imaging is examined

ideals and involutive filters in generalizations of fuzzy structures bounded integral residuated lattices which need not be commutative form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics congruences of such algebras are usually defined and investigated by means of their normal filters in the paper we introduce and investigate ideals of residuated lattices we show that one can define in some cases congruences also using ideals and that the corresponding quotient residuated lattices are involutive

fuzzy boolean and positive implicative filters of bl algebras the aim of this paper is to introduce the notions of fuzzy boolean filters and fuzzy positive implicative filters in bl algebras and to investigate their properties several characterizations of fuzzy boolean filters and fuzzy positive implicative filters are derived the extension theorems of fuzzy boolean filters and fuzzy positive implicative filters are obtained the relation between fuzzy boolean filters and fuzzy positive implicative filters is investigated and it is proved that every fuzzy boolean filter is a fuzzy positive implicative filter but the converse may not be true furthermore the conditions under which a fuzzy positive implicative filter is a fuzzy boolean filter are established

the pseudo linear semantics of interval valued fuzzy logics triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals which are called interval valued residuated lattices ivrls triangle algebras have been used to construct triangle logic tl a formal fuzzy logic that is sound and complete w r t the class of ivrls in this paper we prove that the so called pseudo prelinear triangle algebras are subdirect products of pseudo linear triangle algebras this can be compared with mtl algebras prelinear residuated lattices being subdirect products of linear residuated lattices as a consequence we are able to prove the pseudo chain completeness of pseudo linear triangle logic ptl an axiomatic extension of tl introduced in this paper this kind of completeness is the analogue of the chain completeness of monoidal t norm based logic mtl this result also provides a better insight in the structure of triangle algebras it enables us amongst others to prove properties of pseudo prelinear triangle algebras more easily it is known that there is a one to one correspondence between triangle algebras and couples l a in which l is a residuated lattice and a an element in that residuated lattice we give a schematic overview of some properties of pseudo prelinear triangle algebras and a number of others that can be imposed on a triangle algebra and the according necessary and sufficient conditions on l and a

vertex reinforced random walk on z has finite range a stochastic process called vertex reinforced random walk vrrw is defined in pemantle ann probab 16 1229 1241 we consider this process in the case where the underlying graph is an infinite chain i e process in the case where the underlying graph is an infinite chain i e the one dimensional integer lattice we show that the range is almost surely finite that at least five points are visited infinitely often almost surely and that with positive probability the range contains exactly five points there are always points visited infinitely often but at a set of times of zero density and we show that the number of visits to such a point to time n may be asymptotically n for a dense set of values 0 1 the power law analysis relies on analysis of a related urn model

beta stacy processes and a generalization of the polya urn scheme beta stacy process is dened it is shown to be neutral to the right and a generalization of the dirichlet process the posterior distribution is also a beta stacy process given independent and identically distributed iid observations possibly with right censoring from f a generalization of the p olya urn scheme is introduced which characterizes the discrete betastacy process 1 introduction let f be the space of cumulative distribution functions cdfs oni0 1e this paper considers placing a probability distribution on f by dening a stochastic process f onei0 1e ae where a is the borel eld of subsets such that fe0e d 0 a s f is a s nondecreasing a s right continuous and lim t 1 fete d 1 a s thus with probability 1 the sample paths of f are cdf s previous work includes the dirichlet process ferguson 1973 1974 neutral to the right processes doksum 1974 the extended gamma process dykstra and laud 1981 the beta process hjort 1990 and p olya trees lavine 1992 1994 mauldin sudderth and williams 1992 the purpose of this paper is twofold 1 to introduce a new stochastic process which generalizes the dirichlet process in that more exible prior beliefs are able to be represented and unlike the dirichlet process is conjugate to right censored observations and 2 to introduce a generalization of the p olyaurn scheme in order to characterize the discrete time version of the process the property of conjugacy to right censored observations is also a feature of the beta process however with the beta process the statistician is required to consider hazard rates and cumulative hazards when constructing the prior the beta stacy process only requires considerations on the distribution of the observations the process is shown to be neutral to the right the present paper is restricted to considering the estimation of an unknown cdf oni0 1e although it is trivially extended to includee1 1e finally for ease of notation f is written to mean either the cdf or the corresponding probability measure the organization of the paper is as follows in section 2 the process is dened and its connections with other processes given we also provide an

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

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

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

distribution of runs and longest runs a new generating function approach exact distributions of run statistics are traditionally obtained using combinatorial methods which under certain situations become very tedious run distributions of multiple object systems although appearing frequently in applications from various fields such as computational biology are not commonly used due in part to the lack of easy to use formulas in this article a method for evaluating partition functions of lattice models in the field of statistical mechanics is used to develop a systematic method to study various run statistics in multiple object systems by using particular generating functions for the specified situation under study many new distributions can be obtained in a unified and coherent way the method makes it possible to manipulate formulas of run statistics by using binomial identities to obtain more general yet simpler formulas to illustrate the applications of the general method the distributions of the total number of runs and the longest runs are investigated nove

bayesian nonparametric multiple imputation of partially observed data with ignorable nonresponse summary we present a new nonparametric bayesian method for multiple imputation of partially observed data for which the pattern of missingness is arbitrary and the data are missing at random with ignorable nonresponse with respect to the model specification motivation for the method is provided followed by an overview of p61lya trees and their application to multiple imputation and a comparison of the new method to existing approaches is presented the method is illustrated on a dataset of colleges and universities in the united states partially observed information frequently occurs in the analysis of multivariate data often resulting in an arbitrary pattern of missingness a popular method for modelling such data is multiple imputation which entails specifying a probability model for the parameters of interest and the missing data the missing data are treated as unknown quantities which are to be estimated and the posterior distributions of the model parameters of interest are obtained by marginalising over the uncertainty induced by the missing data in practice multiple imputation is implemented by simulating m copies of the missing data combining each copy of the missing data with the observed data to yield an estimate of the parameters of interest and combining the resulting m estimates to create one final estimate rubin 1987 ch 3 in contrast to the case with alternative methods the variances of estimated parameters based on multiply imputed and observed data can be correctly estimated provided necessary assumptions are met rubin 1987 ch 4 meng 1994

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

some types of generalized fuzzy filters of bl algebras the aim of this paper is to introduce the notions of interval valued q fuzzy boolean implicative positive implicative and fantastic filters in bl algebras and to investigate some related properties some characterizations of these generalized fuzzy filters are derived finally the relations among these generalized fuzzy filters are discussed it is proved that an interval valued q fuzzy filter in bl algebras is an interval valued q fuzzy boolean implicative filter if and only if it is both an interval valued q fuzzy positive implicative filter and an interval valued q fuzzy fantastic filter

statistical inference in hidden markov models using k segment constraints hidden markov models hmms are one of the most widely used statistical methods for analyzing sequence data however the reporting of output from hmms has largely been restricted to the presentation of the most probable map hidden state sequence found via the viterbi algorithm or the sequence of most probable marginals using the forward backward algorithm in this article we expand the amount of information we could obtain from the posterior distribution of an hmm by introducing linear time dynamic programming recursions that conditional on a user specified constraint in the number of segments allow us to i find map sequences ii compute posterior probabilities and iii simulate sample paths we collectively call these recursions k segment algorithms and illustrate their utility using simulated and real examples we also highlight the prospective and retrospective use of k segment constraints for fitting hmms or exploring existing model fits supplementary materials for this article are available online

optional polya tree and bayesian inference we introduce an extension of the polya tree approach for constructing distributions on the space of probability measures by using optional stopping and optional choice of splitting variables the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data the resulting optional polya tree distribution has large support in total variation topology and yields posterior distributions that are also optional polya trees with computable parameter values

state bck algebras and state morphism bck algebras abstract in the paper we define the notion of a state bck algebra and a state morphism bck algebra extending the language of bck algebras by adding a unary operator which models probabilistic reasoning we present a relation between state operators and state morphism operators and measures and states on bck algebras respectively we study subdirectly irreducible state morphism bck algebras we introduce the concept of an adjoint pair in bck algebras and show that there is a one to one correspondence between adjoint pairs and state morphism operators in addition we show the generators of quasivarieties of state morphism bck algebras

on success runs of a fixed length in bernoulli sequences exact and asymptotic results consider a sequence of n bernoulli success failure or 1 0 trials the exact and limiting distribution of the random variable e n k denoting the number of success runs of a fixed length k email protected email protected n is derived along with its mean and variance an associated waiting time is examined as well the exact distribution is given in terms of binomial coefficients and an extension of it covering exchangeable sequences is also discussed limiting distributions of e n k are obtained using poisson and normal approximations the exact mean and variance of e n k which are given in explicit forms are also used to derive bounds and an additional approximation of the distribution of e n k numbers associated with e n k and related random variables counting binary strings and runs of 1 s useful in applications of computer science are provided the overall study is illustrated by an extensive numerical experimentation

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

bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives testing the fit of data to a parametric model can be done by embedding the parametric model in a nonparametric alternative and computing the bayes factor of the parametric model to the nonparametric alternative doing so by specifying the nonparametric alternative via a polya tree process is particularly attractive from both theoretical and methodological perspectives among the benefits is a degree of computational simplicity that even allows for robustness analyses to be implemented default nonsubjective versions of this analysis are developed herein in the sense that recommended choices are provided for the many features of the polya tree process that need to be specified considerable discussion of these features is also provided to assist those who might be interested in subjective choices a variety of examples involving location scale models are studied finally it is shown that the resulting procedure can be viewed as a conditional frequentist test resulting in data dependent reported err

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

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

on filter theory of residuated lattices the aim of this paper is to develop the filter theory of general residuated lattices first we extend some particular types of filters and fuzzy filters in bl algebras and mtl algebras naturally to general residuated lattices and further enumerate some relative results obtained in bl algebras or mtl algebras which still hold in general residuated lattices next we introduce the concepts of regular filters and fuzzy regular filters to general residuated lattices which are two new types of filters and fuzzy filters and derive some of their characterizations finally we discuss the relations between fuzzy regular filters and several other special fuzzy filters and also characterize some special classes of residuated lattices by filters or fuzzy filters

measures states and de finetti maps on pseudo bck algebras in this paper we extend the notions of states and measures presented in dvurecenskij and pulmannova 2000 12 to the case of pseudo bck algebras and study similar properties we prove that under some conditions the notion of a state in the sense of dvurecenskij and pulmannova 2000 12 coincides with the bosbach state and we extend to the case of pseudo bck algebras some results proved by kuhr only for pseudo bck semilattices we characterize extremal states and show that the quotient pseudo bck algebra over the kernel of a measure can be embedded into the negative cone of an archimedean group additionally we introduce a borel state and using results by kuhr and mundici 2007 28 we prove a relationship between de finetti maps bosbach states and borel states

the multivariate beta process and an extension of the polya tree model we introduce a novel stochastic process that we term the multivariate beta process the process is defined for modelling dependent random probabilities and has beta marginal distributions we use this process to define a probability model for a family of unknown distributions indexed by covariates the marginal model for each distribution is a polya tree prior an important feature of the proposed prior is the easy centring of the nonparametric model around any parametric regression model we use the model to implement nonparametric inference for survival distributions the nonparametric model that we introduce can be adopted to extend the support of prior distributions for parametric regression models

fuzzy implicative and boolean ideals of mv algebras abstract we show how to obtain results in mv algebras by considering their fuzzy ideals in particular we prove the following theorem let be a fuzzy ideal of an mv algebra x then the folllowing are equivalent 1 x x 0 for all x x 2 x n x for all x x and all n 1 3 x x is a boolean algebra 4 is fuzzy implicative if i is an ideal of x and we take i then we obtain corresponding results for the ideal i and x we show how to extend fuzzy prime and fuzzy implicative ideals various fuzzy radicals are considered and related to the corresponding radicals of the algebra and we show how they live in the spectrum of the algebra

run related probability functions applied to sampling inspection run related distributions are frequently encountered in sampling inspection in the application of stopping rules for different phases of sampling in many cases the generating function of these distributions is known nevertheless it is too complicated to derive the pdf using the ordinary method and only the expectation and variance are obtained we present an approach based on partial fraction expansion to derive the exact pdf of several run related variables from their generating function using efficient algorithms for finding roots of polynomials and simple recursive formulas we complete the method presented by feller we derive and present exact probability functions of some run related variables an application to sampling inspection of attribute data in batches and for continuous production is suggested

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

distribution theory of runs a markov chain approach abstract the statistics of the number of success runs in a sequence of bernoulli trials have been used in many statistical areas for almost a century even in the simplest case of independent and identically distributed bernoulli trials the exact distributions of many run statistics still remain unknown departing from the traditional combinatorial approach in this article we present a simple unified approach for the distribution theory of runs based on a finite markov chain imbedding technique our results cover not only the identical bernoulli trials but also the nonidentical bernoulli trials as a byproduct our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run

commutative deductive systems in probability theory on generalizations of fuzzy structures abstract the aim of this paper is to introduce the notion of commutative deductive systems on generalizations of fuzzy structures and to emphasize their role in the probability theory on these algebras we give a characterization of commutative pseudo be algebras and we generalize an axiom system consisting of four identities to the case of commutative pseudo be algebras we define the commutative deductive systems of pseudo be algebras and we investigate their properties it is proved that if a pseudo be a algebra a is commutative then all deductive systems of a are commutative moreover we generalize the notions of measures state measures and measure morphisms to the case of pseudo be algebras and we also prove that there is a one to one correspondence between the set of all bosbach states on a bounded pseudo be algebra and the set of its state measures the notions of internal states and state morphism operators on pseudo bck algebras are extended to the case of pseudo be algebras and we also prove that any type ii state operator on a pseudo be algebra is a state morphism operator on it the notions of pseudo valuation and commutative pseudo valuation on pseudo be algebras are defined and investigated for the case of commutative pseudo be algebras we prove that the two kind of pseudo valuations coincide characterizations of pseudo valuations and commutative pseudo valuations are given we show that the kernel of a bosbach state state morphism measure type ii state operator pseudo valuation is a commutative deductive system

start up demonstration tests with sparse connection abstract based on the concept of sparse connection three start up demonstration tests with sparse connection are introduced which are called cstf with sparse d1 tscf with sparse d2 and cscf with sparse d3 and d4 the traditional start up demonstration tests such as cstf tscf and cscf are special cases of these new tests furthermore the new tests exhibit obvious improvement in test efficiency in this paper by using the finite markov chain imbedding approach several probabilistic indexes are given for these new start up demonstration tests based on the assumption that the tests are i i d case the analyses are also extended to independent and non identical and markov dependent cases in addition procedures are provided in order to determine the optimal parameters needed in a demonstration test for selecting the products to meet the reliability requirement three comparison analyses are finally presented in order to illustrate the high efficiency of these new start up demonstration tests and the effectiveness of this method

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

every state on semisimple mv algebra is integral integral representation theorem will be established for finitely additive probability measures states on semisimple mv algebras this result generalizes the well known theorem of butnariu and klement in case of order continuous states on tribes of fuzzy sets precisely it will be demonstrated that every state on a separating clan of continuous fuzzy sets arises as an integral with respect to a unique borel probability measure the key technique leading to this result exploits the geometrical topological properties of the state space the set of all states on every mv algebra forms a bauer simplex

a bayesian goodness of fit test and semiparametric generalization of logistic regression with measurement data summary logistic regression is a popular tool for risk analysis in medical and population health science with continuous response data it is common to create a dichotomous outcome for logistic regression analysis by specifying a threshold for positivity fitting a linear regression to the nondichotomized response variable assuming a logistic sampling model for the data has been empirically shown to yield more efficient estimates of odds ratios than ordinary logistic regression of the dichotomized endpoint we illustrate that risk inference is not robust to departures from the parametric logistic distribution moreover the model assumption of proportional odds is generally not satisfied when the condition of a logistic distribution for the data is violated leading to biased inference from a parametric logistic analysis we develop novel bayesian semiparametric methodology for testing goodness of fit of parametric logistic regression with continuous measurement data the testing procedures hold for any cutoff threshold and our approach simultaneously provides the ability to perform semiparametric risk estimation bayes factors are calculated using the savage dickey ratio for testing the null hypothesis of logistic regression versus a semiparametric generalization we propose a fully bayesian and a computationally efficient empirical bayesian approach to testing and we present methods for semiparametric estimation of risks relative risks and odds ratios when parametric logistic regression fails theoretical results establish the consistency of the empirical bayes test results from simulated data show that the proposed approach provides accurate inference irrespective of whether parametric assumptions hold or not evaluation of risk factors for obesity shows that different inferences are derived from an analysis of a real data set when deviations from a logistic distribution are permissible in a flexible semiparametric framework

markovian start up demonstration tests with rejection of units upon observing d failures abstract by conditioning on the time of the first failure several results are derived for demonstration tests of the start up reliability of equipment the start ups are assumed to follow a markov chain the equipment is accepted if k consecutive successful start ups occur before d failures we compute the probability of the demonstration test ending with acceptance of the unit and the expectation and variance of the number of start ups until termination of the test we also give recursive formulas for computing the probability distribution of the number of start ups and the probability of acceptance or rejection of the equipment in a specified number of trials the conditional distribution of the number of start ups in the test given that the unit is accepted or rejected is obtained as a by product examples are given to illustrate the usefulness of these results

a statistical multiscale framework for poisson inverse problems this paper describes a statistical multiscale modeling and analysis framework for linear inverse problems involving poisson data the framework itself is founded upon a multiscale analysis associated with recursive partitioning of the underlying intensity a corresponding multiscale factorization of the likelihood induced by this analysis and a choice of prior probability distribution made to match this factorization by modeling the splits in the underlying partition the class of priors used here has the interesting feature that the noninformative member yields the traditional maximum likelihood solution other choices are made to reflect prior belief as to the smoothness of the unknown intensity adopting the expectation maximization em algorithm for use in computing the maximum a posteriori map estimate corresponding to our model we find that our model permits remarkably simple closed form expressions for the em update equations the behavior of our em algorithm is examined and it is shown that convergence to the global map estimate can be guaranteed applications in emission computed tomography and astronomical energy spectral analysis demonstrate the potential of the new approach

a bayesian semiparametric accelerated failure time model a bayesian semiparametric approach is described for an accelerated failure time model the error distribution is assigned a polya tree prior and the regression parameters a noninformative hierarchical prior two cases are considered the first assumes error terms are exchangeable the second assumes that error terms are partially exchangeable a markov chain monte carlo algorithm is described to obtain a predictive distribution for a future observation given both uncensored and censored data

representable pseudo bck algebras and integral residuated lattices abstract pseudo bck algebras arise as the 1 subreducts of integral residuated lattices in this note we characterize pseudo bck algebras that are subdirect products of linearly ordered pseudo bck algebras

on fuzzy filters of pseudo bl algebras abstract we introduce the concept of fuzzy filters of pseudo bl algebras and obtain some of their important properties we further give several kinds of fuzzy filters such as fuzzy boolean filter fuzzy normal filter fuzzy prime filter fuzzy ultrafilter and fuzzy obstinate filter and discuss the relations among the above fuzzy filters we establish the prime fuzzy filter theorem in pseudo bl algebras by studying the relation between fuzzy boolean filter and fuzzy normal filter in pseudo bl algebras we solve an open problem that whether or not every boolean filter is normal in pseudo bl algebras

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 generalized linear models and frailty models with bayesian nonparametric mixing summary this paper proposes bayesian nonparametric mixing for some well known and popular models the distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term a function of the observed covariates and an additive or multiplicative random effects term typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family this assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution as a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately this paper therefore proposes a bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates effect on the distribution of the mixed effects

prior distributions on symmetric groups fully and partially ranked data arise in a variety of contexts from a bayesian perspective attention has focused on distance based models in particular the mallows model and extensions thereof in this paper a class of prior distributions the binary tree is developed on the symmetric group the attractive features of the class are it provides a closed form solution to the posterior distribution and a simple way to interpret the parameters of the prior distribution the advantages of the proposed method are illustrated by comparing it to metric based models using data analyzed by other researchers in this context

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

bayesian methods for partial stochastic orderings summary we discuss two methods of making nonparametric bayesian inference on probability measures subject to a partial stochastic ordering the first method involves a nonparametric prior for a measure on partially ordered latent observations and the second involves rejection sampling computational approaches are discussed for each method and interpretations of prior and posterior information are discussed an application is presented in which inference is made on the number of independently segregating quantitative trait loci present in an animal population

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

the analysis and comparison of start up demonstration tests two new start up demonstration tests are introduced as alternatives to a previously studied one the first test is based on total successes and total failures tstf while the second is based on consecutive successes and consecutive failures cscf the probabilistic analysis of these tests in the independent and identically distributed case uses a markov chain approach to avoid the complexities of the probability generating function approach we discuss advantages of these new tests in certain situations practical guidance on choosing tests estimation and comparisons of the various criteria are studied the markov chain approach can be easily extended and generalized to study the probabilistic analysis of the non i i d case

a bayesian hierarchical model for related densities by using polya trees bayesian hierarchical models are used to share information between related samples and to obtain more accurate estimates of sample level parameters common structure and variation between samples when the parameter of interest is the distribution or density of a continuous variable a hierarchical model for continuous distributions is required various such models have been described in the literature using extensions of the dirichlet process and related processes typically as a distribution on the parameters of a mixing kernel we propose a new hierarchical model based on the polya tree which enables direct modelling of densities and enjoys some computational advantages over the dirichlet process the polya tree also enables more flexible modelling of the variation between samples providing more informed shrinkage and permitting posterior inference on the dispersion function which quantifies the variation between sample densities we also show how the model can be extended to cluster samples in situations where the observed samples are believed to have been drawn from several latent populations

the consistency of posterior distributions in nonparametric problems we give conditions that guarantee that the posterior probability of every hellinger neighborhood of the true distribution tends to 1 almost surely the conditions are 1 a requirement that the prior not put high mass near distributions with very rough densities and 2 a requirement that the prior put positive mass in kullback leibler neighborhoods of the true distribution the results are based on the idea of approximating the set of distributions with a finite dimensional set of distributions with sufficiently small hellinger bracketing metric entropy we apply the results to some examples

reliability computing method for generalized k out of n system the generalized k out of n f system g k n f consists of n modules ordered in a line or circle the ith module is composed of ni components in parallel ni1 i 1 2 n the g k n f fails if and only if there exist at least f failed components or if there exist at least k consecutive failed modules to evaluate the reliability of g k n f we introduce the concept of a generalized sequence of multivariate bernoulli trials gmvbt and define the bivariate run statistic based on this sequence we bring out the relation between the probability distribution of the bivariate run statistic and the reliability of g k n f we demonstrate the evaluation of reliability of g k n f and some other related systems through a numerical example

bayesian nonparametric meta analysis using polya tree mixture models summary a common goal in meta analysis is estimation of a single effect measure using data from several studies that are each designed to address the same scientific inquiry because studies are typically conducted in geographically disperse locations recent developments in the statistical analysis of meta analytic data involve the use of random effects models that account for study to study variability attributable to differences in environments demographics genetics and other sources that lead to heterogeneity in populations stemming from asymptotic theory study specific summary statistics are modeled according to normal distributions with means representing latent true effect measures a parametric approach subsequently models these latent measures using a normal distribution which is strictly a convenient modeling assumption absent of theoretical justification to eliminate the influence of overly restrictive parametric models on inferences we consider a broader class of random effects distributions we develop a novel hierarchical bayesian nonparametric polya tree mixture ptm model we present methodology for testing the ptm versus a normal random effects model these methods provide researchers a straightforward approach for conducting a sensitivity analysis of the normality assumption for random effects an application involving meta analysis of epidemiologic studies designed to characterize the association between alcohol consumption and breast cancer is presented which together with results from simulated data highlight the performance of ptms in the presence of nonnormality of effect measures in the source population

latent factor models for density estimation although discrete mixture modelling has formed the backbone of the literature on bayesian density estimation there are some well known disadvantages as an alternative to discrete mixtures we propose a class of priors based on random nonlinear functions of a uniform latent variable with an additive residual the induced prior for the density is shown to have desirable properties including ease of centring on an initial guess large support posterior consistency and straightforward computation via gibbs sampling some advantages over discrete mixtures such as dirichlet process mixtures of gaussian kernels are discussed and illustrated via simulations and an application

states on commutative basic algebras the paper deals with states on commutative basic algebras that are a non associative generalization of mv algebras or in other words the algebraic semantics for a fuzzy logic which generalizes the lukasiewicz logic in that the conjunction is not associative states are defined in the same way as mundici s states on mv algebras as normalized finitely additive 0 1 valued functions and some results analogous to the results that are known from mv algebras are proved

fuzzy implicative and boolean filters of r 0 algebras the notions of fuzzy filters fuzzy implicative filters and fuzzy boolean filters are introduced in r0 algebras respectively some of their properties are investigated the relations between fuzzy implicative filters and fuzzy boolean filters are discussed the characterizations of fuzzy implicative filters are studied and the following is proved to be equivalent 1 a fuzzy filter f is implicative 2 f is a fuzzy boolean filter 3 x y z l f x z f x z y f y z 4 x y l f x y f x y y 5 x l n 1 f nx f x

fuzzy positive implicative and fuzzy associative filters of lattice implication algebras we fuzzify the concept of positive implicative filters and associative filters in lattice implication algebras we prove that i every fuzzy positive implicative filter is a fuzzy implicative filter and ii every fuzzy associative filter is a fuzzy filter we provide equivalent conditions for both fuzzy positive implicative filter and fuzzy associative filter

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

tree based models for random distribution of mass a mathematical model for distribution of mass ind dimensional space based upon randomly embedding random trees into space is introduced and studied the model is a variant of thesuper brownian motion process studied by mathematicians we present calculations relating to i the distribution of position of a typical mass element ii moments of the center of mass iii large deviation behavior and iv a recursive self similarity property

run probabilities in sequences of markov dependent trials abstract the probability of the occurrence of a run r is obtained as a function of the composition of r the number n of trials and the probabilities of the v 2 possible outcomes at each trial the run r can consist of any specified sequence of outcomes and the probability that one or more of a given collection of runs occurs is also evaluated the probabilities of the v possible outcomes can vary arbitrarily from trial to trial and can be l order markov dependent on the l preceding outcomes the practical application of these results is discussed

on runs and longest run tests a method of finite markov chain imbedding abstract in this article under very general assumptions on bernoulli trials a simple numerical method based on the finite markov chain imbedding technique is systematically developed to determine a the joint distribution of the number of success runs and the number of successes b the conditional distribution of the number of success runs given the number of successes that is the exact distribution of the success runs test statistic c the joint distribution of the length of the longest success run and the number of successes and d the conditional distribution of the length of the longest success run given the number of successes that is the exact distribution of the longest success run test statistic the critical regions and powers of these two tests success runs and longest success run are derived under the null hypothesis of independence and identical distribution iid as well as under the alternative hypothesis of markov dependence the application of the success runs test is illust

regression analysis using dependent polya trees many commonly used models for linear regression analysis force overly simplistic shape and scale constraints on the residual structure of data we propose a semiparametric bayesian model for regression analysis that produces data driven inference by using a new type of dependent polya tree prior to model arbitrary residual distributions that are allowed to evolve across increasing levels of an ordinal covariate e g time in repeated measurement studies by modeling residual distributions at consecutive covariate levels or time points using separate but dependent polya tree priors distributional information is pooled while allowing for broad pliability to accommodate many types of changing residual distributions we can use the proposed dependent residual structure in a wide range of regression settings including fixed effects and mixed effects linear and nonlinear models for cross sectional prospective and repeated measurement data a simulation study illustrates the flexibility of our novel semiparametric regression model to accurately capture evolving residual distributions in an application to immune development data on immunoglobulin g antibodies in children our new model outperforms several contemporary semiparametric regression models based on a predictive model selection criterion copyright 2013 john wiley sons ltd

regenerative tree growth binary self similar continuum random trees and poisson dirichlet compositions we use a natural ordered extension of the chinese restaurant process to grow a twoparameter family of binary self similar continuum fragmentation trees we provide an explicit embedding of ford s sequence of alpha model trees in the continuum tree which we identified in a previous article as a distributional scaling limit of ford s trees in general the markov branching trees induced by the two parameter growth rule are not sampling consistent so the existence of compact limiting trees cannot be deduced from previous work on the sampling consistent case we develop here a new approach to establish such limits based on regenerative interval partitions and the urn model description of sampling from dirichlet random distributions ams 2000 subject classifications 60j80

on the distribution of runs of ones in binary strings in this paper we derive the number of binary strings which contain for a given i k exactly i k runs of 1 s of length k in all possible binary strings of length n email protected email protected n such a knowledge about the distribution pattern of runs of 1 s in binary strings is useful in many engineering applications for example data compression bus encoding techniques to reduce crosstalk in vlsi chip design computer arithmetic using redundant binary number system and design of energy efficient communication schemes in wireless sensor networks by transformation of runs of 1 s into compressed information patterns among others we present here a generating function based approach to derive a solution to this counting problem our experimental results demonstrate that for most commonly used file formats the observed distributions of exactly i k runs of length k email protected email protected n closely follow the theoretically derived distributions for a given n for n 8 we find that the experimentally obtained values for most file formats agree within 5 of the theoretically obtained values for all i k runs of length k email protected email protected n also the root mean square rms values of these deviations across all file types studied in this paper are less than 5 for n 8 in view of these facts the results presented in this paper could be useful in various application domains like the ones mentioned above

a compound negative binomial distribution with mutative termination conditions based on a change point abstract in this paper an extended negative binomial distribution called nbm is proposed by considering mutative termination conditions based on a change point if the condition a is satisfied before the occurrence of the change point the trial is terminated according to condition a otherwise if the condition a does not happen and the change point is satisfied the termination condition of the trial changes from condition a to condition b we consider the conditions under which the resulting distribution can be degenerated to the existing negative binomial distributions and other new negative binomial distributions the finite markov chain imbedding approach is employed to derive the new negative binomial distribution nbm and to obtain the related probabilistic indexes furthermore we study the distribution of the compound negative binomial distribution with mutative termination conditions based on a change point cnbm by means of phase type representations

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

notes on redefined fuzzy implicative filters of lattice implication algebras the concept of q fuzzy implicative filters of lattice implication algebras is introduced and some of its related properties are investigated in particular the relationships among the ordinary fuzzy implicative filters the q fuzzy implicative filters and the q fuzzy implicative filters of lattice implication algebras will be studied

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

modeling regression error with a mixture of polya trees we model the error distribution in the standard linear model as a mixture of absolutely continuous polya trees constrained to have median 0 by considering a mixture we smooth out the partitioning effects of a simple polya tree and the predictive error density has a derivative everywhere except 0 the error distribution is centered around a standard parametric family of distributions and thus may be viewed as a generalization of standard models in which important data driven features such as skewness and multimodality are allowed by marginalizing the polya tree exact inference is possible up to markov chain monte carlo error

application of auxiliary markov chains to start up demonstration tests we use auxiliary markov chains to derive probabilistic results for five types of start up demonstration tests with start ups that are markovian of a general order four of the tests are based on consecutive or total successful start ups and consecutive or total failures the fifth has two rejection criteria for each test type we obtain the probability of the test ending with acceptance of the unit the probability distribution and moments of the number of start ups in the test the probability of acceptance or rejection of the equipment in a specified number of trials and the conditional distribution of the number of start ups in the test given that the unit is accepted or rejected numerical examples are given though the results are for these specific types of start up demonstration tests the method of derivation may be used for tests with other stopping criteria and in other situations as well